The Political Declaration on Responsible Military Use of Artificial Intelligence and Autonomy is an international norms and arms control proposal by the U.S. government for artificial intelligence in the military. It was announced at the Summit on Responsible Artificial Intelligence in the Military Domain by Bonnie Jenkins, Under Secretary of State for Arms Control. As of January 2024, fifty-one countries have signed the declaration. The US government sees it as an extension of the Department of Defense Directive 3000.09 which is the current US policy on autonomous weapons. It covers areas such as Lethal autonomous weapons and weapons decision-making.
Geometric primitive
In vector computer graphics, CAD systems, and geographic information systems, a geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segments, which were all that early vector graphics systems had. In constructive solid geometry, primitives are simple geometric shapes such as a cube, cylinder, sphere, cone, pyramid, torus. Modern 2D computer graphics systems may operate with primitives which are curves (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles). A common set of two-dimensional primitives includes lines, points, and polygons, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles (polygon triangulation). All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as Bézier curves, circles, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes. == Common primitives == The set of geometric primitives is based on the dimension of the region being represented: Point (0-dimensional), a single location with no height, width, or depth. Line or curve (1-dimensional), having length but no width, although a linear feature may curve through a higher-dimensional space. Planar surface or curved surface (2-dimensional), having length and width. Volumetric region or solid (3-dimensional), having length, width, and depth. In GIS, the terrain surface is often spoken of colloquially as "2 1/2 dimensional," because only the upper surface needs to be represented. Thus, elevation can be conceptualized as a scalar field property or function of two-dimensional space, affording it a number of data modeling efficiencies over true 3-dimensional objects. A shape of any of these dimensions greater than zero consists of an infinite number of distinct points. Because digital systems are finite, only a sample set of the points in a shape can be stored. Thus, vector data structures typically represent geometric primitives using a strategic sample, organized in structures that facilitate the software interpolating the remainder of the shape at the time of analysis or display, using the algorithms of Computational geometry. A Point is a single coordinate in a Cartesian coordinate system. Some data models allow for Multipoint features consisting of several disconnected points. A Polygonal chain or Polyline is an ordered list of points (termed vertices in this context). The software is expected to interpolate the intervening shape of the line between adjacent points in the list as a parametric curve, most commonly a straight line, but other types of curves are frequently available, including circular arcs, cubic splines, and Bézier curves. Some of these curves require additional points to be defined that are not on the line itself, but are used for parametric control. A Polygon is a polyline that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior. Some data models allow for a single feature to consist of multiple polylines, which could collectively connect to form a single closed boundary, could represent a set of disjoint regions (e.g., the state of Hawaii), or could represent a region with holes (e.g., a lake with an island). A Parametric shape is a standardized two-dimensional or three-dimensional shape defined by a minimal set of parameters, such as an ellipse defined by two points at its foci, or three points at its center, vertex, and co-vertex. A Polyhedron or Polygon mesh is a set of polygon faces in three-dimensional space that are connected at their edges to completely enclose a volumetric region. In some applications, closure may not be required or may be implied, such as modeling terrain. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior. A triangle mesh is a subtype of polyhedron in which all faces must be triangles, the only polygon that will always be planar, including the Triangulated irregular network (TIN) commonly used in GIS. A parametric mesh represents a three-dimensional surface by a connected set of parametric functions, similar to a spline or Bézier curve in two dimensions. The most common structure is the Non-uniform rational B-spline (NURBS), supported by most CAD and animation software. == Application in GIS == A wide variety of vector data structures and formats have been developed during the history of Geographic information systems, but they share a fundamental basis of storing a core set of geometric primitives to represent the location and extent of geographic phenomena. Locations of points are almost always measured within a standard Earth-based coordinate system, whether the spherical Geographic coordinate system (latitude/longitude), or a planar coordinate system, such as the Universal Transverse Mercator. They also share the need to store a set of attributes of each geographic feature alongside its shape; traditionally, this has been accomplished using the data models, data formats, and even software of relational databases. Early vector formats, such as POLYVRT, the ARC/INFO Coverage, and the Esri shapefile support a basic set of geometric primitives: points, polylines, and polygons, only in two dimensional space and the latter two with only straight line interpolation. TIN data structures for representing terrain surfaces as triangle meshes were also added. Since the mid 1990s, new formats have been developed that extend the range of available primitives, generally standardized by the Open Geospatial Consortium's Simple Features specification. Common geometric primitive extensions include: three-dimensional coordinates for points, lines, and polygons; a fourth "dimension" to represent a measured attribute or time; curved segments in lines and polygons; text annotation as a form of geometry; and polygon meshes for three-dimensional objects. Frequently, a representation of the shape of a real-world phenomenon may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines). == In 3D modelling == In CAD software or 3D modelling, the interface may present the user with the ability to create primitives which may be further modified by edits. For example, in the practice of box modelling the user will start with a cuboid, then use extrusion and other operations to create the model. In this use the primitive is just a convenient starting point, rather than the fundamental unit of modelling. A 3D package may also include a list of extended primitives which are more complex shapes that come with the package. For example, a teapot is listed as a primitive in 3D Studio Max. == In graphics hardware == Various graphics accelerators exist with hardware acceleration for rendering specific primitives such as lines or triangles, frequently with texture mapping and shaders. Modern 3D accelerators typically accept sequences of triangles as triangle strips.
