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.

Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general model for decision-making under uncertainty in decentralized settings, but are difficult to solve optimally (NEXP-Complete). As a new way of solving these problems, we introduce the idea of transforming a Dec-POMDP into a continuous-state deterministic MDP with a piecewise-linear and convex value function. This approach makes use of the fact that planning can be accomplished in a centralized offline manner, while execution can still be decentralized. 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. To provide scalability, we refine this approach by combining heuristic search and compact representations that exploit the structure present in multi-agent domains, without losing the ability to converge to an optimal solution. In particular, we introduce a feature-based heuristic search value iteration (FB-HSVI) algorithm that relies on feature-based compact representations, point-based updates and efficient action selection. A theoretical analysis demonstrates that FB-HSVI terminates in finite time with an optimal solution. We include an extensive empirical analysis using well-known benchmarks, thereby demonstrating that our approach provides significant scalability improvements compared to the state of the art.