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Workplace robotics safety

Workplace robotics safety is an aspect of occupational safety and health when robots are used in the workplace. This includes traditional industrial robots as well as emerging technologies such as drone aircraft and wearable robotic exoskeletons. Types of accidents include collisions, crushing, and injuries from mechanical parts. Hazard controls include physical barriers, good work practices, and proper maintenance. == Background == Many workplace robots are industrial robots used in manufacturing. According to the International Federation of Robotics, 1.7 million new robots are expected to be used in factories between 2017 and 2020. Emerging robot technologies include collaborative robots, personal care robots, construction robots, exoskeletons, autonomous vehicles, and drone aircraft (also known as unmanned aerial vehicles or UAVs). Advances in automation technologies (e.g. fixed robots, collaborative and mobile robots, and exoskeletons) have the potential to improve work conditions but also to introduce workplace hazards in manufacturing workplaces. Fifty-six percent of robot injuries are classified as pinch injuries and 44% of injuries are classified as impact injuries. A 1987 study found that line workers are at the greatest risk, followed by maintenance workers, and programmers. Poor workplace design and human error caused most injuries. Despite the lack of occupational surveillance data on injuries associated specifically with robots, researchers from the US National Institute for Occupational Safety and Health (NIOSH) identified 61 robot-related deaths between 1992 and 2015 using keyword searches of the Bureau of Labor Statistics (BLS) Census of Fatal Occupational Injuries research database (see info from Center for Occupational Robotics Research). Using data from the Bureau of Labor Statistics, NIOSH and its state partners have investigated 4 robot-related fatalities under the Fatality Assessment and Control Evaluation Program. In addition the Occupational Safety and Health Administration (OSHA) has investigated robot-related deaths and injuries, which can be reviewed at OSHA Accident Search page. Injuries and fatalities could increase over time because of the increasing number of collaborative and co-existing robots, powered exoskeletons, and autonomous vehicles into the work environment. Safety standards are being developed by the Robotic Industries Association (RIA) in conjunction with the American National Standards Institute (ANSI). On October 5, 2017, OSHA, NIOSH and RIA signed an alliance to work together to enhance technical expertise, identify and help address potential workplace hazards associated with traditional industrial robots and the emerging technology of human-robot collaboration installations and systems, and help identify needed research to reduce workplace hazards. On October 16 NIOSH launched the Center for Occupational Robotics Research to "provide scientific leadership to guide the development and use of occupational robots that enhance worker safety, health, and well being". So far, the research needs identified by NIOSH and its partners include: tracking and preventing injuries and fatalities, intervention and dissemination strategies to promote safe machine control and maintenance procedures, and on translating effective evidence-based interventions into workplace practice. == Hazards == Many hazards and injuries can result from the use of robots in the workplace. Some robots, notably those in a traditional industrial environment, are fast and powerful. This increases the potential for injury as one swing from a robotic arm, for example, could cause serious bodily harm. There are additional risks when a robot malfunctions or is in need of maintenance. A worker who is working on the robot may be injured because a malfunctioning robot is typically unpredictable. For example, a robotic arm that is part of a car assembly line may experience a jammed motor. A worker who is working to fix the jam may suddenly get hit by the arm the moment it becomes unjammed. Additionally, if a worker is standing in a zone that is overlapping with nearby robotic arms, he or she may get injured by other moving equipment. There are four types of accidents that can occur with robots: impact or collision accidents, crushing and trapping accidents, mechanical part accidents, and other accidents. Impact or collision accidents occur generally from malfunctions and unpredicted changes. Crushing and trapping accidents occur when a part of a worker's body becomes trapped or caught on robotic equipment. Mechanical part accidents can occur when a robot malfunctions and starts to "break down", where the ejection of parts or exposed wire can cause serious injury. Other accidents at just general accidents that occur from working with robots. There are seven sources of hazards that are associated with human interaction with robots and machines: human errors, control errors, unauthorized access, mechanical failures, environmental sources, power systems, and improper installation. Human errors could be anything from one line of incorrect code to a loose bolt on a robotic arm. Many hazards can stem from human-based error. Control errors are intrinsic and are usually not controllable nor predictable. Unauthorized access hazards occur when a person who is not familiar with the area enters the domain of a robot. Mechanical failures can happen at any time, and a faulty unit is usually unpredictable. Environmental sources are things such as electromagnetic or radio interference in the environment that can cause a robot to malfunction. Power systems are pneumatic, hydraulic, or electrical power sources; these power sources can malfunction and cause fires, leaks, or electrical shocks. Improper installation is fairly self-explanatory; a loose bolt or an exposed wire can lead to inherent hazards. === Emerging technologies === Emerging robotic technologies can reduce hazards to workers, but can also introduce new hazards. For example, robotic exoskeletons can be used in construction to reduce load to the spine, improve posture, and reduce fatigue; however, they can also increase chest pressure, limit mobility when moving out of the way of a falling object, and cause balance problems. Unmanned aerial vehicles are being used in the construction industry to do monitoring and inspections of buildings under construction. This reduces the need for humans to be in hazardous locations, but the risk of a UAV collision presents a hazard to workers. For collaborative robots, isolation is not possible. Possible hazard controls include collision avoidance systems, and making the robot less stiff to lessen the impact force. Robotic tech vest is a wearable device for humans, worn in Amazon warehouses. == Hazard controls == There are a few ways to prevent injuries by implementing hazard controls. There can be risk assessments at each of the various stages of a robot's development. Risk assessments can help gather information about a robot's status, how well it is being maintained, and if repairs are needed soon. By being aware of the status of a robot, injuries can be prevented and hazards reduced. Safeguarding devices can be implemented to reduce the risk of injuries. These can include engineering controls such as physical barriers, guard rails, presence-sensing safeguarding devices, etc. Awareness devices are usually used in conjunction with safeguarding devices. They are usually a system of rope or chain barriers with lights, signs, whistles, and horns. Their purpose it to be able to alert workers or personnel of certain dangers. Operator safeguards can also be in place. These usually utilize safeguarding devices to protect the operator and reduce risk of injury. Additionally, when an operator is within close proximity of a robot, the working speed of the robot can be reduced to ensure that the operator is in full control. This can be done by placing the robot in the manual or teach mode. It is also crucial to inform the programmer of the robot of what type of work the robot will be doing, how it will interact with other robots, and how it will work in relation to an operator. Proper maintenance of robotic equipment is also critical in order to reduce hazards. Maintaining a robot insures that it continues to function properly, thereby reducing the risks associated with a malfunction. One common safeguard used in industrial settings is the installation of robot safety fencing. These barriers, often made from durable materials such as mesh or polycarbonate, prevent accidental interactions between workers and robotic systems, reducing the risk of injury. Robot safety fencing is particularly important in environments where high-speed or powerful robots are used. == Regulations == Some existing regulations regarding robots and robotic systems include: ANSI/RIA R15.06 OSHA 29 CFR 1910.333 OSHA 29 CFR 1910.147 ISO 10218 ISO/TS 15066 ISO/DIS 13482
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Business process automation

