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213
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 1095 (38 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.
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 515 (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...
Stochastic Dynamic Programming with Factored Representations
, 1997
"... Markov decision processes(MDPs) have proven to be popular models for decisiontheoretic planning, but standard dynamic programming algorithms for solving MDPs rely on explicit, statebased specifications and computations. To alleviate the combinatorial problems associated with such methods, we prop ..."
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Cited by 189 (10 self)
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Markov decision processes(MDPs) have proven to be popular models for decisiontheoretic planning, but standard dynamic programming algorithms for solving MDPs rely on explicit, statebased specifications and computations. To alleviate the combinatorial problems associated with such methods, we propose new representational and computational techniques for MDPs that exploit certain types of problem structure. We use dynamic Bayesian networks (with decision trees representing the local families of conditional probability distributions) to represent stochastic actions in an MDP, together with a decisiontree representation of rewards. Based on this representation, we develop versions of standard dynamic programming algorithms that directly manipulate decisiontree representations of policies and value functions. This generally obviates the need for statebystate computation, aggregating states at the leaves of these trees and requiring computations only for each aggregate state. The key to these algorithms is a decisiontheoretic generalization of classic regression analysis, in which we determine the features relevant to predicting expected value. We demonstrate the method empirically on several planning problems,
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 187 (18 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.
EXACT AND APPROXIMATE ALGORITHMS FOR PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES
, 1998
"... Automated sequential decision making is crucial in many contexts. In the face of uncertainty, this task becomes even more important, though at the same time, computing optimal decision policies becomes more complex. The more sources of uncertainty there are, the harder the problem becomes to solve. ..."
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Cited by 186 (2 self)
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Automated sequential decision making is crucial in many contexts. In the face of uncertainty, this task becomes even more important, though at the same time, computing optimal decision policies becomes more complex. The more sources of uncertainty there are, the harder the problem becomes to solve. In this work, we look at sequential decision making in environments where the actions have probabilistic outcomes and in which the system state is only partially observable. We focus on using a model called a partially observable Markov decision process (POMDP) and explore algorithms which address computing both optimal and approximate policies for use in controlling processes that are modeled using POMDPs. Although solving for the optimal policy is PSPACEcomplete (or worse), the study and improvements of exact algorithms lends insight into the optimal solution structure as well as providing a basis for approximate solutions. We present some improvements, analysis and empirical comparisons for some existing and some novel approaches for computing the optimal POMDP policy exactly. Since it is also hard (NPcomplete or worse) to derive close approximations to the optimal solution for POMDPs, we consider a number of approaches for deriving policies that yield suboptimal control and empirically explore their performance on a range of problems. These approaches
Valuefunction approximations for partially observable Markov decision processes
 Journal of Artificial Intelligence Research
, 2000
"... Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advanta ..."
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Cited by 167 (1 self)
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Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advantage of POMDPs, however, comes at a price — exact methods for solving them are computationally very expensive and thus applicable in practice only to very simple problems. We focus on efficient approximation (heuristic) methods that attempt to alleviate the computational problem and trade off accuracy for speed. We have two objectives here. First, we survey various approximation methods, analyze their properties and relations and provide some new insights into their differences. Second, we present a number of new approximation methods and novel refinements of existing techniques. The theoretical results are supported by experiments on a problem from the agent navigation domain. 1.
Convergence Results for SingleStep OnPolicy ReinforcementLearning Algorithms
 MACHINE LEARNING
, 1998
"... An important application of reinforcement learning (RL) is to finitestate control problems and one of the most difficult problems in learning for control is balancing the exploration/exploitation tradeoff. Existing theoretical results for RL give very little guidance on reasonable ways to perform e ..."
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Cited by 154 (7 self)
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An important application of reinforcement learning (RL) is to finitestate control problems and one of the most difficult problems in learning for control is balancing the exploration/exploitation tradeoff. Existing theoretical results for RL give very little guidance on reasonable ways to perform exploration. In this paper, we examine the convergence of singlestep onpolicy RL algorithms for control. Onpolicy algorithms cannot separate exploration from learning and therefore must confront the exploration problem directly. We prove convergence results for several related onpolicy algorithms with both decaying exploration and persistent exploration. We also provide examples of exploration strategies that can be followed during learning that result in convergence to both optimal values and optimal policies.
Hierarchical Control and Learning for Markov Decision Processes
, 1998
"... This dissertation investigates the use of hierarchy and problem decomposition as a means of solving large, stochastic, sequential decision problems. These problems are framed as Markov decision problems (MDPs). The new technical content of this dissertation begins with a discussion of the concept o ..."
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Cited by 122 (2 self)
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This dissertation investigates the use of hierarchy and problem decomposition as a means of solving large, stochastic, sequential decision problems. These problems are framed as Markov decision problems (MDPs). The new technical content of this dissertation begins with a discussion of the concept of temporal abstraction. Temporal abstraction is shown to be equivalent to the transformation of a policy defined over a region of an MDP to an action in a semiMarkov decision problem (SMDP). Several algorithms are presented for performing this transformation efficiently. This dissertation introduces the HAM method for generating hierarchical, temporally abstract actions. This method permits the partial specification of abstract actions in a way that corresponds to an abstract plan or strategy. Abstr...
CoEvolution in the Successful Learning of Backgammon Strategy
 Machine Learning
, 1998
"... Following Tesauro's work on TDGammon, we used a 4000 parameter feedforward neural network to develop a competitive backgammon evaluation function. Play proceeds by a roll of the dice, application of the network to all legal moves, and choosing the move with the highest evaluation. However, no ..."
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Cited by 119 (24 self)
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Following Tesauro's work on TDGammon, we used a 4000 parameter feedforward neural network to develop a competitive backgammon evaluation function. Play proceeds by a roll of the dice, application of the network to all legal moves, and choosing the move with the highest evaluation. However, no backpropagation, reinforcement or temporal difference learning methods were employed. Instead we apply simple hillclimbing in a relative fitness environment. We start with an initial champion of all zero weights and proceed simply by playing the current champion network against a slightly mutated challenger and changing weights if the challenger wins. Surprisingly, this worked rather well. We investigate how the peculiar dynamics of this domain enabled a previously discarded weak method to succeed, by preventing suboptimal equilibria in a "metagame" of selflearning. Keywords: coevolution, backgammon, reinforcement, temporal difference learning, selflearning Running Head: COEVOLUTIONARY LEA...
Autonomous Helicopter Control using Reinforcement Learning Policy Search Methods
 In International Conference on Robotics and Automation
, 2001
"... Many control problems in the robotics field can be cast as Partially Observed Markovian Decision Problems (POMDPs), an optimal control formalism. Finding optimal solutions to such problems in general, however is known to be intractable. It has often been observed that in practice, simple structured ..."
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Cited by 118 (1 self)
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Many control problems in the robotics field can be cast as Partially Observed Markovian Decision Problems (POMDPs), an optimal control formalism. Finding optimal solutions to such problems in general, however is known to be intractable. It has often been observed that in practice, simple structured controllers suffice for good suboptimal control, and recent research in the artificial intelligence community has focused on policy search methods as techniques for finding suboptimal controllers when such structured controllers do exist. Traditional modelbased reinforcement learning algorithms make a certainty equivalence assumption on their learned models and calculate optimal policies for a maximumlikelihood Markovian model. In this work, we consider algorithms that evaluate and synthesize controllers under distributions of Markovian models. Previous work has demonstrated that algorithms that maximize mean reward with respect to model uncertainty leads to safer and more robust controll...