Behavior-based robotics (BBR) or behavioral robotics is an approach in robotics that focuses on robots that are able to exhibit complex-appearing behaviors despite little internal variable state to model its immediate environment, mostly gradually correcting its actions via sensory-motor links. == Principles == Behavior-based robotics sets itself apart from traditional artificial intelligence by using biological systems as a model. Classic artificial intelligence typically uses a set of steps to solve problems, it follows a path based on internal representations of events compared to the behavior-based approach. Rather than use preset calculations to tackle a situation, behavior-based robotics relies on adaptability. This advancement has allowed behavior-based robotics to become commonplace in researching and data gathering. Most behavior-based systems are also reactive, which means they need no programming of what a chair looks like, or what kind of surface the robot is moving on. Instead, all the information is gleaned from the input of the robot's sensors. The robot uses that information to gradually correct its actions according to the changes in immediate environment. Behavior-based robots (BBR) usually show more biological-appearing actions than their computing-intensive counterparts, which are very deliberate in their actions. A BBR often makes mistakes, repeats actions, and appears confused, but can also show the anthropomorphic quality of tenacity. Comparisons between BBRs and insects are frequent because of these actions. BBRs are sometimes considered examples of weak artificial intelligence, although some have claimed they are models of all intelligence. == Features == Most behavior-based robots are programmed with a basic set of features to start them off. They are given a behavioral repertoire to work with dictating what behaviors to use and when, obstacle avoidance and battery charging can provide a foundation to help the robots learn and succeed. Rather than build world models, behavior-based robots simply react to their environment and problems within that environment. They draw upon internal knowledge learned from their past experiences combined with their basic behaviors to resolve problems. == History == The school of behavior-based robots owes much to work undertaken in the 1980s at the Massachusetts Institute of Technology by Rodney Brooks, who with students and colleagues built a series of wheeled and legged robots utilizing the subsumption architecture. Brooks' papers, often written with lighthearted titles such as "Planning is just a way of avoiding figuring out what to do next", the anthropomorphic qualities of his robots, and the relatively low cost of developing such robots, popularized the behavior-based approach. Brooks' work builds—whether by accident or not—on two prior milestones in the behavior-based approach. In the 1950s, W. Grey Walter, an English scientist with a background in neurological research, built a pair of vacuum tube-based robots that were exhibited at the 1951 Festival of Britain, and which have simple but effective behavior-based control systems. The second milestone is Valentino Braitenberg's 1984 book, "Vehicles – Experiments in Synthetic Psychology" (MIT Press). He describes a series of thought experiments demonstrating how simply wired sensor/motor connections can result in some complex-appearing behaviors such as fear and love. Later work in BBR is from the BEAM robotics community, which has built upon the work of Mark Tilden. Tilden was inspired by the reduction in the computational power needed for walking mechanisms from Brooks' experiments (which used one microcontroller for each leg), and further reduced the computational requirements to that of logic chips, transistor-based electronics, and analog circuit design. A different direction of development includes extensions of behavior-based robotics to multi-robot teams. The focus in this work is on developing simple generic mechanisms that result in coordinated group behavior, either implicitly or explicitly.
Projection-slice theorem
In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal: Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice the function through its origin, parallel to the projection line. In operator terms, if F1 and F2 are the 1- and 2-dimensional Fourier transform operators mentioned above, P1 is the projection operator (which projects a 2-D function onto a 1-D line), S1 is a slice operator (which extracts a 1-D central slice from a function), then F 1 P 1 = S 1 F 2 . {\displaystyle F_{1}P_{1}=S_{1}F_{2}.} This idea can be extended to higher dimensions. This theorem is used, for example, in the analysis of medical CT scans where a "projection" is an x-ray image of an internal organ. The Fourier transforms of these images are seen to be slices through the Fourier transform of the 3-dimensional density of the internal organ, and these slices can be interpolated to build up a complete Fourier transform of that density. The inverse Fourier transform is then used to recover the 3-dimensional density of the object. This technique was first derived by Ronald N. Bracewell in 1956 for a radio-astronomy problem. == The projection-slice theorem in N dimensions == In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection submanifold. In operator terms: F m P m = S m F N . {\displaystyle F_{m}P_{m}=S_{m}F_{N}.