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Reinforcement Learning I: Introduction
, 1998
"... In which we try to give a basic intuitive sense of what reinforcement learning is and how it differs and relates to other fields, e.g., supervised learning and neural networks, genetic algorithms and artificial life, control theory. Intuitively, RL is trial and error (variation and selection, search ..."
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Cited by 5512 (123 self)
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In which we try to give a basic intuitive sense of what reinforcement learning is and how it differs and relates to other fields, e.g., supervised learning and neural networks, genetic algorithms and artificial life, control theory. Intuitively, RL is trial and error (variation and selection, search) plus learning (association, memory). We argue that RL is the only field that seriously addresses the special features of the problem of learning from interaction to achieve longterm goals.
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 1693 (27 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.
Planning and acting in partially observable stochastic domains
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable mdps (pomdps). We then outline a novel algorithm ..."
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Cited by 1089 (42 self)
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In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable mdps (pomdps). We then outline a novel algorithm for solving pomdps offline and show how, in some cases, a finitememory controller can be extracted from the solution to a pomdp. We conclude with a discussion of how our approach relates to previous work, the complexity of finding exact solutions to pomdps, and of some possibilities for finding approximate solutions.
Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition
 Journal of Artificial Intelligence Research
, 2000
"... This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. Th ..."
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Cited by 440 (6 self)
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This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semanticsas a subroutine hierarchyand a declarative semanticsas a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consisten...
AntNet: Distributed stigmergetic control for communications networks
 Journal of Artificial Intelligence Research
, 1998
"... This paper introduces AntNet, a novel approach to the adaptive learning of routing tables in communications networks. AntNet is a distributed, mobile agents based Monte Carlo system that was inspired by recent work on the ant colony metaphor for solving optimization problems. AntNet's agents co ..."
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Cited by 333 (29 self)
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This paper introduces AntNet, a novel approach to the adaptive learning of routing tables in communications networks. AntNet is a distributed, mobile agents based Monte Carlo system that was inspired by recent work on the ant colony metaphor for solving optimization problems. AntNet's agents concurrently explore the network and exchange collected information. The communication among the agents is indirect and asynchronous, mediated by the network itself. This form of communication is typical of social insects and is called stigmergy. We compare our algorithm with six stateoftheart routing algorithms coming from the telecommunications and machine learning elds. The algorithms' performance is evaluated over a set of realistic testbeds. We run many experiments over real and arti cial IP datagram networks with increasing number of nodes and under several paradigmatic spatial and temporal tra c distributions. Results are very encouraging. AntNet showed superior performance under all the experimental conditions with respect to its competitors. We analyze the main characteristics of the algorithm and try to explain the reasons for its superiority. 1.
An analysis of temporaldifference learning with function approximation
 IEEE Transactions on Automatic Control
, 1997
"... We discuss the temporaldifference learning algorithm, as applied to approximating the costtogo function of an infinitehorizon discounted Markov chain. The algorithm weanalyze updates parameters of a linear function approximator online, duringasingle endless trajectory of an irreducible aperiodi ..."
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Cited by 314 (8 self)
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We discuss the temporaldifference learning algorithm, as applied to approximating the costtogo function of an infinitehorizon discounted Markov chain. The algorithm weanalyze updates parameters of a linear function approximator online, duringasingle endless trajectory of an irreducible aperiodic Markov chain with a finite or infinite state space. We present a proof of convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. Furthermore, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporaldifference learning. In addition to proving new and stronger positive results than those previously available, we identify the significance of online updating and potential hazards associated with the use of nonlinear function approximators. First, we prove that divergence may occur when updates are not based on trajectories of the Markov chain. This fact reconciles positive and negative results that have been discussed in the literature, regarding the soundness of temporaldifference learning. Second, we present anexample illustrating the possibility of divergence when temporaldifference learning is used in the presence of a nonlinear function approximator.
ActorCritic Algorithms
 SIAM JOURNAL ON CONTROL AND OPTIMIZATION
, 2001
"... In this paper, we propose and analyze a class of actorcritic algorithms. These are twotimescale algorithms in which the critic uses temporal difference (TD) learning with a linearly parameterized approximation architecture, and the actor is updated in an approximate gradient direction based on in ..."
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Cited by 245 (1 self)
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In this paper, we propose and analyze a class of actorcritic algorithms. These are twotimescale algorithms in which the critic uses temporal difference (TD) learning with a linearly parameterized approximation architecture, and the actor is updated in an approximate gradient direction based on information provided by the critic. We show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor. We study actorcritic algorithms for Markov decision processes with general state and action spaces. We state and prove two results regarding their convergence.
The linear programming approach to approximate dynamic programming
 Operations Research
, 2001
"... The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear ..."
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Cited by 227 (17 self)
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The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear combination of preselected basis functions to the dynamic programming costtogo function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and “staterelevance weights ” that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology. (Dynamic programming/optimal control: approximations/largescale problems. Queues, algorithms: control of queueing networks.)
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 ..."
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Cited by 213 (9 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,
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 188 (21 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.