Business process automation (BPA), also known as business automation, refers to the technology-enabled automation of business processes. == Development approaches == There are three main approaches to developing BPA: traditional business process automation involves developing BPA software in a programming language for integrating relevant applications in the digital ecosystem to execute a given process; robotic process automation uses software robots (also called agents, bots, or workers) to emulate human-computer interaction for executing a combination of processes, activities, transactions, and tasks in one or more unrelated software systems; hyperautomation (also called intelligent automation (IA), intelligent process automation (IPA), integrated automation platform (IAP), and cognitive automation (CA) combines business process automation, artificial intelligence (AI), and machine learning (ML) to discover, validate, and execute organizational processes automatically with no or minimal human intervention. == Deployment == BPA toolsets vary in capability. With the increasing adoption of artificial intelligence (AI), organizations are implementing AI-driven technologies that can process natural language, interpret unstructured datasets, and interact with users. These systems are designed to adapt to new types of problems with reduced reliance on human intervention. == Business process management implementation == A business process management system differs from BPA. However, it is possible to implement automation based on a BPM implementation. The methods to achieve this vary, from writing custom application code to using specialist BPA tools. == Robotic process automation == Robotic process automation (RPA) involves the deployment of attended or unattended software agents in an organization's environment. These software agents, or robots, are programmed to perform predefined structured and repetitive sets of business tasks or processes. Robotic process automation is designed to streamline workflows by delegating repetitive tasks to software agents, allowing human workers to focus on more complex and strategic activities. BPA providers typically focus on different industry sectors, but the underlying approach is generally similar in that they aim to provide the shortest route to automation by interacting with the user interface rather than modifying the application code or database behind it. == Use of artificial intelligence == Artificial intelligence software robots are used to handle unstructured data sets (like images, texts, audios) and are often deployed after implementing robotic process automation. They can, for instance, generate an automatic transcript from a video. The combination of automation and artificial intelligence (AI) enables autonomy for robots, along with the capability to perform cognitive tasks. At this stage, robots can learn and improve processes by analyzing and adapting them.
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Sparkles emoji