GITEX Vietnam
GITEX AI Vietnam is an upcoming technology exhibition and conference scheduled to take place in Hanoi, Vietnam, on 1–2 October 2026. The event is organised by KAOUN International in partnership with the Dubai World Trade Centre and the Vietnam National Innovation Center (NIC). It is part of the global GITEX network of technology exhibitions. The event supported by Vietnam's Ministry of Finance and Ministry of Science and Technology. == Activity == GITEX AI Vietnam was announced in 2025 as part of GITEX's expansion into Southeast Asia. Its launch coincides with Vietnam's National Innovation Week. Media reports linked to the announcement projected Vietnam's digital economy could reach around US$200 billion by 2030. The event includes exhibitions, conferences, and networking sessions. Co-located platforms include AI Everything Vietnam, Startups North Star Vietnam, GITEX Cyber Valley Vietnam, and FDX Vietnam. Expected participants include policymakers, technology companies, startups, investors, and researchers.
AI Seoul Summit 2024
The AI Seoul Summit 2024 was an event in May 2024 co-hosted by the South Korean and British governments. The Seoul Declaration was adopted to address artificial intelligence technology and related challenges and opportunities. == Background == The AI Seoul Summit is the second such meeting following the AI Safety Summit held in the United Kingdom in November 2023. In the Bletchley Declaration, the participating countries agreed to prioritize identifying AI safety risks of shared concern, a shared concern, but at the Seoul Summit, the leaders also recognized the importance of AI. == Notable attendees == The summit was attended by the leaders of Group of Seven countries, including the United States, Canada, France, and Germany, South Korea, Singapore and Australia, representatives of the United Nations, the Organisation for Economic Co-operation and Development, and the European Union. Also in attendance were representatives of global companies such as Tesla CEO Elon Musk, Samsung Electronics Chairman Lee Jae-yong, ChatGPT maker OpenAI, Google, Microsoft, Meta, and South Korea's top portal operator Naver. == Topics == === South Korean AI safety center === "South Korea will push forward with the establishment of an AI safety research center in Korea and join a network to boost the global safety of AI." Minister of Science, Lee Jong-ho said that South Korea was planning to open an AI Safety Institute in 2024. He also expressed his intention to strengthen cooperation for the development of international standards. === Seoul Declaration for Safe, Innovative and Inclusive AI === The Seoul Declaration was adopted at the summit by leaders representing the EU, the US, the UK, Australia, Canada, Germany, France, Italy, Japan, South Korea, and Singapore. The declaration is a commitment to foster international cooperation to help develop AI governance frameworks that are interoperable between countries, partly by integrating the Hiroshima Process International Code of Conduct for Organizations Developing Advanced AI Systems. It advocates for the development of human-centric AI in collaboration with the private sector, academia, and civil society. === Seoul Ministerial Statement for advancing AI safety === At the ministerial meeting of the summit, the Seoul Ministerial Statement, a joint statement calling for the improvement of the safety, innovation, and inclusivity of AI technologies, was adopted by ministers from Australia, Canada, Chile, France, Germany, India, Indonesia, Israel, Italy, Japan, Kenya, Mexico, the Netherlands, Nigeria, New Zealand, the Philippines, South Korea, Rwanda, Saudi Arabia, Singapore, Spain, Switzerland, Turkey, Ukraine, the United Arab Emirates, the UK, and the US, as well as an EU representative. It aims to develop low-power chips as the AI industry rapidly expands and massive consumption is expected. == Global AI Summit series ==
Thompson sampling
Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.