\,} == The generalized Fourier-slice theorem == In addition to generalizing to N dimensions, the projection-slice theorem can be further generalized with an arbitrary change of basis. For convenience of notation, we consider the change of basis to be represented as B, an N-by-N invertible matrix operating on N-dimensional column vectors. Then the generalized Fourier-slice theorem can be stated as F m P m B = S m B − T | B − T | F N {\displaystyle F_{m}P_{m}B=S_{m}{\frac {B^{-T}}{|B^{-T}|}}F_{N}} where B − T = ( B − 1 ) T {\displaystyle B^{-T}=(B^{-1})^{T}} is the transpose of the inverse of the change of basis transform. == Proof in two dimensions == The projection-slice theorem is easily proven for the case of two dimensions. Without loss of generality, we can take the projection line to be the x-axis. There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transform results. The rotated function is the Fourier pair of the rotated Fourier transform, for which the theorem again holds. If f(x, y) is a two-dimensional function, then the projection of f(x, y) onto the x axis is p(x) where p ( x ) = ∫ − ∞ ∞ f ( x , y ) d y . {\displaystyle p(x)=\int _{-\infty }^{\infty }f(x,y)\,dy.} The Fourier transform of f ( x , y ) {\displaystyle f(x,y)} is F ( k x , k y ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i ( x k x + y k y ) d x d y . {\displaystyle F(k_{x},k_{y})=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi i(xk_{x}+yk_{y})}\,dxdy.} The slice is then s ( k x ) {\displaystyle s(k_{x})} s ( k x ) = F ( k x , 0 ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i x k x d x d y {\displaystyle s(k_{x})=F(k_{x},0)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi ixk_{x}}\,dxdy} = ∫ − ∞ ∞ [ ∫ − ∞ ∞ f ( x , y ) d y ] e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }\left[\int _{-\infty }^{\infty }f(x,y)\,dy\right]\,e^{-2\pi ixk_{x}}dx} = ∫ − ∞ ∞ p ( x ) e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }p(x)\,e^{-2\pi ixk_{x}}dx} which is just the Fourier transform of p(x). The proof for higher dimensions is easily generalized from the above example. == The FHA cycle == If the two-dimensional function f(r) is circularly symmetric, it may be represented as f(r), where r = |r|. In this case the projection onto any projection line will be the Abel transform of f(r). The two-dimensional Fourier transform of f(r) will be a circularly symmetric function given by the zeroth-order Hankel transform of f(r), which will therefore also represent any slice through the origin. The projection-slice theorem then states that the Fourier transform of the projection equals the slice or F 1 A 1 = H , {\displaystyle F_{1}A_{1}=H,} where A1 represents the Abel-transform operator, projecting a two-dimensional circularly symmetric function onto a one-dimensional line, F1 represents the 1-D Fourier-transform operator, and H represents the zeroth-order Hankel-transform operator. == Extension to fan beam or cone-beam CT == The projection-slice theorem is suitable for CT image reconstruction with parallel beam projections. It does not directly apply to fanbeam or conebeam CT. The theorem was extended to fan-beam and conebeam CT image reconstruction by Shuang-ren Zhao in 1995.
Rule induction
Rule induction is an area of machine learning in which formal rules are extracted from a set of observations. The rules extracted may represent a full scientific model of the data, or merely represent local patterns in the data. Data mining in general and rule induction in detail are trying to create algorithms without human programming but with analyzing existing data structures. In the easiest case, a rule is expressed with “if-then statements” and was created with the ID3 algorithm for decision tree learning. Rule learning algorithm are taking training data as input and creating rules by partitioning the table with cluster analysis. A possible alternative over the ID3 algorithm is genetic programming which evolves a program until it fits to the data. Creating different algorithm and testing them with input data can be realized in the WEKA software. Additional tools are machine learning libraries for Python, like scikit-learn. == Paradigms == Some major rule induction paradigms are: Association rule learning algorithms (e.g., Agrawal) Decision rule algorithms (e.g., Quinlan 1987) Hypothesis testing algorithms (e.g., RULEX) Horn clause induction Version spaces Rough set rules Inductive Logic Programming Boolean decomposition (Feldman) == Algorithms == Some rule induction algorithms are: Charade Rulex Progol CN2
Gibberlink
GibberLink is an acoustic data transmission project, with an open-source client available on GitHub, in which two conversational AI agents switch from speaking to one another in a Human-listenable language (such as English) to their own unique language that consists of a sound-level protocol after confirming they are both AI agents. The project was created by Anton Pidkuiko and Boris Starkov. == Reception == The project won the global top prize at the ElevenLabs Worldwide Hackathon. It has also been cited as raising questions around AI ethics and oversight. On February 23, 2025, a YouTube video of two independent conversational ElevenLabs AI agents being prompted to chat about booking a hotel (one as a caller, one as a receptionist) received coverage for going viral. In this video, both agents are prompted to switch to ggwave data-over-sound protocol when they identify the other side as AI, and keep speaking in English otherwise.
Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise when the number of datapoints is small (in a suitably defined sense) relative to the intrinsic dimension of the data. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting areas where objects form groups with similar properties; in high dimensional data, however, all objects appear to be sparse and dissimilar in many ways, which prevents common data organization strategies from being efficient. == Domains == === Combinatorics === In some problems, each variable can take one of several discrete values, or the range of possible values is divided to give a finite number of possibilities. Taking the variables together, a huge number of combinations of values must be considered. This effect is also known as the combinatorial explosion. Even in the simplest case of d {\displaystyle d} binary variables, the number of possible combinations already is 2 d {\displaystyle 2^{d}} , exponential in the dimensionality. Naively, each additional dimension doubles the effort needed to try all combinations. === Sampling === There is an exponential increase in volume associated with adding extra dimensions to a mathematical space. For example, 102 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube, i.e. a line) with no more than 10−2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10−2 = 0.01 between adjacent points would require 1020 = [(102)10] sample points. In general, with a spacing distance of 10−n the 10-dimensional hypercube appears to be a factor of 10n(10−1) = [(10n)10/(10n)] "larger" than the 1-dimensional hypercube, which is the unit interval. In the above example n = 2: when using a sampling distance of 0.01 the 10-dimensional hypercube appears to be 1018 "larger" than the unit interval. This effect is a combination of the combinatorics problems above and the distance function problems explained below. === Optimization === When solving dynamic optimization problems by numerical backward induction, the objective function must be computed for each combination of values. This is a significant obstacle when the dimension of the "state variable" is large. === Machine learning === In machine learning problems that involve learning a "state-of-nature" from a finite number of data samples in a high-dimensional feature space with each feature having a range of possible values, typically an enormous amount of training data is required to ensure that there are several samples with each combination of values. In an abstract sense, as the number of features or dimensions grows, the amount of data we need to generalize accurately grows exponentially. A typical rule of thumb is that there should be at least 5 training examples for each dimension in the representation. In machine learning and insofar as predictive performance is concerned, the curse of dimensionality is used interchangeably with the peaking phenomenon, which is also known as Hughes phenomenon. This phenomenon states that with a fixed number of training samples, the average (expected) predictive power of a classifier or regressor first increases as the number of dimensions or features used is increased but beyond a certain dimensionality it starts deteriorating instead of improving steadily. Nevertheless, in the context of a simple classifier (e.g., linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix), Zollanvari et al. showed both analytically and empirically that as long as the relative cumulative efficacy of an additional feature set (with respect to features that are already part of the classifier) is greater (or less) than the size of this additional feature set, the expected error of the classifier constructed using these additional features will be less (or greater) than the expected error of the classifier constructed without them. In other words, both the size of additional features and their (relative) cumulative discriminatory effect are important in observing a decrease or increase in the average predictive power. In metric learning, higher dimensions can sometimes allow a model to achieve better performance. After normalizing embeddings to the surface of a hypersphere, FaceNet achieves the best performance using 128 dimensions as opposed to 64, 256, or 512 dimensions in one ablation study. A loss function for unitary-invariant dissimilarity between word embeddings was found to be minimized in high dimensions. === Data mining === In data mining, the curse of dimensionality refers to a data set with too many features. Consider the first table, which depicts 200 individuals and 2000 genes (features) with a 1 or 0 denoting whether or not they have a genetic mutation in that gene. A data mining application to this data set may be finding the correlation between specific genetic mutations and creating a classification algorithm such as a decision tree to determine whether an individual has cancer or not. A common practice of data mining in this domain would be to create association rules between genetic mutations that lead to the development of cancers. To do this, one would have to loop through each genetic mutation of each individual and find other genetic mutations that occur over a desired threshold and create pairs. They would start with pairs of two, then three, then four until they result in an empty set of pairs. The complexity of this algorithm can lead to calculating all permutations of gene pairs for each individual or row. Given the formula for calculating the permutations of n items with a group size of r is: n ! ( n − r ) ! {\displaystyle {\frac {n!}{(n-r)!