The Sparkles emoji (U+2728 ✨ SPARKLES) is an emoji that has one large star surrounded by smaller stars. Originating from Japan to represent sparkles used in anime and manga, the sparkles are often used as emphasis in text by surrounding words or phrases with it. It is the third most-used emoji in the world on Twitter as of 2021. Since the early 2020s it has been used by major software companies to represent artificial intelligence, marketing the technology as "like magic". == Development == According to Emojipedia, the Sparkles emoji was first used by Japanese mobile operators SoftBank, Docomo and au in the late 1990s. The emoji was added to Unicode 6.0 in 2010 and Emoji 1.0 in 2015. On some platforms the Sparkles emoji has been multicoloured whilst on other platforms it has been one colour. Twitter and Microsoft's Sparkles have changed from being multicoloured to being a single colour. Samsung's version of the emoji previously had a night sky in the background. == Usage == === Interpersonal communication === The Sparkles emoji was originally meant to represent the usage of sparkles in Japanese anime and manga, where the sparkles are used to represent beauty, happiness or awe. The emoji has several meanings and depends upon context. Starting in the late 2010s, the emoji started being used to surround words or phrases to be used as emphasis, an example from the book Because Internet being "I would simply ✨pass away✨". It can also be used as sarcasm, irony or as a way to mock people. Without emoji this could be represented with tildes or asterisks, for example, "~tildes~" or "~asterisk plus tilde~" or "~~true sparkle exuberance~~". The sparkles emoji can be used to represent stars in text, be used to represent cleanliness or can be used to mean "orgasm" whilst sexting. In September 2021 the Sparkles emoji overtook the Pleading Face (🥺) emoji to become the third most-used emoji in the world according to Emojipedia, with approximately 1 per cent of all tweets containing the Sparkles emoji. === Artificial intelligence === In the early 2020s, the Sparkles emoji started being used as an icon to represent artificial intelligence (AI). Companies who use the emoji this way include Google, OpenAI, Samsung, Microsoft, Adobe, Spotify and Zoom. As of August 2024, seven of the top 10 software companies by market capitalisation use the Sparkles emojis with AI. OpenAI has different versions of the Sparkles for different versions of the models that ChatGPT uses. One explanation is that Sparkles is being used by these companies as a way to market AI as "magic". Marketing technology as "magic" has been used before AI, particularly by Apple. Another explanation given by designers and marketers choosing to use Sparkles to signify AI is simply that other platforms are doing it, making it familiar to users. Around 2024, some of these companies started removing two of the smaller stars from the emoji in their AI services and have kept the one large star, an example being Google's Gemini chatbot. In early 2024, the Nielsen Norman Group provided test subjects with the star in isolation and found that people did not associate the symbol with AI, but instead mostly with "optimisation" or "favourite or save an item".
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Algorithmic bias