Stability (learning theory)
Stability, also known as algorithmic stability, is a notion in computational learning theory of how a machine learning algorithm output is changed with small perturbations to its inputs. A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly. For instance, consider a machine learning algorithm that is being trained to recognize handwritten letters of the alphabet, using 1000 examples of handwritten letters and their labels ("A" to "Z") as a training set. One way to modify this training set is to leave out an example, so that only 999 examples of handwritten letters and their labels are available. A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type of information being learned. The study of stability gained importance in computational learning theory in the 2000s when it was shown to have a connection with generalization. It was shown that for large classes of learning algorithms, notably empirical risk minimization algorithms, certain types of stability ensure good generalization. == History == A central goal in designing a machine learning system is to guarantee that the learning algorithm will generalize, or perform accurately on new examples after being trained on a finite number of them. In the 1990s, milestones were reached in obtaining generalization bounds for supervised learning algorithms. The technique historically used to prove generalization was to show that an algorithm was consistent, using the uniform convergence properties of empirical quantities to their means. This technique was used to obtain generalization bounds for the large class of empirical risk minimization (ERM) algorithms. An ERM algorithm is one that selects a solution from a hypothesis space H {\displaystyle H} in such a way to minimize the empirical error on a training set S {\displaystyle S} . A general result, proved by Vladimir Vapnik for an ERM binary classification algorithms, is that for any target function and input distribution, any hypothesis space H {\displaystyle H} with VC-dimension d {\displaystyle d} , and n {\displaystyle n} training examples, the algorithm is consistent and will produce a training error that is at most O ( d n ) {\displaystyle O\left({\sqrt {\frac {d}{n}}}\right)} (plus logarithmic factors) from the true error. The result was later extended to almost-ERM algorithms with function classes that do not have unique minimizers. Vapnik's work, using what became known as VC theory, established a relationship between generalization of a learning algorithm and properties of the hypothesis space H {\displaystyle H} of functions being learned. However, these results could not be applied to algorithms with hypothesis spaces of unbounded VC-dimension. Put another way, these results could not be applied when the information being learned had a complexity that was too large to measure. Some of the simplest machine learning algorithms—for instance, for regression—have hypothesis spaces with unbounded VC-dimension. Another example is language learning algorithms that can produce sentences of arbitrary length. Stability analysis was developed in the 2000s for computational learning theory and is an alternative method for obtaining generalization bounds. The stability of an algorithm is a property of the learning process, rather than a direct property of the hypothesis space H {\displaystyle H} , and it can be assessed in algorithms that have hypothesis spaces with unbounded or undefined VC-dimension such as nearest neighbor. A stable learning algorithm is one for which the learned function does not change much when the training set is slightly modified, for instance by leaving out an example. A measure of Leave one out error is used in a Cross Validation Leave One Out (CVloo) algorithm to evaluate a learning algorithm's stability with respect to the loss function. As such, stability analysis is the application of sensitivity analysis to machine learning. == Summary of classic results == Early 1900s - Stability in learning theory was earliest described in terms of continuity of the learning map L {\displaystyle L} , traced to Andrey Nikolayevich Tikhonov. 1979 - Devroye and Wagner observed that the leave-one-out behavior of an algorithm is related to its sensitivity to small changes in the sample. 1999 - Kearns and Ron discovered a connection between finite VC-dimension and stability. 2002 - In a landmark paper, Bousquet and Elisseeff proposed the notion of uniform hypothesis stability of a learning algorithm and showed that it implies low generalization error. Uniform hypothesis stability, however, is a strong condition that does not apply to large classes of algorithms, including ERM algorithms with a hypothesis space of only two functions. 2002 - Kutin and Niyogi extended Bousquet and Elisseeff's results by providing generalization bounds for several weaker forms of stability which they called almost-everywhere stability. Furthermore, they took an initial step in establishing the relationship between stability and consistency in ERM algorithms in the Probably Approximately Correct (PAC) setting. 2004 - Poggio et al. proved a general relationship between stability and ERM consistency. They proposed a statistical form of leave-one-out-stability which they called CVEEEloo stability, and showed that it is a) sufficient for generalization in bounded loss classes, and b) necessary and sufficient for consistency (and thus generalization) of ERM algorithms for certain loss functions such as the square loss, the absolute value and the binary classification loss. 2010 - Shalev Shwartz et al. noticed problems with the original results of Vapnik due to the complex relations between hypothesis space and loss class. They discuss stability notions that capture different loss classes and different types of learning, supervised and unsupervised. 