Many exact and approximate solution methods for Markov Decision Processes (MDPs) attempt to exploit structure in the problem and are based on factorization of the value function. Especially multiagent settings, however, are known to suffer from an exponential increase in value component sizes as interactions become denser, meaning that approximation architectures are restricted in the problem sizes and types they can handle. We present an approach to mitigate this limitation for certain types of multiagent systems, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. Anonymous influence summarizes joint variable effects efficiently whenever the explicit representation of variable identity in the problem can be avoided. We show how representational benefits from anonymity translate into computational efficiencies, both for general variable elimination in a factor graph but in particular also for the approximate linear programming solution to factored MDPs. The latter allows to scale linear programming to factored MDPs that were previously unsolvable. Our results are shown for the control of a stochastic disease process over a densely connected graph with 50 nodes and 25 agents.
Many recent algorithms tackle domains with large (structured) state spaces. For exact planning in factored domains, SPUDD exploits a decision diagram-based representation @cite_28 . Monte Carlo tree search (MCTS) has been a popular online approximate planning method to scale to large domains @cite_20 . These methods do not apply to exponential action spaces without further approximations. Ho+al15:CDC ( Ho+al15:CDC ), for example, evaluated MCTS with three agents for a targeted version of the disease control problem. Recent variants that exploit factorization @cite_19 may be applicable.
@cite_28 @cite_19 @cite_20
1530444831 329015778 2097778153
Recently, structured methods for solving factored Markov decisions processes (MDPs) with large state spaces have been proposed recently to allow dynamic programming to be applied without the need for complete state enumeration. We propose and examine a new value iteration algorithm for MDPs that uses algebraic decision diagrams (ADDs) to represent value functions and policies, assuming an ADD input representation of the MDP. Dynamic programming is implemented via ADD manipulation. We demonstrate our method on a class of large MDPs (up to 63 million states) and show that significant gains can be had when compared to tree-structured representations (with up to a thirty-fold reduction in the number of nodes required to represent optimal value functions). Online, sample-based planning algorithms for POMDPs have shown great promise in scaling to problems with large state spaces, but they become intractable for large action and observation spaces. This is particularly problematic in multiagent POMDPs where the action and observation space grows exponentially with the number of agents. To combat this intractability, we propose a novel scalable approach based on sample-based planning and factored value functions that exploits structure present in many multiagent settings. This approach applies not only in the planning case, but also in the Bayesian reinforcement learning setting. Experimental results show that we are able to provide high quality solutions to large multiagent planning and learning problems. We present a reinforcement learning architecture, Dyna-2, that encompasses both sample-based learning and sample-based search, and that generalises across states during both learning and search. We apply Dyna-2 to high performance Computer Go. In this domain the most successful planning methods are based on sample-based search algorithms, such as UCT, in which states are treated individually, and the most successful learning methods are based on temporal-difference learning algorithms, such as Sarsa, in which linear function approximation is used. In both cases, an estimate of the value function is formed, but in the first case it is transient, computed and then discarded after each move, whereas in the second case it is more permanent, slowly accumulating over many moves and games. The idea of Dyna-2 is for the transient planning memory and the permanent learning memory to remain separate, but for both to be based on linear function approximation and both to be updated by Sarsa. To apply Dyna-2 to 9x9 Computer Go, we use a million binary features in the function approximator, based on templates matching small fragments of the board. Using only the transient memory, Dyna-2 performed at least as well as UCT. Using both memories combined, it significantly outperformed UCT. Our program based on Dyna-2 achieved a higher rating on the Computer Go Online Server than any handcrafted or traditional search based program.