Algorithmic bias describes systematic and repeatable harmful tendency in a computerized sociotechnical system to create "unfair" outcomes, such as "privileging" one category over another in ways that may or may not be different from the intended function of the algorithm. Bias can emerge from many factors, including intentionally biased design decisions or the unintended or unanticipated use or decisions relating to the way data is coded, collected, selected or used to train the algorithm. For example, algorithmic bias has been observed in search engine results and social media platforms. This bias can have impacts ranging from privacy violations to reinforcing social biases of race, gender, sexuality, and ethnicity. The study of algorithmic bias is most concerned with algorithms that reflect "systematic and unfair" discrimination. This bias has only recently been addressed in legal frameworks, such as the European Union's General Data Protection Regulation (enforced in 2018) and the Artificial Intelligence Act (proposed in 2021 and adopted in 2024). As algorithms expand their ability to organize society, politics, institutions, and behavior, sociologists have become concerned with the ways in which unanticipated output and manipulation of data can impact the physical world. Because algorithms are often considered to be neutral and unbiased, they can inaccurately project greater authority than human expertise (in part due to the psychological phenomenon of automation bias), and in some cases, reliance on algorithms can displace human responsibility for their outcomes, without last mile thinking. Bias can enter into algorithmic systems as a result of pre-existing cultural, social, or institutional expectations; by how features and labels are chosen; because of technical limitations of their design; or by being used in unanticipated contexts or by audiences who are not considered in the software's initial design. Algorithmic bias has been cited in cases ranging from election outcomes to the spread of online hate speech. It has also arisen in criminal justice, healthcare, and hiring, compounding existing racial, socioeconomic, and gender biases. The relative inability of facial recognition technology to accurately identify darker-skinned faces has been linked to multiple wrongful arrests of black men, an issue stemming from imbalanced datasets. Problems in understanding, researching, and discovering algorithmic bias persist due to the proprietary nature of algorithms, which are typically treated as trade secrets. Even when full transparency is provided, the complexity of certain algorithms poses a barrier to understanding their functioning. Furthermore, algorithms may change, or respond to input or output in ways that cannot be anticipated or easily reproduced for analysis. In many cases, even within a single website or application, there is no single "algorithm" to examine, but a network of many interrelated programs and data inputs, even between users of the same service. A 2021 survey identified multiple forms of algorithmic bias, including historical, representation, and measurement biases, each of which can contribute to unfair outcomes. == Definitions == Algorithms are difficult to define, but may be generally understood as lists of instructions that determine how programs read, collect, process, and analyze data to generate a usable output. For a rigorous technical introduction, see Algorithms. Advances in computer hardware and software have led to an increased capability to process, store and transmit data. This has in turn made the design and adoption of technologies such as machine learning and artificial intelligence technically and commercially feasible. By analyzing and processing data, algorithms are the backbone of search engines, social media websites, recommendation engines, online retail, online advertising, and more. Contemporary social scientists are concerned with algorithmic processes embedded into hardware and software applications because of their political and social impact, and question the underlying assumptions of an algorithm's neutrality. The term algorithmic bias describes systematic and repeatable errors that create unfair outcomes, such as privileging one arbitrary group of users over others. For example, a credit score algorithm may deny a loan without being unfair, if it is consistently weighing relevant financial criteria. If the algorithm recommends loans to one group of users, but denies loans to another set of nearly identical users based on unrelated criteria, and if this behavior can be repeated across multiple occurrences, an algorithm can be described as biased. This bias may be intentional or unintentional (for example, it can come from biased data obtained from a worker that previously did the job the algorithm is going to do from now on). == Methods == Bias can be introduced to an algorithm in several ways. During the assemblage of a dataset, data may be collected, digitized, adapted, and entered into a database according to human-designed cataloging criteria. Next, programmers assign priorities, or hierarchies, for how a program assesses and sorts that data. This requires human decisions about how data is categorized, and which data is included or discarded. Some algorithms collect their own data based on human-selected criteria, which can also reflect the bias of human designers. Other algorithms may reinforce stereotypes and preferences as they process and display "relevant" data for human users, for example, by selecting information based on previous choices of a similar user or group of users. Beyond assembling and processing data, bias can emerge as a result of design. For example, algorithms that determine the allocation of resources or scrutiny (such as determining school placements) may inadvertently discriminate against a category when determining risk based on similar users (as in credit scores). Meanwhile, recommendation engines that work by associating users with similar users, or that make use of inferred marketing traits, might rely on inaccurate associations that reflect broad ethnic, gender, socio-economic, or racial stereotypes. Another example comes from determining criteria for what is included and excluded from results. These criteria could present unanticipated outcomes for search results, such as with flight-recommendation software that omits flights that do not follow the sponsoring airline's flight paths. Algorithms may also display an uncertainty bias, offering more confident assessments when larger data sets are available. This can skew algorithmic processes toward results that more closely correspond with larger samples, which may disregard data from underrepresented populations. == History == === Early critiques === The earliest computer programs were designed to mimic human reasoning and deductions, and were deemed to be functioning when they successfully and consistently reproduced that human logic. In his 1976 book Computer Power and Human Reason, artificial intelligence pioneer Joseph Weizenbaum suggested that bias could arise both from the data used in a program, but also from the way a program is coded. Weizenbaum wrote that programs are a sequence of rules created by humans for a computer to follow. By following those rules consistently, such programs "embody law", that is, enforce a specific way to solve problems. The rules a computer follows are based on the assumptions of a computer programmer for how these problems might be solved. That means the code could incorporate the programmer's imagination of how the world works, including their biases and expectations. While a computer program can incorporate bias in this way, Weizenbaum also noted that any data fed to a machine additionally reflects "human decision making processes" as data is being selected. Finally, he noted that machines might also transfer good information with unintended consequences if users are unclear about how to interpret the results. Weizenbaum warned against trusting decisions made by computer programs that a user doesn't understand, comparing such faith to a tourist who can find his way to a hotel room exclusively by turning left or right on a coin toss. Crucially, the tourist has no basis of understanding how or why he arrived at his destination, and a successful arrival does not mean the process is accurate or reliable. An early example of algorithmic bias resulted in as many as 60 women and ethnic minorities denied entry to St. George's Hospital Medical School per year from 1982 to 1986, based on implementation of a new computer-guidance assessment system that denied entry to women and men with "foreign-sounding names" based on historical trends in admissions. While many schools at the time employed similar biases in their selection process, St. George was most notable for automating said bias through the use of an algorithm, thus gaining the attention of people on a much
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Keka HR