2016 - Moritz Hardt et al. proved stability of gradient descent given certain assumption on the hypothesis and number of times each instance is used to update the model. == Preliminary definitions == We define several terms related to learning algorithms training sets, so that we can then define stability in multiple ways and present theorems from the field. A machine learning algorithm, also known as a learning map L {\displaystyle L} , maps a training data set, which is a set of labeled examples ( x , y ) {\displaystyle (x,y)} , onto a function f {\displaystyle f} from X {\displaystyle X} to Y {\displaystyle Y} , where X {\displaystyle X} and Y {\displaystyle Y} are in the same space of the training examples. The functions f {\displaystyle f} are selected from a hypothesis space of functions called H {\displaystyle H} . The training set from which an algorithm learns is defined as S = { z 1 = ( x 1 , y 1 ) , . . , z m = ( x m , y m ) } {\displaystyle S=\{z_{1}=(x_{1},\ y_{1})\ ,..,\ z_{m}=(x_{m},\ y_{m})\}} and is of size m {\displaystyle m} in Z = X × Y {\displaystyle Z=X\times Y} drawn i.i.d. from an unknown distribution D. Thus, the learning map L {\displaystyle L} is defined as a mapping from Z m {\displaystyle Z_{m}} into H {\displaystyle H} , mapping a training set S {\displaystyle S} onto a function f S {\displaystyle f_{S}} from X {\displaystyle X} to Y {\displaystyle Y} . Here, we consider only deterministic algorithms where L {\displaystyle L} is symmetric with respect to S {\displaystyle S} , i.e. it does not depend on the order of the elements in the training set. Furthermore, we assume that all functions are measurable and all sets are countable. The loss V {\displaystyle V} of a hypothesis f {\displaystyle f} with respect to an example z = ( x , y ) {\displaystyle z=(x,y)} is then defined as V ( f , z ) = V ( f ( x ) , y ) {\displaystyle V(f,z)=V(f(x),y)} . The empirical error of f {\displaystyle f} is I S [ f ] = 1 n ∑ V ( f , z i ) {\displaystyle I_{S}[f]={\frac {1}{n}}\sum V(f,z_{i})} . The true error of f {\displaystyle f} is I [ f ] = E z V ( f , z ) {\displaystyle I[f]=\mathbb {E} _{z}V(f,z)} Given a training set S of size m, we will build, for all i = 1....,m, modified training sets as follows: By removing the i-th element S | i = { z 1 , . . . , z i − 1 , z i + 1 , . . . , z m } {\displaystyle S^{|i}=\{z_{1},...,\ z_{i-1},\ z_{i+1},...,\ z_{m}\}} By replacing the i-th element S i = { z 1 , . . . , z i − 1 , z i ′ , z i + 1 , . . . , z m } {\displaystyle S^{i}=\{z_{1},...,\ z_{i-1},\ z_{i}',\ z_{i+1},...,\ z_{m}\}} == Definitions of stability == === Hypothesis Stability === An algorithm L {\displaystyle L} has hypothesis stability β with respect to the loss function V if the following holds: ∀ i ∈ { 1 , . . . , m } , E S , z [ | V ( f S , z ) − V ( f S |
Autonomic computing
Autonomic computing (AC) is distributed computing resources with self-managing characteristics, adapting to unpredictable changes while hiding intrinsic complexity to operators and users. Initiated by IBM in 2001, this initiative ultimately aimed to develop computer systems capable of self-management, to overcome the rapidly growing complexity of computing systems management, and to reduce the barrier that complexity poses to further growth. == Description == The AC system concept is designed to make adaptive decisions, using high-level policies. It will constantly check and optimize its status and automatically adapt itself to changing conditions. An autonomic computing framework is composed of autonomic components (AC) interacting with each other. An AC can be modeled in terms of two main control schemes (local and global) with sensors (for self-monitoring), effectors (for self-adjustment), knowledge and planner/adapter for exploiting policies based on self- and environment awareness. This architecture is sometimes referred to as Monitor-Analyze-Plan-Execute (MAPE). Driven by such vision, a variety of architectural frameworks based on "self-regulating" autonomic components has been recently proposed. A similar trend has recently characterized significant research in the area of multi-agent systems. However, most of these approaches are typically conceived with centralized or cluster-based server architectures in mind and mostly address the need of reducing management costs rather than the need of enabling complex software systems or providing innovative services. Some autonomic systems involve mobile agents interacting via loosely coupled communication mechanisms. Autonomy-oriented computation is a paradigm proposed by Jiming Liu in 2001 that uses artificial systems imitating social animals' collective behaviours to solve difficult computational problems. For example, ant colony optimization could be studied in this paradigm. == Problem of growing complexity == Forecasts suggested that the computing devices in use would grow at 38% per year and the average complexity of each device was increasing. This volume and complexity was managed by highly skilled humans; but the demand for skilled IT personnel was already outstripping supply, with labour costs exceeding equipment costs by a ratio of up to 18:1. Computing systems have brought great benefits of speed and automation but there is now an overwhelming economic need to automate their maintenance. In a 2003 IEEE Computer article, Kephart and Chess warn that the dream of interconnectivity of computing systems and devices could become the "nightmare of pervasive computing" in which architects are unable to anticipate, design and maintain the complexity of interactions. They state the essence of autonomic computing is system self-management, freeing administrators from low-level task management while delivering better system behavior. A general problem of modern distributed computing systems is that their complexity, and in particular the complexity of their management, is becoming a