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78
Reinforcement learning: a survey
 Journal of Artificial Intelligence Research
, 1996
"... This paper surveys the field of reinforcement learning from a computerscience perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem ..."
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Cited by 1298 (23 self)
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This paper surveys the field of reinforcement learning from a computerscience perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trialanderror interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word "reinforcement." The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.
Markov games as a framework for multiagent reinforcement learning
 IN PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON MACHINE LEARNING
, 1994
"... In the Markov decision process (MDP) formalization of reinforcement learning, a single adaptive agent interacts with an environment defined by a probabilistic transition function. In this solipsistic view, secondary agents can only be part of the environment and are therefore fixed in their behavior ..."
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Cited by 500 (10 self)
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In the Markov decision process (MDP) formalization of reinforcement learning, a single adaptive agent interacts with an environment defined by a probabilistic transition function. In this solipsistic view, secondary agents can only be part of the environment and are therefore fixed in their behavior. The framework of Markov games allows us to widen this view to include multiple adaptive agents with interacting or competing goals. This paper considers a step in this direction in which exactly two agents with diametrically opposed goals share an environment. It describes a Qlearninglike algorithm for finding optimal policies and demonstrates its application to a simple twoplayer game in which the optimal policy is probabilistic.
DecisionTheoretic Planning: Structural Assumptions and Computational Leverage
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1999
"... Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives ..."
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Cited by 417 (4 self)
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Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory. This paper presents an overview and synthesis of MDPrelated methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to de...
Algorithms for Sequential Decision Making
, 1996
"... Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one ..."
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Cited by 175 (8 self)
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Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one of a finite set of actions, "should" is maximize a longrun measure of reward, and "I" is an automated planning or learning system (agent). In particular,
Recent advances in hierarchical reinforcement learning
, 2003
"... A preliminary unedited version of this paper was incorrectly published as part of Volume ..."
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Cited by 161 (23 self)
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A preliminary unedited version of this paper was incorrectly published as part of Volume
Reinforcement Learning Algorithm for Partially Observable Markov Decision Problems
 Advances in Neural Information Processing Systems 7
, 1995
"... Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable ..."
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Cited by 151 (7 self)
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Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of nonMarkov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a MonteCarlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuouseven for a discrete action spaceour algorith...
Learning Without StateEstimation in Partially Observable Markovian Decision Processes
 In Proceedings of the Eleventh International Conference on Machine Learning
, 1994
"... Reinforcement learning (RL) algorithms provide a sound theoretical basis for building learning control architectures for embedded agents. Unfortunately all of the theory and much of the practice (see Barto et al., 1983, for an exception) of RL is limited to Markovian decision processes (MDPs). Many ..."
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Cited by 128 (5 self)
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Reinforcement learning (RL) algorithms provide a sound theoretical basis for building learning control architectures for embedded agents. Unfortunately all of the theory and much of the practice (see Barto et al., 1983, for an exception) of RL is limited to Markovian decision processes (MDPs). Many realworld decision tasks, however, are inherently nonMarkovian, i.e., the state of the environment is only incompletely known to the learning agent. In this paper we consider only partially observable MDPs (POMDPs), a useful class of nonMarkovian decision processes. Most previous approaches to such problems have combined computationally expensive stateestimation techniques with learning control. This paper investigates learning in POMDPs without resorting to any form of state estimation. We present results about what TD(0) and Qlearning will do when applied to POMDPs. It is shown that the conventional discounted RL framework is inadequate to deal with POMDPs. Finally we develop a new fr...
MachineLearning Research  Four Current Directions
"... Machine Learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up super ..."
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Cited by 114 (1 self)
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Machine Learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up supervised learning algorithms, (c) reinforcement learning, and (d) learning complex stochastic models.
ZCS: A zeroth level classifier system
 Evolutionary Computation
, 1994
"... A basic classifier system, ZCS, is presented that keeps much of Holland’s original framework but simplifies it to increase understandability and performance. ZCS’s relation to Qlearning is brought out, and their performances compared in environments of two difficulty levels. Extensions to ZCS are p ..."
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Cited by 105 (7 self)
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A basic classifier system, ZCS, is presented that keeps much of Holland’s original framework but simplifies it to increase understandability and performance. ZCS’s relation to Qlearning is brought out, and their performances compared in environments of two difficulty levels. Extensions to ZCS are proposed for temporary memory, better action selection, more efficient use of the genetic algorithm, and more general classifier representation.
Average Reward Reinforcement Learning: Foundations, Algorithms, and Empirical Results
, 1996
"... This paper presents a detailed study of average reward reinforcement learning, an undiscounted optimality framework that is more appropriate for cyclical tasks than the much better studied discounted framework. A wide spectrum of average reward algorithms are described, ranging from synchronous dyna ..."
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Cited by 99 (12 self)
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This paper presents a detailed study of average reward reinforcement learning, an undiscounted optimality framework that is more appropriate for cyclical tasks than the much better studied discounted framework. A wide spectrum of average reward algorithms are described, ranging from synchronous dynamic programming methods to several (provably convergent) asynchronous algorithms from optimal control and learning automata. A general sensitive discount optimality metric called ndiscountoptimality is introduced, and used to compare the various algorithms. The overview identifies a key similarity across several asynchronous algorithms that is crucial to their convergence, namely independent estimation of the average reward and the relative values. The overview also uncovers a surprising limitation shared by the different algorithms: while several algorithms can provably generate gainoptimal policies that maximize average reward, none of them can reliably filter these to produce biasoptimal (or Toptimal) policies that also maximize the finite reward to absorbing goal states. This paper also presents a detailed empirical study of Rlearning, an average reward reinforcement learning method, using two empirical testbeds: a stochastic grid world domain and a simulated robot environment. A detailed sensitivity analysis of Rlearning is carried out to test its dependence on learning rates and exploration levels. The results suggest that Rlearning is quite sensitive to exploration strategies, and can fall into suboptimal limit cycles. The performance of Rlearning is also compared with that of Qlearning, the best studied discounted RL method. Here, the results suggest that Rlearning can be finetuned to give better performance than Qlearning in both domains.