The Data Management Association (DAMA), formerly known as the Data Administration Management Association, is a global not-for-profit organization which aims to advance concepts and practices about information management and data management. It describes itself as vendor-independent, all-volunteer organization, and has a membership consisting of technical and business professionals. Its international branch is called DAMA International (or DAMA-I), and DAMA also has various continental and national branches around the world. == History == The Data Management Association International was founded in 1980 in Los Angeles. Other early chapters were: San Francisco, Portland, Seattle, Minneapolis, New York, and Washington D.C. == Data Management Body of Knowledge == DAMA has published the Data Management Body of Knowledge (DMBOK), which contains suggestions on best practices and suggestions of a common vernacular for enterprise data management. The first edition (DAMA-DMBOK) was published on 2009 November 1, the second edition (DAMA-DMBOK2) was published on 2017 July 1., and the Revised second edition (DAMA-DMBOK2 rev.2) was published on 2019 March 19. DMBOK has been described by the authors as being an "equivalent" to the Project Management Body of Knowledge (PMBOK) and Business Analysis Body of Knowledge (BABOK). It encompasses topics such as data architecture, security, quality, modelling, governance, big data, data science, and more. DMBOK also includes the DAMA Data Wheel, an infographic which represents core data management practices. The center of the infographic is data governance, and the surrounding segments each represent a different aspect of data management: Data architecture Data modeling and design Data storage and operations Data security Data integration and interoperability Document management Content management Master data management Reference data and master data Data warehousing Metadata management Data quality Business intelligence Data science == Professional Accreditation == DAMA also provides a professional data management certification for individuals known as a Certified Data Management Professional (CDMP), which is based on the DMBOK as a study reference. There are four levels of certification based on career experience and exam results. The highest level, Fellow, requires 25 years of experience and nomination by DAMA members. It is an example of one of many competing certifications for data management professionals.
Colloquis
Colloquis, previously known as ActiveBuddy and Conversagent, was a company that created conversation-based interactive agents originally distributed via instant messaging platforms. The company had offices in New York, New York, and Sunnyvale, California. == History == Founded in 2000, the company was the brainchild of Robert Hoffer, Timothy Kay, and Peter Levitan. The idea for interactive agents (also known as Internet bots) came from the team's vision to add functionality to increasingly popular instant messaging services. The original implementation took shape as a word-based adventure game but quickly grew to include a wide range of database applications, including access to news, weather, stock information, movie times, Yellow Pages listings, and detailed sports data, as well as a variety of tools (calculators, translator, etc.). These various applications were bundled into one entity and launched as SmarterChild in 2001. SmarterChild acted as a showcase for the quick data access and possibilities for fun conversation that the company planned to turn into customized, niche-specific products. The rapid success of SmarterChild led to targeted promotional products for Radiohead, Austin Powers, The Sporting News, and others. ActiveBuddy sought to strengthen its hold on the interactive agent market for the future by filing for, and receiving, a controversial patent on their creation in 2002. The company also released the BuddyScript SDK, a free developer kit that allow programmers to design and launch their own interactive agents using ActiveBuddy's proprietary scripting language, in 2002. Ultimately, however, the decline in ad spending in 2001 and 2002 led to a shift in corporate strategy towards business focused Automated Service Agents, building products for clients including Cingular, Comcast and Cox Communications. The company subsequently changed its name from ActiveBuddy to Conversagent in 2003, and then again to Colloquis in 2006. Colloquis was purchased by Microsoft in October 2006.