Keka HR is a software company that provides cloud-based human resource management and payroll automation software. Keka HR specializes in providing business services in the field of HR technology, payroll automation, recruiting, leave, attendance and performance management. The company was founded by Vijay Yalamanchili on July 21, 2014. The company is headquartered in Hyderabad, with operations in Singapore and the United States. == History == Keka HR was established in 2014 in Hyderabad, Telangana, India. In 2015, the company entered the Indian HR market and received the HYSEA Startup Award. By 2019, Keka HR had surpassed $1 million in annual recurring revenue (ARR). During the COVID-19 pandemic in 2020, the company reported a sevenfold increase in sales. By 2021, the company had raised $1.6 million through Recur Club. In 2022, Keka HR secured $57 million in Series A funding from West Bridge Capital. The company's headquarters are located in Gachibowli, Hyderabad, with offices in Singapore and Seattle, Washington.
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Decision tree pruning

Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as the horizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information. Pruning should reduce the size of a learning tree without reducing predictive accuracy as measured by a cross-validation set. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance. == Techniques == Pruning processes can be divided into two types (pre- and post-pruning). Pre-pruning procedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered to be more efficient because they do not induce an entire set, but rather trees remain small from the start. Prepruning methods share a common problem, the horizon effect. This is to be understood as the undesired premature termination of the induction by the stop () criterion. Post-pruning (or just pruning) is the most common way of simplifying trees. Here, nodes and subtrees are replaced with leaves to reduce complexity. Pruning can not only significantly reduce the size but also improve the classification accuracy of unseen objects. It may be the case that the accuracy of the assignment on the train set deteriorates, but the accuracy of the classification properties of the tree increases overall. The procedures are differentiated on the basis of their approach in the tree (top-down or bottom-up). === Bottom-up pruning === These procedures start at the last node in the tree (the lowest point). Following recursively upwards, they determine the relevance of each individual node. If the relevance for the classification is not given, the node is dropped or replaced by a leaf. The advantage is that no relevant sub-trees can be lost with this method. These methods include Reduced Error Pruning (REP), Minimum Cost Complexity Pruning (MCCP), or Minimum Error Pruning (MEP). === Top-down pruning === In contrast to the bottom-up method, this method starts at the root of the tree. Following the structure below, a relevance check is carried out which decides whether a node is relevant for the classification of all n items or not. By pruning the tree at an inner node, it can happen that an entire sub-tree (regardless of its relevance) is dropped. One of these representatives is pessimistic error pruning (PEP), which brings quite good results with unseen items. == Pruning algorithms == === Reduced error pruning === One of the simplest forms of pruning is reduced error pruning. Starting at the leaves, each node is replaced with its most popular class. If the prediction accuracy is not affected then the change is kept. While somewhat naive, reduced error pruning has the advantage of simplicity and speed. === Cost complexity pruning === Cost complexity pruning generates a series of trees ⁠ T 0 … T m {\displaystyle T_{0}\dots T_{m}} ⁠ where ⁠ T 0 {\displaystyle T_{0}} ⁠ is the initial tree and ⁠ T m {\displaystyle T_{m}} ⁠ is the root alone. At step ⁠ i {\displaystyle i} ⁠, the tree is created by removing a subtree from tree ⁠ i − 1 {\displaystyle i-1} ⁠ and replacing it with a leaf node with value chosen as in the tree building algorithm. The subtree that is removed is chosen as follows: Define the error rate of tree ⁠ T {\displaystyle T} ⁠ over data set ⁠ S {\displaystyle S} ⁠ as ⁠ err ⁡ ( T , S ) {\displaystyle \operatorname {err} (T,S)} ⁠. The subtree t {\displaystyle t} that minimizes err ⁡ ( prune ⁡ ( T , t ) , S ) − err ⁡ ( T , S ) | leaves ⁡ ( T ) | − | leaves ⁡ ( prune ⁡ ( T , t ) ) | {\displaystyle {\frac {\operatorname {err} (\operatorname {prune} (T,t),S)-\operatorname {err} (T,S)}{\left\vert \operatorname {leaves} (T)\right\vert -\left\vert \operatorname {leaves} (\operatorname {prune} (T,t))\right\vert }}} is chosen for removal. The function ⁠ prune ⁡ ( T , t ) {\displaystyle \operatorname {prune} (T,t)} ⁠ defines the tree obtained by pruning the subtrees ⁠ t {\displaystyle t} ⁠ from the tree ⁠ T {\displaystyle T} ⁠. Once the series of trees has been created, the best tree is chosen by generalized accuracy as measured by a training set or cross-validation. == Examples == Pruning could be applied in a compression scheme of a learning algorithm to remove the redundant details without compromising the model's performances. In neural networks, pruning removes entire neurons or layers of neurons.
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Manifold regularization

