Results 1  10
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100
A sparse sampling algorithm for nearoptimal planning in large Markov decision processes
 Machine Learning
, 1999
"... An issue that is critical for the application of Markov decision processes (MDPs) to realistic problems is how the complexity of planning scales with the size of the MDP. In stochastic environments with very large or even innite state spaces, traditional planning and reinforcement learning algorith ..."
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Cited by 238 (7 self)
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An issue that is critical for the application of Markov decision processes (MDPs) to realistic problems is how the complexity of planning scales with the size of the MDP. In stochastic environments with very large or even innite state spaces, traditional planning and reinforcement learning algorithms are often inapplicable, since their running time typically scales linearly with the state space size in the worst case. In this paper we present a new algorithm that, given only a generative model (simulator) for an arbitrary MDP, performs nearoptimal planning with a running time that has no dependence on the number of states. Although the running time is exponential in the horizon time (which depends only on the discount factor and the desired degree of approximation to the optimal policy), our results establish for the rst time that there are no theoretical barriers to computing nearoptimal policies in arbitrarily large, unstructured MDPs. 1
Multiagent Planning with Factored MDPs
 In NIPS14
, 2001
"... We present a principled and efficient planning algorithm for cooperative multiagent dynamic systems. A striking feature of our method is that the coordination and communication between the agents is not imposed, but derived directly from the system dynamics and function approximation architecture ..."
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Cited by 174 (15 self)
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We present a principled and efficient planning algorithm for cooperative multiagent dynamic systems. A striking feature of our method is that the coordination and communication between the agents is not imposed, but derived directly from the system dynamics and function approximation architecture. We view the entire multiagent system as a single, large Markov decision process (MDP), which we assume can be represented in a factored way using a dynamic Bayesian network (DBN). The action space of the resulting MDP is the joint action space of the entire set of agents. Our approach is based on the use of factored linear value functions as an approximation to the joint value function. This factorization of the value function allows the agents to coordinate their actions at runtime using a natural message passing scheme. We provide a simple and efficient method for computing such an approximate value function by solving a single linear program, whose size is determined by the interaction between the value function structure and the DBN. We thereby avoid the exponential blowup in the state and action space. We show that our approach compares favorably with approaches based on reward sharing. We also show that our algorithm is an efficient alternative to more complicated algorithms even in the single agent case.
Efficient Solution Algorithms for Factored MDPs
, 2003
"... This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the re ..."
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Cited by 174 (4 self)
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This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and contextspecific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomialsized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on maxnorm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 10^40 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing stateoftheart approach, showing, in some problems, exponential gains in computation time.
Reinforcement learning for RoboCupsoccer keepaway
 Adaptive Behavior
, 2005
"... 1 RoboCup simulated soccer presents many challenges to reinforcement learning methods, including a large state space, hidden and uncertain state, multiple independent agents learning simultaneously, and long and variable delays in the effects of actions. We describe our application of episodic SMD ..."
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Cited by 133 (35 self)
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1 RoboCup simulated soccer presents many challenges to reinforcement learning methods, including a large state space, hidden and uncertain state, multiple independent agents learning simultaneously, and long and variable delays in the effects of actions. We describe our application of episodic SMDP Sarsa(λ) with linear tilecoding function approximation and variable λ to learning higherlevel decisions in a keepaway subtask of RoboCup soccer. In keepaway, one team, “the keepers, ” tries to keep control of the ball for as long as possible despite the efforts of “the takers. ” The keepers learn individually when to hold the ball and when to pass to a teammate. Our agents learned policies that significantly outperform a range of benchmark policies. We demonstrate the generality of our approach by applying it to a number of task variations including different field sizes and different numbers of players on each team.
Scaling Reinforcement Learning toward RoboCup Soccer
, 2001
"... RoboCup simulated soccer presents many challenges to reinforcement learning methods, including a large state space, hidden and uncertain state, multiple agents, and long and variable delays in the eects of actions. We describe our application of episodic SMDP Sarsa() with linear tilecoding funct ..."
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Cited by 122 (23 self)
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RoboCup simulated soccer presents many challenges to reinforcement learning methods, including a large state space, hidden and uncertain state, multiple agents, and long and variable delays in the eects of actions. We describe our application of episodic SMDP Sarsa() with linear tilecoding function approximation and variable to learning higherlevel decisions in a keepaway subtask of RoboCup soccer. In keepaway, one team, \the keepers," tries to keep control of the ball for as long as possible despite the eorts of \the takers." The keepers learn individually when to hold the ball and when to pass to a teammate, while the takers learn when to charge the ballholder and when to cover possible passing lanes. Our agents learned policies that signi cantly outperformed a range of benchmark policies. We demonstrate the generality of our approach by applying it to a number of task variations including dierent eld sizes and dierent numbers of players on each team.