}}} , calculating the number of three pair permutations of any given individual would be 7988004000 different pairs of genes to evaluate for each individual. The number of pairs created will grow by an order of factorial as the size of the pairs increase. The growth is depicted in the permutation table (see right). As we can see from the permutation table above, one of the major problems data miners face regarding the curse of dimensionality is that the space of possible parameter values grows exponentially or factorially as the number of features in the data set grows. This problem critically affects both computational time and space when searching for associations or optimal features to consider. Another problem data miners may face when dealing with too many features is that the number of false predictions or classifications tends to increase as the number of features grows in the data set. In terms of the classification problem discussed above, keeping every data point could lead to a higher number of false positives and false negatives in the model. This may seem counterintuitive, but consider the genetic mutation table from above, depicting all genetic mutations for each individual. Each genetic mutation, whether they correlate with cancer or not, will have some input or weight in the model that guides the decision-making process of the algorithm. There may be mutations that are outliers or ones that dominate the overall distribution of genetic mutations when in fact they do not correlate with cancer. These features may be working against one's model, making it more difficult to obtain optimal results. This problem is up to the data miner to solve, and there is no universal solution. The first step any data miner should take is to explore the data, in an attempt to gain an understanding of how it can be used to solve the problem. One must first understand what the data means, and what they are trying to discover before they can decide if anything must be removed from the data set. Then they can create or use a feature selection or dimensionality reduction algorithm to remove samples or features from the data set if they deem it necessary. One example of such methods is the interquartile range method, used to remove outliers in a data set by calculating the standard deviation of a feature or occurrence. === Distance function === When a measure such as a Euclidean distance is defined using many coordinat
Coolgorilla
Coolgorilla was one of the earliest software developers that created 3rd party native applications for Apple iPod devices. Coolgorilla was an early adopter of using a sponsorship business model to enable mobile applications to be given away freely. Coolgorilla developed a series of Talking Phrasebooks for iPods in 2006. They partnered with online travel company lastminute.com who sponsored the applications enabling them to be made available to download completely free of charge. As mobile devices became more sophisticated, Coolgorilla developed the Talking Phrasebooks for Sony Ericsson and Nokia Mobile Devices which at the time were considerably noteworthy since the applications used real voice audio translations. With Apple's introduction of the iPhone in 2007, Coolgorilla developed a Web App before having four of the iPhone Talking Phrasebooks available to download from Apple's App Store on the day it opened in 2008. == Almanac in Chronological Order == On 23 December 2005, CoolGorilla, a new start-up, launched a trivia game for the iPod. It was titled "Rock and Pop Quiz". It was a quiz game that tested users' knowledge on bands such as U2, Metallica, Beyonce, and the Beatles. The quiz contained twenty megabytes of audible trivia questions. The free game was compatible with 3rd, 4th and 5th generation iPods, iPod mini and nano. In March 2006, Coolgorilla released "Movie Quiz for iPods" with a price of $5. It was an audio game narrated by New York's DJ Thomas, a radio and television host, voice over artist and event Master of Ceremonies. There were questions on Star Wars, Spiderman, The Godfather, Pulp Fiction, The Matrix, James Bond, and others. The user could keep track of their score. The game included a secret code for players who answered all questions correctly which enabled users to enter their name on the Coolgorilla Hall of Fame. In May 2006, Coolgorilla launched a World Cup Encyclopedia which was released prior to the 2006 FIFA World Cup. It had information on the World Cup schedule, details of every player from every team, every score from every world cup game ever played, stadium details, and manager profiles. It was a free download. In June 2006, Coolgorilla released a series of iPod Phrasebooks in German, Greek, French and Spanish. They were sponsored by lastminute.com and were free. The phrasebooks included common words and phrases for tourists with 750 sound files. They were accessed through the iPod's Notes feature. In April 2007, Coolgorilla released a downloadable version of the Talking Phrasebooks for Nokia and Sony Ericsson mobile devices. French, Spanish, German, Greek, Italian, and Portuguese were produced. The application provided real voice translations. They initially sold for £3 but 3 months later were offered for free. The branding was lastminute.com branding. Apple's iPhone was released at the end of June 2007. Soon after, Coolgorilla released an online all-in-one version of their Talking Phrasebooks for iPhone (Web App). The Phrasebooks were made available online in the form of a web app as iPhone did not yet allow for the download of additional apps. The app provided both text and audio translations in French, Spanish, Portuguese, Italian, German, and Greek. The iPhone translated the phrases using the recordings of real, native voice-over artists. A text translation on screen was also displayed. Apple's App Store opened in July 2008 with approximately 500 native apps available. Four of these Apps were Coolgorilla's Talking Phrasebooks for iPhone (Native Apps). There was French, German, Italian, and Spanish. These Apps carried lastminute.com branding and were available for free download. In the first three weeks following their release, the phrasebooks had over 350,000 downloads. Subsequently, Dutch, Arabic, Mandarin and Cantonese were also released. In October 2008, Coolgorilla released an iPhone London Travel Guide. Coolgorilla featured on NBC News in August 2009. In 2010, FIAT used the Italian Phrasebook to help promote the release of their FIAT 500 in the US. There has been no further activity since.
Hyperparameter optimization
In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a