In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm
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Pattern theory

Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. Broad in its mathematical coverage, Pattern Theory spans algebra and statistics, as well as local topological and global entropic properties. In addition to the new algebraic vocabulary, its statistical approach is novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was previously commonplace. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with them. The Brown University Pattern Theory Group was formed in 1972 by Ulf Grenander. Many mathematicians are currently working in this group, noteworthy among them being the Fields Medalist David Mumford. Mumford regards Grenander as his "guru" in Pattern Theory.
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POP-11

POP-11 is a reflective, incrementally compiled programming language with many of the features of an interpreted language. It is the core language of the Poplog programming environment developed originally by the University of Sussex, and recently in the School of Computer Science at the University of Birmingham, which hosts the main Poplog website. POP-11 is an evolution of the language POP-2, developed in Edinburgh University, and features an open stack model (like Forth, among others). It is mainly procedural, but supports declarative language constructs, including a pattern matcher, and is mostly used for research and teaching in artificial intelligence, although it has features sufficient for many other classes of problems. It is often used to introduce symbolic programming techniques to programmers of more conventional languages like Pascal, who find POP syntax more familiar than that of Lisp. One of POP-11's features is that it supports first-class functions. POP-11 is the core language of the Poplog system. The availability of the compiler and compiler subroutines at run-time (a requirement for incremental compiling) gives it the ability to support a far wider range of extensions (including run-time extensions, such as adding new data-types) than would be possible using only a macro facility. This made it possible for (optional) incremental compilers to be added for Prolog, Common Lisp and Standard ML, which could be added as required to support either mixed language development or development in the second language without using any POP-11 constructs. This made it possible for Poplog to be used by teachers, researchers, and developers who were interested in only one of the languages. The most successful product developed in POP-11 was the Clementine data mining system, developed by ISL. After SPSS bought ISL, they renamed Clementine to SPSS Modeler and decided to port it to C++ and Java, and eventually succeeded with great effort, and perhaps some loss of the flexibility provided by the use of an AI language. POP-11 was for a time available only as part of an expensive commercial package (Poplog), but since about 1999 it has been freely available as part of the open-source software version of Poplog, including various added packages and teaching libraries. An online version of ELIZA using POP-11 is available at Birmingham. At the University of Sussex, David Young used POP-11 in combination with C and Fortran to develop a suite of teaching and interactive development tools for image processing and vision, and has made them available in the Popvision extension to Poplog. == Simple code examples == Here is an example of a simple POP-11 program: define Double(Source) -> Result; Source2 -> Result; enddefine; Double(123) => That prints out: 246 This one includes some list processing: define RemoveElementsMatching(Element, Source) -> Result; lvars Index; [[% for Index in Source do unless Index = Element or Index matches Element then Index; endunless; endfor; %]] -> Result; enddefine; RemoveElementsMatching("the", [[the cat sat on the mat]]) => ;;; outputs [[cat sat on mat]] RemoveElementsMatching("the", [[the cat] [sat on] the mat]) => ;;; outputs [[the cat] [sat on] mat] RemoveElementsMatching([[= cat]], [[the cat]] is a [[big cat]]) => ;;; outputs [[is a]] Examples using the POP-11 pattern matcher, which makes it relatively easy for students to learn to develop sophisticated list-processing programs without having to treat patterns as tree structures accessed by 'head' and 'tail' functions (CAR and CDR in Lisp), can be found in the online introductory tutorial. The matcher is at the heart of the SimAgent (sim_agent) toolkit. Some of the powerful features of the toolkit, such as linking pattern variables to inline code variables, would have been very difficult to implement without the incremental compiler facilities.
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Automated Mathematician

The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.
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Perusall

Perusall is a social web annotation tool intended for use by students at schools and universities. It allows users to annotate the margins of a text in a virtual group setting that is similar to social media—with upvoting, emojis, chat functionality, and notification. It also includes automatic AI grading. == History == Perusall began as a research project at Harvard University. It later became an educational product for students and teachers. As of 2024, Perusall states more than 5 million students have used the tool at over 5,000 educational institutions in 112 countries." == Functionality == Perusall integrates with learning management systems such as Moodle, Canvas and Blackboard to aid with collaborative annotation. The tool supports annotation of a range of media including text, images, equations, videos, PDFs and snapshots of webpages.
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Purged cross-validation