Microsoft SQL Server Master Data Services
Microsoft SQL Server Master Data Services (MDS) is a Master Data Management (MDM) product from Microsoft that ships as a part of the Microsoft SQL Server relational database management system. Master data management (MDM) allows an organization to discover and define non-transactional lists of data, and compile maintainable, reliable master lists. Master Data Services first shipped with Microsoft SQL Server 2008 R2. Microsoft SQL Server 2016 introduced enhancements to Master Data Services, such as improved performance and security, and the ability to clear transaction logs, create custom indexes, share entity data between different models, and support for many-to-many relationships. == Overview == In Master Data Services, the model is the highest level container in the structure of your master data. You create a model to manage groups of similar data. A model contains one or more entities, and entities contain members that are the data records. An entity is similar to a table. Like other MDM products, Master Data Services aims to create a centralized data source and keep it synchronized, and thus reduce redundancies, across the applications which process the data. Sharing the architectural core with Stratature +EDM, Master Data Services uses a Microsoft SQL Server database as the physical data store. It is a part of the Master Data Hub, which uses the database to store and manage data entities. It is a database with the software to validate and manage the data, and keep it synchronized with the systems that use the data. The master data hub has to extract the data from the source system, validate, sanitize and shape the data, remove duplicates, and update the hub repositories, as well as synchronize the external sources. The entity schemas, attributes, data hierarchies, validation rules and access control information are specified as metadata to the Master Data Services runtime. Master Data Services does not impose any limitation on the data model. Master Data Services also allows custom Business rules, used for validating and sanitizing the data entering the data hub, to be defined, which is then run against the data matching the specified criteria. All changes made to the data are validated against the rules, and a log of the transaction is stored persistently. Violations are logged separately, and optionally the owner is notified, automatically. All the data entities can be versioned. Master Data Services allows the master data to be categorized by hierarchical relationships, such as employee data are a subtype of organization data. Hierarchies are generated by relating data attributes. Data can be automatically categorized using rules, and the categories are introspected programmatically. Master Data Services can also expose the data as Microsoft SQL Server views, which can be pulled by any SQL-compatible client. It uses a role-based access control system to restrict access to the data. The views are generated dynamically, so they contain the latest data entities in the master hub. It can also push out the data by writing to some external journals. Master Data Services also includes a web-based UI for viewing and managing the data. It uses ASP.NET in the back-end. The Silverlight front-end was replaced with HTML5 in SQL Server 2019. Master Data Services provides a Web service interface to expose the data, as well as an API, which internally uses the exposed web services, exposing the feature set, programmatically, to access and manipulate the data. It also integrates with Active Directory for authentication purposes. Unlike +EDM, Master Data Services supports Unicode characters, as well as support multilingual user interfaces. SQL Server 2016 introduced a significant performance increase in Master Data Services over previous versions. == Terminology == Model is the highest level of an MDS instance. It is the primary container for specific groupings of master data. In many ways it is very similar to the idea of a database. Entities are containers created within a model. Entities provide a home for members, and are in many ways analogous to database tables. (e.g. Customer) Members are analogous to the records in a database table (Entity) e.g. Will Smith. Members are contained within entities. Each member is made up of two or more attributes. Attributes are analogous to the columns within a database table (Entity) e.g. Surname. Attributes exist within entities and help describe members (the records within the table). Name and Code attributes are created by default for each entity and serve to describe and uniquely identify leaf members. Attributes can be related to other attributes from other entities which are called 'domain-based' attributes. This is similar to the concept of a foreign key. Other attributes however, will be of type 'free-form' (most common) or 'file'. Attribute Groups are explicitly defined collections of particular attributes. Say you have an entity "customer" that has 50 attributes — too much information for many of your users. Attribute groups enable the creation of custom sets of hand-picked attributes that are relevant for specific audiences. (e.g. "customer - delivery details" that would include just their name and last known delivery address). This is very similar to a database view. Hierarchies organize members into either Derived or Explicit hierarchical structures. Derived hierarchies, as the name suggests, are derived by the MDS engine based on the relationships that exist between attributes. Explicit hierarchies are created by hand using both leaf and consolidated members. Business Rules can be created and applied against model data to ensure that custom business logic is adhered to. In order to be committed into the system data must pass all business rule validations applied to them. e.g. Within the Customer Entity you may want to create a business rule that ensures all members of the 'Country' Attribute contain either the text "USA" or "Canada". The Business Rule once created and ran will then verify all the data is correct before it accepts it into the approved model. Versions provide system owners / administrators with the ability to Open, Lock or Commit a particular version of a model and the data contained within it at a particular point in time. As the content within a model varies, grows or shrinks over time versions provide a way of managing metadata so that subscribing systems can access to the correct content.