Approximate Planning in Large POMDPs via Reusable Trajectories
, 1999
"... We consider the problem of choosing a nearbest strategy from a restricted class of strategies in a partially observable Markov decision process (POMDP). We assume we are given the ability to simulate the behavior of the POMDP, and we provide methods for generating simulated experience su cient to a ..."
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Cited by 119 (13 self)
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We consider the problem of choosing a nearbest strategy from a restricted class of strategies in a partially observable Markov decision process (POMDP). We assume we are given the ability to simulate the behavior of the POMDP, and we provide methods for generating simulated experience su cient to accurately approximate the expected return of any strategy in the class. We prove upper bounds on the amount of simulated experience our methods must generate in order to achieve such uniform approximation. These bounds have no dependence on the size or complexity of the underlying POMDP, but depend only on the complexity of the restricted strategy class. The main challenge is in generating trajectories in the POMDP that can be reused, in the sense that they simultaneously provide estimates of the return of many strategies in the class. Our measure of strategy class complexity generalizes the classical notion of VC dimension, and our methods develop connections between problems of current interest in reinforcement learning and wellstudied issues in the theory of supervised learning. We also discuss a number of practical planning algorithms for POMDPs that arise from our reusable trajectories.
Programmable reinforcement learning agents
, 2001
"... We present an expressive agent design language for reinforcement learning that allows the user to constrain the policies considered by the learning process.The language includes standard features such as parameterized subroutines, temporary interrupts, aborts, and memory variables, but also allows f ..."
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Cited by 115 (1 self)
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We present an expressive agent design language for reinforcement learning that allows the user to constrain the policies considered by the learning process.The language includes standard features such as parameterized subroutines, temporary interrupts, aborts, and memory variables, but also allows for unspecified choices in the agent program. For learning that which isn’t specified, we present provably convergent learning algorithms. We demonstrate by example that agent programs written in the language are concise as well as modular. This facilitates state abstraction and the transferability of learned skills. 1
Policy Iteration for Factored MDPs
 In Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI00
, 2000
"... Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has suggested that value functions in factored MDPs can often be approximated well using a factored value functi ..."
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Cited by 94 (6 self)
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Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has suggested that value functions in factored MDPs can often be approximated well using a factored value function: a linear combination of restricted basis functions, each of which refers only to a small subset of variables. An approximate factored value function for a particular policy can be computed using approximate dynamic programming, but this approach (and others) can only produce an approximation relative to a distance metric which is weighted by the stationary distribution of the current policy. This type of weighted projection is illsuited to policy improvement.
Exploiting Structure to Efficiently Solve Large Scale Partially Observable Markov Decision Processes
, 2005
"... Partially observable Markov decision processes (POMDPs) provide a natural and principled framework to model a wide range of sequential decision making problems under uncertainty. To date, the use of POMDPs in realworld problems has been limited by the poor scalability of existing solution algorithm ..."
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Cited by 91 (6 self)
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Partially observable Markov decision processes (POMDPs) provide a natural and principled framework to model a wide range of sequential decision making problems under uncertainty. To date, the use of POMDPs in realworld problems has been limited by the poor scalability of existing solution algorithms, which can only solve problems with up to ten thousand states. In fact, the complexity of finding an optimal policy for a finitehorizon discrete POMDP is PSPACEcomplete. In practice, two important sources of intractability plague most solution algorithms: large policy spaces and large state spaces. On the other hand,
Efficient Reinforcement Learning in Factored MDPs
, 1999
"... We present a provably efficient and nearoptimal algorithm for reinforcement learning in Markov decision processes (MDPs) whose transition model can be factored as a dynamic Bayesian network (DBN). Our algorithm generalizes the recent algorithm of Kearns and Singh, and assumes that we are given both ..."
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Cited by 88 (3 self)
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We present a provably efficient and nearoptimal algorithm for reinforcement learning in Markov decision processes (MDPs) whose transition model can be factored as a dynamic Bayesian network (DBN). Our algorithm generalizes the recent algorithm of Kearns and Singh, and assumes that we are given both an algorithm for approximate planning, and the graphical structure (but not the parameters) of the DBN. Unlike the original algorithm, our new algorithm exploits the DBN structure to achieve a running time that scales polynomially in the number of parameters of the DBN, which may be exponentially smaller than the number of global states. 1