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Bandit Problem
In probability theory and machine learning, the multi-armed bandit problem (sometimes called the ''K''- or ''N''-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. This is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. The name comes from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each mach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Routing
Dynamic routing, also called adaptive routing, is a process where a router can forward data via a different route for a given destination based on the current conditions of the communication circuits within a system. The term is most commonly associated with data networking to describe the capability of a network to 'route around' damage, such as loss of a node or a connection between nodes, so long as other path choices are available. Dynamic routing allows as many routes as possible to remain valid in response to the change. Systems that do not implement dynamic routing are described as using static routing, where routes through a network are described by fixed paths. A change, such as the loss of a node, or loss of a connection between nodes, is not compensated for. This means that anything that wishes to take an affected path will either have to wait for the failure to be repaired before restarting its journey, or will have to fail to reach its destination and give up the journ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Softmax Function
The softmax function, also known as softargmax or normalized exponential function, converts a vector of real numbers into a probability distribution of possible outcomes. It is a generalization of the logistic function to multiple dimensions, and used in multinomial logistic regression. The softmax function is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom. Definition The softmax function takes as input a vector of real numbers, and normalizes it into a probability distribution consisting of probabilities proportional to the exponentials of the input numbers. That is, prior to applying softmax, some vector components could be negative, or greater than one; and might not sum to 1; but after applying softmax, each component will be in the interval (0, 1), and the components will add up to 1, so that they can be interpreted as probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. Specifics Greedy algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Katehakis
Michael N. Katehakis ( el, Μιχαήλ Ν. Κατεχάκης; born 1952) is a Professor of Management Science at Rutgers University. He is noted for his work in Markov decision process, Gittins index, the multi-armed bandit, Markov chains and other related fields. Early life Katehakis was born and grew up in Heraklion Greece. He received his BS degree from the School of Physics and Mathematics of the University of Athens – Greece, an M.A. degree in Statistics from the University of South Florida, an M.S.. degree in Mathematical Methods in Engineering and Operations Research and a Ph.D. degree in Operations Research from Columbia University. His dissertation advisor at Columbia was Cyrus Derman. While a graduate student at Columbia Katehakis worked developing mathematical simulation programs for the Two-rotor engine and the Tri-rotor engine projects under George Doundoulakis. Career After a member of technical staff position at Bell Laboratories, in 1981 he joined the Dep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References * External linksSIAM Journal on Computing on |
Asymptotic
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος (''asumptōtos'') which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve. There are three kinds of asymptotes: ''horizontal'', ''vertical'' and ''oblique''. For curves given by the graph of a function , horizontal asymptotes are horizontal lines that the graph of the function approaches as ''x'' tends to Vertical asymptotes are vertical lines near which the fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regret (decision Theory)
In decision theory, on making decisions under uncertainty—should information about the best course of action arrive ''after'' taking a fixed decision—the human emotional response of regret is often experienced, and can be measured as the value of difference between a made decision and the optimal decision. The theory of regret aversion or anticipated regret proposes that when facing a decision, individuals might ''anticipate'' regret and thus incorporate in their choice their desire to eliminate or reduce this possibility. Regret is a negative emotion with a powerful social and reputational component, and is central to how humans learn from experience and to the human psychology of risk aversion. Conscious anticipation of regret creates a feedback loop that transcends regret from the emotional realm—often modeled as mere human behavior—into the realm of the rational choice behavior that is modeled in decision theory. Description Regret theory is a model in theoretical eco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated between the Baltic and North seas to the north, and the Alps to the south; it covers an area of , with a population of almost 84 million within its 16 constituent states. Germany borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The nation's capital and most populous city is Berlin and its financial centre is Frankfurt; the largest urban area is the Ruhr. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity. A region named Germania was documented before AD 100. In 962, the Kingdom of Germany formed the bulk of the Holy Roman Empire. During the 16th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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