Artificial intelligence in architecture
Artificial intelligence in architecture is the use of artificial intelligence in automation, design, and planning in the architectural process or in assisting human skills in the field of architecture. AI has been used by some architects for design, and has been proposed as a way to automate planning and routine tasks in the field. == Implications == === Benefits === Artificial intelligence, according to ArchDaily, is said to potentially significantly augment the architectural profession through its ability to improve the design and planning process as well as increasing productivity. Through its ability to handle a large amount of data, AI is said to potentially allow architects a range of design choices with criteria considerations such as budget, requirements adjusted to space, and sustainability goals calculated as part of the design process. ArchDaily said this may allow the design of optimized alternatives that can then undergo human review. AI tools are also said to potentially allow architects to assimilate urban and environmental data to inform their designs, streamlining initial stages of project planning and increasing efficiency and productivity. The advances in generative design through the input of specific prompts allow architects to produce visual designs, including photorealistic images, and thus render and explore various material choices and spatial configurations. ArchDaily noted this could speed the creative process as well as allow for experimentation and sophistication in the design. Additionally, AI's capacity for pattern recognition and coding could aid architects in organizing design resources and developing custom applications, thus enhancing the efficiency and collaboration between both architects and AI. AI is thought to also be able to contribute to the sustainability of buildings by analyzing various factors and following recommended energy-efficient modifications, thus pushing the industry towards greener practices. The use of AI in building maintenance, project management, and the creation of immersive virtual reality experiences are also thought of as potentially augmenting the architectural design process and workflow. Examples include the use of text-to-image systems such as Midjourney to create detailed architectural images, and the use of AI optimization systems from companies such as Finch3D and Autodesk to automatically generate floor plans from simple programmatic inputs. In contrast to digital-only creative practices, the high materiality of architectural outputs requires transitions from ephemeral digital files to permanent physical structures that are subject to strict safety regulations, material constraints, sensory intuition, and site-specific cultural contexts, making full automation difficult. Early adopters such as architect Stephen Coorlas have actively challenged the boundaries of architectural practice through AI. His early experimental initiative, Speculations on AI and Architecture, confronts the discipline's traditional workflows by training text-to-image AI tools such as Midjourney, Luma AI, and PromeAI to generate more nuanced architectural illustrations including construction documents, architectural details, and assembly sequences for various structures. Coorlas inputs precise terminology and architectural language to provoke the AI into producing axonometric drawings that resemble conventional documentation, then experiments with animating the outputs using AI generated depth maps and other AI image-to-3D wireframe tools. Stephen's inventive process invites architects and designers to reconsider authorship, automation, and the future of visual communication in the built environment. Rather than treating AI as a peripheral tool, Stephen has advocated for AI to be a speculative collaborator capable of engaging with discipline-specific challenges. His work contributes to the growing discourse on generative design, parametric optimization, and the philosophical implications of machine-assisted creativity raising urgent questions about how such technologies will reshape architectural agency, precision, and pedagogy. Another prominent advocate is Architect Andrew Kudless, who in an interview to Dezeen recounted that he uses AI to innovate in architectural design by incorporating materials and scenes not usually present in initial plans, which he believes can significantly alter client presentations. He told Dezeen he believes one should show clients renderings from the onset, with AI assisting in this work, arguing that changes in design should be a positive aspect of the client-designer relationship by actively involving clients in the process. Additionally, Kudless highlighted the AI's potential to facilitate labor in architectural firms, particularly in automating rendering tasks, thus reducing the workload on junior