significant limiting factor in their further development. Large companies and institutions are employing large-scale computer networks for communication and computation. The distributed applications running on these computer networks are diverse and deal with multiple tasks, ranging from internal control processes to presenting web content to customer support. Additionally, mobile computing is pervading these networks at an increasing speed: employees need to communicate with their companies while they are not in their office. They do so by using laptops, personal digital assistants, or mobile phones with diverse forms of wireless technologies to access their companies' data. This creates an enormous complexity in the overall computer network which is hard to control manually by human operators. Manual control is time-consuming, expensive, and error-prone. The manual effort needed to control a growing networked computer-system tends to increase quickly. 80% of such problems in infrastructure happen at the client specific application and database layer. Most 'autonomic' service providers guarantee only up to the basic plumbing layer (power, hardware, operating system, network and basic database parameters). == Characteristics of autonomic systems == A possible solution could be to enable modern, networked computing systems to manage themselves without direct human intervention. The Autonomic Computing Initiative (ACI) aims at providing the foundation for autonomic systems. It is inspired by the autonomic nervous system of the human body. This nervous system controls important bodily functions (e.g. respiration, heart rate, and blood pressure) without any conscious intervention. In a self-managing autonomic system, the human operator takes on a new role: instead of controlling the system directly, he/she defines general policies and rules that guide the self-management process. For this process, IBM defined the following four types of property referred to as self-star (also called self-, self-x, or auto-) properties. Self-configuration: Automatic configuration of components; Self-healing: Automatic discovery, and correction of faults; Self-optimization: Automatic monitoring and control of resources to ensure the optimal functioning with respect to the defined requirements; Self-protection: Proactive identification and protection from arbitrary attacks. Others such as Poslad and Nami and Sharifi have expanded on the set of self-star as follows: Self-regulation: A system that operates to maintain some parameter, e.g., Quality of service, within a reset range without external control; Self-learning: Systems use machine learning techniques such as unsupervised learning which does not require external control; Self-awareness (also called Self-inspection and Self-decision): System must know itself. It must know the extent of its own resources and the resources it links to. A system must be aware of its internal components and external links in order to control and manage them; Self-organization: System structure driven by physics-type models without explicit pressure or involvement from outside the system; Self-creation (also called Self-assembly, Self-replication): System driven by ecological and social type models without explicit pressure or involvement from outside the system. A system's members are self-motivated and self-driven, generating complexity and order in a creative response to a continuously changing strategic demand; Self-management (also called self-governance): A system that manages itself without external intervention. What is being managed can vary dependent on the system and application. Self -management also refers to a set of self-star processes such as autonomic computing rather than a single self-star process; Self-description (also called self-explanation or Self-representation): A system explains itself. It is capable of being understood (by humans) without further explanation. IBM has set forth eight conditions that define an autonomic system: The system must know itself in terms of what resources it has access to, what its capabilities and limitations are and how and why it is connected to other systems; be able to automatically configure and reconfigure itself depending on the changing computing environment; be able to optimize its performance to ensure the most efficient computing process; be able to work around encountered problems by either repairing itself or routing functions away from the trouble; detect, identify and protect itself against various types of attacks to maintain overall system security and integrity; adapt to its environment as it changes, interacting with neighboring systems and establishing communication protocols; rely on open standards and cannot exist in a proprietary environment; anticipate the demand on its resources while staying transparent to users. Even though the purpose and thus the behaviour of autonomic systems vary from system to system, every autonomic system should be able to exhibit a minimum set of properties to achieve its purpose: Automatic: This essentially means being able to self-control its internal functions and operations. As such, an autonomic system must be self-contained and able to start-up and operate without any manual intervention or external help. Again, the knowledge required to bootstrap the system (Know-how) must be inherent to the system. Adaptive: An autonomic system must be able to change its operation (i.e., its configuration, state and functions). This will allow the system to cope with temporal and spatial changes in its operational context either long term (environment customisation/optimisation) or short term (exceptional conditions such as malicious attacks, faults, etc.). Aware: An autonomic system must be able to monitor (sense) its operational context as well as its internal state in order to be able to asses