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Register a new userPerformance Bounds for Lambda Policy Iteration and Application to the Game of Tetris
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Bruno Scherrer
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Authors
Bruno Scherrer
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We consider the discrete-time infinite-horizon optimal control problem formalized by Markov Decision Processes. We revisit the work of Bertsekas and Ioffe, that introduced $lambda$ Policy Iteration, a family of algorithms parameterized by $lambda$ that generalizes the standard algorithms Value Iteration and Policy Iteration, and has some deep connections with the Temporal Differences algorithm TD($lambda$) described by Sutton and Barto. We deepen the original theory developped by the authors by providing convergence rate bounds which generalize standard bounds for Value Iteration described for instance by Puterman. Then, the main contribution of this paper is to develop the theory of this algorithm when it is used in an approximate form and show that this is sound. Doing so, we extend and unify the separate analyses developped by Munos for Approximate Value Iteration and Approximate Policy Iteration. Eventually, we revisit the use of this algorithm in the training of a Tetris playing controller as originally done by Bertsekas and Ioffe. We provide an original performance bound that can be applied to such an undiscounted control problem. Our empirical results are different from those of Bertsekas and Ioffe (which were originally qualified as paradoxical and intriguing), and much more conform to what one would expect from a learning experiment. We discuss the possible reason for such a difference.
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Coordination of distributed agents is required for problems arising in many areas, including multi-robot systems, networking and e-commerce. As a formal framework for such problems, we use the decentralized partially observable Markov decision process (DEC-POMDP). Though much work has been done on optimal dynamic programming algorithms for the single-agent version of the problem, optimal algorithms for the multiagent case have been elusive. The main contribution of this paper is an optimal policy iteration algorithm for solving DEC-POMDPs. The algorithm uses stochastic finite-state controllers to represent policies. The solution can include a correlation device, which allows agents to correlate their actions without communicating. This approach alternates between expanding the controller and performing value-preserving transformations, which modify the controller without sacrificing value. We present two efficient value-preserving transformations: one can reduce the size of the controller and the other can improve its value while keeping the size fixed. Empirical results demonstrate the usefulness of value-preserving transformations in increasing value while keeping controller size to a minimum. To broaden the applicability of the approach, we also present a heuristic version of the policy iteration algorithm, which sacrifices convergence to optimality. This algorithm further reduces the size of the controllers at each step by assuming that probability distributions over the other agents actions are known. While this assumption may not hold in general, it helps produce higher quality solutions in our test problems.
For artificially intelligent learning systems to have widespread applicability in real-world settings, it is important that they be able to operate decentrally. Unfortunately, decentralized control is difficult -- computing even an epsilon-optimal joint policy is a NEXP complete problem. Nevertheless, a recently rediscovered insight -- that a team of agents can coordinate via common knowledge -- has given rise to algorithms capable of finding optimal joint policies in small common-payoff games. The Bayesian action decoder (BAD) leverages this insight and deep reinforcement learning to scale to games as large as two-player Hanabi. However, the approximations it uses to do so prevent it from discovering optimal joint policies even in games small enough to brute force optimal solutions. This work proposes CAPI, a novel algorithm which, like BAD, combines common knowledge with deep reinforcement learning. However, unlike BAD, CAPI prioritizes the propensity to discover optimal joint policies over scalability. While this choice precludes CAPI from scaling to games as large as Hanabi, empirical results demonstrate that, on the games to which CAPI does scale, it is capable of discovering optimal joint policies even when other modern multi-agent reinforcement learning algorithms are unable to do so. Code is available at https://github.com/ssokota/capi .
In the last decades we have witnessed the success of applications of Artificial Intelligence to playing games. In this work we address the challenging field of games with hidden information and card games in particular. Jass is a very popular card game in Switzerland and is closely connected with Swiss culture. To the best of our knowledge, performances of Artificial Intelligence agents in the game of Jass do not outperform top players yet. Our contribution to the community is two-fold. First, we provide an overview of the current state-of-the-art of Artificial Intelligence methods for card games in general. Second, we discuss their application to the use-case of the Swiss card game Jass. This paper aims to be an entry point for both seasoned researchers and new practitioners who want to join in the Jass challenge.
In this paper we consider infinite horizon discounted dynamic programming problems with finite state and control spaces, partial state observations, and a multiagent structure. We discuss and compare algorithms that simultaneously or sequentially optimize the agents controls by using multistep lookahead, truncated rollout with a known base policy, and a terminal cost function approximation. Our methods specifically address the computational challenges of partially observable multiagent problems. In particular: 1) We consider rollout algorithms that dramatically reduce required computation while preserving the key cost improvement property of the standard rollout method. The per-step computational requirements for our methods are on the order of $O(Cm)$ as compared with $O(C^m)$ for standard rollout, where $C$ is the maximum cardinality of the constraint set for the control component of each agent, and $m$ is the number of agents. 2) We show that our methods can be applied to challenging problems with a graph structure, including a class of robot repair problems whereby multiple robots collaboratively inspect and repair a system under partial information. 3) We provide a simulation study that compares our methods with existing methods, and demonstrate that our methods can handle larger and more complex partially observable multiagent problems (state space size $10^{37}$ and control space size $10^{7}$, respectively). Finally, we incorporate our multiagent rollout algorithms as building blocks in an approximate policy iteration scheme, where successive rollout policies are approximated by using neural network classifiers. While this scheme requires a strictly off-line implementation, it works well in our computational experiments and produces additional significant performance improvement over the single online rollout iteration method.
In this paper we consider infinite horizon discounted dynamic programming problems with finite state and control spaces, and partial state observations. We discuss an algorithm that uses multistep lookahead, truncated rollout with a known base policy, and a terminal cost function approximation. This algorithm is also used for policy improvement in an approximate policy iteration scheme, where successive policies are approximated by using a neural network classifier. A novel feature of our approach is that it is well suited for distributed computation through an extended belief space formulation and the use of a partitioned architecture, which is trained with multiple neural networks. We apply our methods in simulation to a class of sequential repair problems where a robot inspects and repairs a pipeline with potentially several rupture sites under partial information about the state of the pipeline.
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