staff while maintaining control over the creative output. === Emergent aesthetics === In an interview for the AItopia series to Dezeen, designer Tim Fu discussed the transformative potential of AI in architecture, and proposed a future where AI could herald a "neoclassical futurist" style, blending the grandeur of classical aesthetics with futuristic design. Through his collaborative project, The AI Stone Carver, Fu showcased how AI can innovate traditional practices by generating design concepts that are then realized through human craftsmanship, such as stone carving by mason Till Apfel. This approach, he believed, celebrated the fusion of diverse architectural styles and also emphasized the unique capabilities of AI in enhancing creative design processes. Fu told Dezeen he envisions the integration of AI in design as a means to revive the ornamentation and detailed aesthetics characteristic of classical architecture, moving away from minimalism, which he said dominates contemporary architecture. He argued that AI's involvement in the ideation phase of design allows for a reversal in the roles of machine and human, enabling architects and designers to focus on creating more intricate and ornamental structures. Fu's optimistic outlook extended to the broader impact of AI on the architectural field, seeing it as an indispensable tool that will shift rather than replace human roles, enriching the field with innovative designs that pay homage to the beauty and qualities of classical architecture not present in contemporary architecture while embracing new technologies. This perspective resonates with designers like Manas Bhatia, whose explorations similarly embrace generative AI as a co-creator and a medium to express ideas, blend architectural traditions, and speculate spatial futures. === Concerns === As AI continues to expand its presence across various industries, its impact on the architectural profession has become a topic of growing discussion. These discussions focus on how AI processes may influence traditional architectural practices, potentially altering job roles, and shaping the nature of creativity. While AI-driven processes may increase efficiency in some aspects of the profession, they also raise questions about the potential loss of unique design perspectives. These thoughts have been countered by many prominent creative figures in the realm of AI architecture, such as Stephen Coorlas, Tim Fu, Hassan Ragab, and Manas Bhatia who have showcased the amplification of creativity in design and potential benefits in terms of restoring creative power to the designer. A key concern is that AI-powered tools could diminish the need for human involvement in specific tasks traditionally performed by architects. This has led to speculation that the profession may increasingly shift toward roles focused on oversight, coordination, and strategic decision-making rather than hands-on design work. In some design scenarios, algorithmically generated solutions can be adjusted to prioritize efficiency and cost-effectiveness, which some argue may overshadow the creative and contextual nuances that define individual architectural styles. As with any discipline though, it has been determined that AI can be configured to provide beneficial results based on inputs and end goals the architect or designer assigns it. There are also concerns about the potential for AI to exacerbate inequalities within the architectural profession. For instance, larger firms with greater resources to invest in advanced AI technologies may gain a competitive edge over smaller firms and independent architects. This dynamic could contribute to industry consolidation, potentially limiting the diversity of architectural practice and stifling innovation. Ethical considerations in regard to cultural sensitivity have also been raised due to the datasets used to train AI. Without proper vetting of data or implementing failsafe overrides, AI generated outcomes can trend toward overly documented and prioritized content.
Super column
A super column is a tuple (a pair) with a binary super column name and a value that maps it to many columns. They consist of a key–value pairs, where the values are columns. Theoretically speaking, super columns are (sorted) associative array of columns. Similar to a regular column family where a row is a sorted map of column names and column values, a row in a super column family is a sorted map of super column names that maps to column names and column values. A super column is part of a keyspace together with other super columns and column families, and columns. == Code example == Written in the JSON-like syntax, a super column definition can be like this: Where: "databases" are keyspace; "Cassandra" and "HBase" are rowKeys; "name" and "address" are super column names; "firstName", "city", "age", etc. are column names.