Purged cross-validation is a variant of k-fold cross-validation designed to prevent look-ahead bias in time series and other structured data, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. It is primarily used in financial machine learning to ensure the independence of training and testing samples when labels depend on future events. It provides an alternative to conventional cross-validation and walk-forward backtesting methods, which often yield overly optimistic performance estimates due to information leakage and overfitting. == Motivation == Standard cross-validation assumes that observations are independently and identically distributed (IID), which often does not hold in time series or financial datasets. If the label of a test sample overlaps in time with the features or labels in the training set, the result may be data leakage and overfitting. Purged cross-validation addresses this issue by removing overlapping observations and, optionally, adding a temporal buffer ("embargo") around the test set to further reduce the risk of leakage. The figure below illustrates standard 5 Fold Cross-Validation == Purging == Purging removes from the training set any observation whose timestamp falls within the time range of formation of a label in the test set. This can be the case for train set observations before and after the test set. Their removal ensures that the algorithm cannot learn during train time information that will be used to assess the performance of the algorithm. See the figure below for an illustration of purging. == Embargoing == Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training. Unlike purging, embargoing can only occur after the test set. The figure below illustrates the application of embargo: == Applications == Purged and embargoed cross-validation has been useful in: Backtesting of trading strategies Validation of classifiers on labeled event-driven returns Any machine learning task with overlapping label horizons == Example == To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set. The second figure applies the Purged CV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting. == Combinatorial Purged Cross-Validation == Walk-forward backtesting analysis, another common cross-validation technique in finance, preserves temporal order but evaluates the model on a single sequence of test sets. This leads to high variance in performance estimation, as results are contingent on a specific historical path. Combinatorial Purged Cross-Validation (CPCV) addresses this limitation by systematically constructing multiple train-test splits, purging overlapping samples, and enforcing an embargo period to prevent information leakage. The result is a distribution of out-of-sample performance estimates, enabling robust statistical inference and more realistic assessment of a model's predictive power. === Methodology === CPCV divides a time-series dataset into N sequential, non-overlapping groups. These groups preserve the temporal order of observations. Then, all combinations of k groups (where k < N) are selected as test sets, with the remaining N − k groups used for training. For each combination, the model is trained and evaluated under strict controls to prevent leakage. To eliminate potential contamination between training and test sets, CPCV introduces two additional mechanisms: Purging: Any training observations whose label horizon overlaps with the test period are excluded. This ensures that future information does not influence model training. Embargoing: After the end of each test period, a fixed number of observations (typically a small percentage) are removed from the training set. This prevents leakage due to delayed market reactions or auto-correlated features. Each data point appears in multiple test sets across different combinations. Because test groups are drawn combinatorially, this process produces multiple backtest "paths," each of which simulates a plausible market scenario. From these paths, practitioners can compute a distribution of performance statistics such as the Sharpe ratio, drawdown, or classification accuracy. === Formal definition === Let N be the number of sequential groups into which the dataset is divided, and let k be the number of groups selected as the test set for each split. Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used in k {\displaystyle k} test sets and contributes to φ [ N , k ] {\displaystyle \varphi [N,k]} unique backtest paths: φ [ N , k ] = k N ( N k ) {\displaystyle \varphi [N,k]={\frac {k}{N}}{\binom {N}{k}}} This yields a distribution of performance metrics rather than a single point estimate, making it possible to apply Monte Carlo-based or probabilistic techniques to assess model robustness. === Illustrative example === Consider the case where N = 6 and k = 2. The number of possible test set combinations is ( 6 2 ) = 15 {\displaystyle {\binom {6}{2}}=15} . Each of the six groups appears in five test splits. Consequently, five distinct backtest paths can be constructed, each incorporating one appearance from every group. ==== Test group assignment matrix ==== This table shows the 15 test combinations. An "x" indicates that the corresponding group is included in the test set for that split. ==== Backtest path assignment ==== Each group contributes to five different backtest paths. The number in each cell indicates the path to which the group's result is assigned for that split. === Advantages === Combinatorial Purged Cross-Validation offers several key benefits over conventional methods: It produces a distribution of performance metrics, enabling more rigorous statistical inference. The method systematically eliminates lookahead bias through purging and embargoing. By simulating multiple historical scenarios, it reduces the dependence on any single market regime or realization. It supports high-confidence comparisons between competing models or strategies. CPCV is commonly used in quantitative strategy research, especially for evaluating predictive models such as classifiers, regressors, and portfolio optimizers. It has been applied to estimate realistic Sharpe ratios, assess the risk of overfitting, and support the use of statistical tools such as the Deflated Sharpe Ratio (DSR). === Limitations === The main limitation of CPCV stems from its high computational cost. However, this cost can be managed by sampling a finite number of splits from the space of all possible combinations.
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Autognostics

