Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

This book introduces multiagent planning under uncertainty as formalized by decentralized partially observable Markov decision processes (Dec-POMDPs). The intended audience is researchers and graduate students working in the fields of artificial intelligence related to sequential decision making: reinforcement learning, decision-theoretic planning for single agents, classical multiagent planning, decentralized control, and operations research.

A Concise Introduction to Decentralized POMDPs

In recent years there have been great strides in artificial intelligence (AI), with games often serving as challenge problems, benchmarks, and milestones for progress. Poker has served for decades as such a challenge problem. Past successes in such benchmarks, including poker, have been limited to two-player games. However, poker in particular is traditionally played with more than two players. Multiplayer games present fundamental additional issues beyond those in two-player games, and multiplayer poker is a recognized AI milestone. In this paper we present Pluribus, an AI that we show is stronger than top human professionals in six-player no-limit Texas hold'em poker, the most popular form of poker played by humans.

https://science.sciencemag.org/content/sci/365/6456/885.full.pdf

Superhuman AI for multiplayer poker

Preface (R.J. Aumann, S. Hart). Strategic equilibrium (E. van Damme). Foundations of strategic equilibrium (J. Hillas, E. Kohlberg). Incomplete information (R.J. Aumann, A. Heifetz). Non-zero-sum two-person games (T.E.S. Raghavan). Computing equilibria for two-person games (B. von Stengel). Non-cooperative games with many players (M. Ali Khan, Y. Sun). Stochastic games (J-F. Mertens). Stochastic games: recent results (N. Vieille). Game theory and industrial organization (K. Bagwell, A. Wolinsky). Bargaining with incomplete information (L.M. Ausubel, P. Cramton, R.J. Deneckere). Inspection Games (R. Avenhaus, B.V. Stengel, S.Zamir). Economic history and game theory (A. Greif). The shapley value (E. Winter). Variations on the shapley value (D. Monderer, D. Samet). Values of non-transferable utility games (R. McLean). Values of games with infinitely many players (A. Neyman). Values of perfectly competitive economies (S. Hart). Some other economic applications of the value (J-F. Mertens). Strategic aspects of political systems (J. Banks). Game-theoretic analysis of legal rules and institutions (J-P. Benoit, L.A. Kornhauser). Implementation Theory (T. Palfrey). Game Theory and experimental Gaming (M. Shubik).

Handbook of game theory with economic applications

In the framework of fully cooperative multi-agent systems, independent (non-communicative) agents that learn by reinforcement must overcome several difficulties to manage to coordinate. This paper identifies several challenges responsible for the non-coordination of independent agents: Pareto-selection, non-stationarity, stochasticity, alter-exploration and shadowed equilibria. A selection of multi-agent domains is classified according to those challenges: matrix games, Boutilier's coordination game, predators pursuit domains and a special multi-state game. Moreover, the performance of a range of algorithms for independent reinforcement learners is evaluated empirically. Those algorithms are Q-learning variants: decentralized Q-learning, distributed Q-learning, hysteretic Q-learning, recursive frequency maximum Q-value and win-or-learn fast policy hill climbing. An overview of the learning algorithms' strengths and weaknesses against each challenge concludes the paper and can serve as a basis for choosing the appropriate algorithm for a new domain. Furthermore, the distilled challenges may assist in the design of new learning algorithms that overcome these problems and achieve higher performance in multi-agent applications.

/pdf/review-independent-reinforcement-learners-in-cooperative-2ofgpfaccu.pdf

Review: independent reinforcement learners in cooperative markov games: A survey regarding coordination problems

Q-learning in single-agent environments is known to converge in the limit given sufficient exploration. The same algorithm has been applied, with some success, in multi-agent environments, where traditional analysis techniques break down. Using established dynamical systems methods, we derive and study an idealization of Q-learning in 2-player 2-action repeated general-sum games. In particular, we address the discontinuous case of e-greedy exploration and use it as a proxy for value-based algorithms to highlight a contrast with existing results in policy search. Analogously to previous results for gradient ascent algorithms, we provide a complete catalog of the convergence behavior of the e-greedy Q-learning algorithm by introducing new subclasses of these games. We identify two subclasses of Prisoner's Dilemma-like games where the application of Q-learning with e-greedy exploration results in higher-than-Nash average payoffs for some initial conditions.