Memory color effect
The memory color effect is the phenomenon that the canonical hue of a type of object acquired through experience (e.g. the sky, a leaf, or a strawberry) can directly modulate the appearance of the actual colors of objects. Human observers acquire memory colors through their experiences with instances of that type. For example, most human observers know that an apple typically has a reddish hue; this knowledge about the canonical color which is represented in memory constitutes a memory color. As an example of the effect, normal human trichromats, when presented with a gray banana, often perceive the gray banana as being yellow - the banana's memory color. In light of this, subjects typically adjust the color of the banana towards the color blue - the opponent color of yellow - when asked to adjust its surface to gray to cancel the subtle activation of banana's memory color. Subsequent empirical studies have also shown the memory color effect on man-made objects (e.g. smurfs, German mailboxes), the effect being especially pronounced for blue and yellow objects. To explain this, researchers have argued that because natural daylight shifts from short wavelengths of light (i.e., bluish hues) towards light of longer wavelengths (i.e., yellowish-orange hues) during the day, the memory colors for blue and yellow objects are recruited by the visual system to a higher degree to compensate for this fluctuation in illumination, thereby providing a stronger memory color effect. == Form identification == Memory color plays a role when detecting an object. In a study where participants were given objects, such as an apple, with two alternate forms for each, a crooked apple and a circular apple, researchers changed the colors of the alternate forms and asked if they could identify them. Most of the participants answered "unsure," suggesting that we use memory color when identifying an object. The research redefined memory color as a phenomenon when "a form's identity affects the phenomenal hue of that form." == Color effect on memorization == Memory color effect can be derived from the human instinct to memorize objects better. Comparing the effect of recognizing gray-scaled images and colored images, results showed that people were able to recall colored images 5% higher compared to gray-scaled images. An important factor was that higher level of contrast between the object and background color influences memory. In a specific study related to this, participants reported that colors were 5% to 10% easier to recognize compared to black and white. == Color constancy and memory color effect == Color constancy is the phenomenon where a surface to appear to be of the same color under a wide rage of illumination. A study tested two hypotheses with regards to color memory; the photoreceptor hypothesis and the surface reflectance hypothesis. The test color was surround either by various color patches forming a complex pattern or a uniform “grey” field at the same chromaticity as that of the illuminant. The test color was presented on a dark background for the control group. It was observed that complex surround results where in line with the surface-reflectance hypothesis and not the photoreceptor hypothesis, showing that the accuracy and precision of color memory are fundamentals to understanding the phenomenon of color constancy. == Significance to the evolution of trichromacy == While objects that possess canonical hues make up a small percentage of the objects which populate humans’ visual experience, the human visual system evolved in an environment populated with objects that possess canonical hues. This suggests that the memory color effect is related to the emergence of trichromacy because it has been argued that trichromacy evolved to optimize the ability to detect ripe fruits—objects that appear in canonical hues. == In perception research == In perception research, the memory color effect is cited as evidence for the opponent color theory, which states that four basic colors can be paired with its opponent color: red—green, blue—yellow. This explains why participants adjust the ripe banana color to a blueish tone to make its memory color yellow as gray. Researchers have also found empirical evidence that suggests memory color is recruited by the visual system to achieve color constancy. For example, participants had a lower percentage of color constancy when looking at a color incongruent scene, such as a purple banana, compared to a color diagnostical scene, a yellow banana. This suggests that color constancy is influenced by the color of objects that we are familiar with, which the memory color effect takes part.