Autognostics is a new paradigm that describes the capacity for computer networks to be self-aware. It is considered one of the major components of Autonomic Networking. == Introduction == One of the most important characteristics of today's Internet that has contributed to its success is its basic design principle: a simple and transparent core with intelligence at the edges (the so-called "end-to-end principle"). Based on this principle, the network carries data without knowing the characteristics of that data (e.g., voice, video, etc.) - only the end-points have application-specific knowledge. If something goes wrong with the data, only the edge may be able to recognize that since it knows about the application and what the expected behavior is. The core has no information about what should happen with that data - it only forwards packets. Although an effective and beneficial attribute, this design principle has also led to many of today's problems, limitations, and frustrations. Currently, it is almost impossible for most end-users to know why certain network-based applications do not work well and what they need to do to make it better. Also, network operators who interact with the core in low-level terms such as router configuration have problems expressing their high-level goals into low-level actions. In high-level terms, this may be summarized as a weak coupling between the network and application layers of the overall system. As a consequence of the Internet end-to-end principle, the network performance experienced by a particular application is difficult to attribute based on the behavior of the individual elements. At any given moment, the measure of performance between any two points is typically unknown and applications must operate blindly. As a further consequence, changes to the configuration of given element, or changes in the end-to-end path, cannot easily be validated. Optimization and provisioning cannot then be automated except against only the simplest design specifications. There is an increasing interest in Autonomic Networking research, and a strong conviction that an evolution from the current networking status quo is necessary. Although to date there have not been any practical implementations demonstrating the benefits of an effective autonomic networking paradigm, there seems to be a consensus as to the characteristics which such implementations would need to demonstrate. These specifically include continuous monitoring, identifying, diagnosing and fixing problems based on high-level policies and objectives. Autognostics, as a major part of the autonomic networking concept, intends to bring networks to a new level of awareness and eliminate the lack of visibility which currently exists in today's networks. == Definition == Autognostics is a new paradigm that describes the capacity for computer networks to be self-aware, in part and as a whole, and dynamically adapt to the applications running on them by autonomously monitoring, identifying, diagnosing, resolving issues, subsequently verifying that any remediation was successful, and reporting the impact with respect to the application's use (i.e., providing visibility into the changes to networks and their effects). Although similar to the concept of network awareness, i.e., the capability of network devices and applications to be aware of network characteristics (see References section below), it is noteworthy that autognostics takes that concept one step further. The main difference is the auto part of autognostics, which entails that network devices are self-aware of network characteristics, and have the capability to adapt themselves as a result of continuous monitoring and diagnostics. == Path to autognostics == Autognostics, or in other words deep self-knowledge, can be best described as the ability of a network to know itself and the applications that run on it. This knowledge is used to autonomously adapt to dynamic network and application conditions such as utilization, capacity, quality of service/application/user experience, etc. In order to achieve autognosis, networks need a means to: Continuously monitor/test the network for application-specific performance Analyze the monitoring/test data to detect problems (e.g., performance degradation) Diagnose, identify and localize sources of degradation Automatically take actions to resolve problems via remediation/provisioning Verify the problems have been resolved (potentially rolling back changes if ineffective) Subsequently, continue to monitor/test for performance
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Multi-armed bandit

In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (
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Intelligent control

Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms. == Overview == Intelligent control can be divided into the following major sub-domains: Neural network control Machine learning control Reinforcement learning Bayesian control Fuzzy control Neuro-fuzzy control Expert Systems Genetic control New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them. === Neural network controller === Neural networks have been used to solve problems in almost all spheres of science and technology. Neural network control basically involves two steps: System identification Control It has been shown that a feedforward network with nonlinear, continuous and differentiable activation functions have universal approximation capability. Recurrent networks have also been used for system identification. Given, a set of input-output data pairs, system identification aims to form a mapping among these data pairs. Such a network is supposed to capture the dynamics of a system. For the control part, deep reinforcement learning has shown its ability to control complex systems. === Bayesian controllers === Bayesian probability has produced a number of algorithms that are in common use in many advanced control systems, serving as state space estimators of some variables that are used in the controller. The Kalman filter and the Particle filter are two examples of popular Bayesian control components. The Bayesian approach to controller design often requires an important effort in deriving the so-called system model and measurement model, which are the mathematical relationships linking the state variables to the sensor measurements available in the controlled system. In this respect, it is very closely linked to the system-theoretic approach to control design.
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