/pdf/classes-of-multiagent-q-learning-dynamics-with-epsilon-23pk9qha6n.pdf

Classes of Multiagent Q-learning Dynamics with epsilon-greedy Exploration

The field of multiagent decision making is extending its tools from classical game theory by embracing reinforcement learning, statistical analysis, and opponent modeling. For example, behavioral economists conclude from experimental results that people act according to levels of reasoning that form a "cognitive hierarchy" of strategies, rather than merely following the hyper-rational Nash equilibrium solution concept. This paper expands this model of the iterative reasoning process by widening the notion of a level within the hierarchy from one single strategy to a distribution over strategies, leading to a more general framework of multiagent decision making. It provides a measure of sophistication for strategies and can serve as a guide for designing good strategies for multiagent games, drawing it's main strength from predicting opponent strategies.We apply these lessons to the recently introduced Lemonade-stand Game, a simple setting that includes both collaborative and competitive elements, where an agent's score is critically dependent on its responsiveness to opponent behavior. The opening moves are significant to the end result and simple heuristics have achieved faster cooperation than intricate learning schemes. Using results from the past two real-world tournaments, we show how the submitted entries fit naturally into our model and explain why the top agents were successful.

/pdf/using-iterated-reasoning-to-predict-opponent-strategies-3tuiwzvawy.pdf

Using iterated reasoning to predict opponent strategies

Agent-based models are a popular way to explore the dynamics of human interactions, but rarely are these models based on empirical observations of actual human behavior. Here we exploit data collected in an experimental setting where over 150 human players played in a series of almost a hundred public goods games. First, we fit a series of deterministic models to the data, finding that a reasonably parsimonious model with just three parameters performs extremely well on the standard test of predicting average contributions. This same model, however, performs extremely poorly when predicting the full distribution of contributions, which is strongly bimodal. In response, we introduce and test a corresponding series of stochastic models, thus identifying a model that both predicts average contribution and also the full distribution. Finally, we deploy this model to explore hypotheses about regions of the parameter space outside of what was experimentally accessible. In particular, we investigate (a) whether a previous conclusion that network topology does not impact contribution levels holds for much larger networks than could be studied in a lab; (b) to what extent observed contributions depend on average network degree and variance in the degree distribution, and (c) the dependency of contributions on degree assortativity as well as the correlation between the generosity of players and the degree of the nodes to which they are assigned.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/w_s_w_EC_13.pdf

Empirical agent based models of cooperation in public goods games

In December 2009 and November 2010, the first and second Lemonade Stand game competitions were held. In each competition, 9 teams competed, from University of Southampton, University College London, Yahoo!, Rutgers, Carnegie Mellon, Brown, Princeton, et cetera. The competition, in the spirit of Axelrod's iterated prisoner's dilemma competition, which addressed whether or not you should cooperate, asks the questions, "how should you cooperate, and with whom?" The third competition (whose results will be announced at IJCAI 2011) is open for submissions until July 1st, 2011.

/pdf/the-lemonade-stand-game-competition-solving-unsolvable-games-2bkaexfkgp.pdf

The lemonade stand game competition: solving unsolvable games

This article presents a population-based cognitive hierarchy model that can be used to estimate the reasoning depth and sophistication of a collection of opponents' strategies from observed behavior in repeated games. This framework provides a compact representation of a distribution of complicated strategies by reducing them to a small number of parameters. This estimated population model can be then used to compute a best response to the observed distribution over these parameters. As such, it provides a basis for building improved strategies given a history of observations of the community of agents. Results show that this model predicts and explains the winning strategies in the recent 2011 Lemonade Stand Game competition, where eight algorithms were pitted against each other. The Lemonade Stand Game is a three-player game with simple rules that includes both cooperative and competitive elements. Despite its apparent simplicity, the fact that success depends crucially on what other players do gives rise to complex interaction patterns, which our new framework captures well.

/pdf/a-framework-for-modeling-population-strategies-by-depth-of-3h8bq15l4c.pdf

A framework for modeling population strategies by depth of reasoning

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