Lai–Robbins lower bound
The Lai–Robbins lower bound gives an asymptotic lower bound on the regret that any uniformly good algorithm must incur in the stochastic multi-armed bandit problem. The original result was proved by Tze Leung Lai and Herbert Robbins in 1985 for parametric exponential families. Later work extended the statement to more general classes of distributions. == Multi-armed bandit problem == The multi-armed bandit problem (MAB) is a sequential game in which the player must trade off exploration (to learn) and exploitation (to earn). The player chooses among K {\displaystyle K} actions (arms) with unknown distributions ν = ( ν 1 , … , ν K ) {\displaystyle \nu =(\nu _{1},\dots ,\nu _{K})} . The player is assumed to know a class of distributions D {\displaystyle {\mathcal {D}}} such that for every k {\displaystyle k} one has ν k ∈ D {\displaystyle \nu _{k}\in {\mathcal {D}}} (for example, D {\displaystyle {\mathcal {D}}} may be the family of Gaussian or Bernoulli distributions). At each round t = 1 , … , T {\displaystyle t=1,\dots ,T} the player selects (pulls) an arm a t {\displaystyle a_{t}} and observes a reward X t ∼ ν a t {\displaystyle X_{t}\sim \nu _{a_{t}}} . We denote N a ( t ) := ∑ s = 1 t 1 { a s = a } {\displaystyle N_{a}(t):=\sum _{s=1}^{t}\mathbf {1} _{\{a_{s}=a\}}} the number of times arm a {\displaystyle a} has been pulled in the first t {\displaystyle t} rounds, μ ( ν ) := ( μ 1 , … , μ K ) {\displaystyle \mu (\nu ):=(\mu _{1},\dots ,\mu _{K})} the vector of arm means, where μ k = E X ∼ ν k [ X ] {\displaystyle \mu _{k}=\mathbb {E} _{X\sim \nu _{k}}[X]} , μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} the highest mean Δ a := μ ∗ − μ a ≥ 0 {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}\geq 0} the gap of arm a {\displaystyle a} . An arm a {\displaystyle a} with μ a = μ ∗ {\displaystyle \mu _{a}=\mu ^{}} is called an optimal arm; otherwise it is a suboptimal arm. The goal is to minimize the regret at horizon T {\displaystyle T} , defined by R T := ∑ a = 1 K Δ a E [ N a ( T ) ] . {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\,\mathbb {E} [N_{a}(T)].} Intuitively, the regret is the (expected) total loss compared to always playing an optimal arm: regret = ∑ a ( cost of playing a ) × ( times a is played ) . {\displaystyle {\text{regret}}=\sum _{a}\ ({\text{cost of playing }}a)\times ({\text{times }}a{\text{ is played}}).} An MAB algorithm is a (possibly randomized) policy that, at each round t {\displaystyle t} , choose an arm a_t by using the observations received from previous turns. === Intuitive example === Suppose a farmer must choose, each year, one of K {\displaystyle K} seed varieties to plant. Each variety k {\displaystyle k} has an unknown average yield μ k {\displaystyle \mu _{k}} . If the farmer knew the best variety (with mean μ ∗ {\displaystyle \mu ^{}} ) he would plant it every year; in reality he must try varieties to learn which is best. The cumulative regret after T {\displaystyle T} years measures the total expected loss in yield due to imperfect knowledge. Remarks The model above is the stochastic MAB; there also exist adversarial variants. One may consider a fixed-horizon setting (known T {\displaystyle T} ) or an anytime setting (unknown T {\displaystyle T} ). == Lai–Robbins lower bound == The theorem gives the right amount of time we should pull a suboptimal arm k {\displaystyle k} to distinguish whether we are in the instance with ν k {\displaystyle \nu _{k}} or with ν ~ k {\displaystyle {\tilde {\nu }}_{k}} where ν ~ k {\displaystyle {\tilde {\nu }}_{k}} is such that μ ~ k > μ ∗ {\displaystyle {\tilde {\mu }}_{k}>\mu ^{}} . Knowning a lower bound on the number of pull of every suboptimal arm gives a lower bound on the regret as only suboptimal arms contribute to the regret. Before stating the formal theorem we need to define what is a consistent algorithm. === Consistency (uniformly good algorithms) === Let D {\displaystyle {\mathcal {D}}} be a class of probability distributions and consider K {\displaystyle K} arms with reward distributions ν = ( ν 1 , … , ν K ) ∈ D K {\displaystyle \nu =(\nu _{1},\dots ,\nu _{K})\in {\mathcal {D}}^{K}} . An algorithm is said to be consistent (also called uniformly good) on D K {\displaystyle {\mathcal {D}}^{K}} if, for every instance ν ∈ D K {\displaystyle \nu \in {\mathcal {D}}^{K}} , the expected regret R T ( ν ) {\displaystyle R_{T}(\nu )} grows subpolynomially: ∀ α > 0 , R T ( ν ) = o ( T α ) as T → ∞ {\displaystyle \forall \alpha >0,\qquad R_{T}(\nu )=o(T^{\alpha })\quad {\text{as }}T\to \infty } This assumption excludes algorithms that perform well on some instances but incur linear regret on others. === Formal lower bound === For any suboptimal arm a {\displaystyle a} . For a distribution ν a ∈ D {\displaystyle \nu _{a}\in {\mathcal {D}}} and a threshold x {\displaystyle x} , define K inf ( ν a , x , D ) := inf { KL ( ν a , ν ′ ) : ν ′ ∈ D , μ ′ > x } {\displaystyle {\mathcal {K}}_{\inf }(\nu _{a},x,{\mathcal {D}}):=\inf {\Bigl \{}\operatorname {KL} (\nu _{a},\nu '):\nu '\in {\mathcal {D}},\ \mu '>x{\Bigr \}}} where KL ( ⋅ , ⋅ ) {\displaystyle \operatorname {KL} (\cdot ,\cdot )} denotes the Kullback-Leibler divergence. Then, for any algorithm consistent on D K {\displaystyle {\mathcal {D}}^{K}} and for every instance ν ∈ D K {\displaystyle \nu \in {\mathcal {D}}^{K}} , every suboptimal arm a {\displaystyle a} satisfies E ν [ N a ( T ) ] ≥ ln T K inf ( ν a , μ ∗ , D ) + o ( ln T ) {\displaystyle \mathbb {E} _{\nu }[N_{a}(T)]\geq {\frac {\ln T}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}+o(\ln T)} Consequently, the regret satisfies R T ( ν ) ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln T + o ( ln T ) {\displaystyle R_{T}(\nu )\geq \left(\sum _{a:\,\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+o(\ln T)} The original 1985 paper established this result for exponential families; later work showed that the bound holds under much weaker assumptions on D {\displaystyle {\mathcal {D}}} . === Intuition === Consistency imposes that, for every ν {\displaystyle \nu } , the number of pulls of an optimal arm must be large. This means that μ ∗ {\displaystyle \mu ^{}} is estimated very accurately. The goal is to determine, for a suboptimal arm k {\displaystyle k} , how many samples are needed to be confident, with the appropriate level of confidence, that μ k < μ ∗ {\displaystyle \mu _{k}<\mu ^{}} . To do so, we use what is called the most confusing instance: an instance close to ν {\displaystyle \nu } such that arm k {\displaystyle k} is optimal. We define it as ν ~ {\displaystyle {\tilde {\nu }}} such that, for all a ≠ k {\displaystyle a\neq k} , ν ~ a = ν a {\displaystyle {\tilde {\nu }}_{a}=\nu _{a}} , and ν ~ k {\displaystyle {\tilde {\nu }}_{k}} is chosen so that μ ~ k > μ ∗ {\displaystyle {\tilde {\mu }}_{k}>\mu ^{}} . The objective is to determine how many samples of arm k {\displaystyle k} are required to distinguish whether we are in the instance with ν k {\displaystyle \nu _{k}} or with ν ~ k {\displaystyle {\tilde {\nu }}_{k}} in terms of KL {\displaystyle \operatorname {KL} } distance. == Algorithms achieving the Lai–Robbins lower bound == Several algorithms are known to achieve the Lai–Robbins asymptotic lower bound under specific assumptions on the reward distribution class D {\displaystyle {\mathcal {D}}} . The following list summarizes a non-exhaustive list of algorithms matching the lower bound. == Extension to other problems == === Structured bandit === A more complexe is structured bandit where we know that the mean of each arm is in a set with some restriction. In this case we can prove a smaller lower bound that use the knowledge of this set. === Best arm identification (BAI) === A similar result has been proved for best arm identification, which is the same game except that, instead of minimizing the regret, the goal is to identify the best arm with probability 1 − δ {\displaystyle 1-\delta } using as few rounds as possible. === Reinforcement Learning (RL) === Similar results have been proved for regret minimization in average-reward reinforcement learning. The order is also ln T {\displaystyle \ln T} , with a constant that depends on the problem.