Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general model for decision-making under uncertainty in cooperative decentralized settings, but are difficult to solve optimally (NEXP-Complete). As a new way of solving these problems, we recently introduced a method for transforming a Dec-POMDP into a continuous-state deterministic MDP with a piecewise-linear and convex value function. This new Dec-POMDP formulation, which we call an occupancy MDP, allows powerful POMDP and continuous-state MDP methods to be used for the first time. However, scalability remains limited when the number of agents or problem variables becomes large. In this paper, we show that, under certain separability conditions of the optimal value function, the scalability of this approach can increase considerably. This separability is present when there is locality of interaction between agents, which can be exploited to improve performance. Unlike most previous methods, the novel continuous-state MDP algorithm retains optimality and convergence guarantees. Results show that the extension using separability can scale to a large number of agents and domain variables while maintaining optimality.

Optimally solving decentralized partially observable Markov decision processes (Dec-POMDPs) is a hard combinatorial problem. Current algorithms search through the space of full histories for each agent. Because of the doubly exponential growth in the number of policies in this space as the planning horizon increases, these methods quickly become intractable. However, in real world problems, computing policies over the full history space is often unnecessary. True histories experienced by the agents often lie near a structured, low-dimensional manifold embedded into the history space. We show that by transforming a Dec-POMDP into a continuous-state MDP, we are able to find and exploit these low-dimensional representations. Using this novel transformation, we can then apply powerful techniques for solving POMDPs and continuous-state MDPs. By combining a general search algorithm and dimension reduction based on feature selection, we introduce a novel approach to optimally solve problems with significantly longer planning horizons than previous methods.

Approximate linear programming (ALP) has emerged recently as one of the most promising methods for solving complex factored MDPs with finite state spaces. In this work we show that ALP solutions are not limited only to MDPs with finite state spaces, but that they can also be applied successfully to factored continuous-state MDPs (CMDPs). We show how one can build an ALPbased approximation for such a model and contrast it to existing solution methods. We argue that this approach offers a robust alternative for solving high dimensional continuous-state space problems. The point is supported by experiments on three CMDP problems with 24-25 continuous state factors.

Approximate linear programming (ALP) has emerged recently as one of the most promising methods for solving complex factored MDPs with finite state spaces. In this work we show that ALP solutions are not limited only to MDPs with finite state spaces, but that they can also be applied successfully to factored continuous-state MDPs (CMDPs). We show how one can build an ALPbased approximation for such a model and contrast it to existing solution methods. We argue that this approach offers a robust alternative for solving high dimensional continuous-state space problems. The point is supported by experiments on three CMDP problems with 24-25 continuous state factors.

Approximate linear programming (ALP) has emerged recently as one of the most promising methods for solving complex factored MDPs with finite state spaces. In this work we show that ALP solutions are not limited only to MDPs with finite state spaces, but that they can also be applied successfully to factored continuous-state MDPs (CMDPs). We show how one can build an ALPbased approximation for such a model and contrast it to existing solution methods. We argue that this approach offers a robust alternative for solving high dimensional continuous-state space problems. The point is supported by experiments on three CMDP problems with 24-25 continuous state factors.