Solving Multi-agent MDPs Optimally with Conditional Return Graphs

In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate in order find an optimal joint policy that maximises joint value. Typical solution algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP setting (MMDP) such structure is not present. We propose a new optimal solver for so-called TI-MMDPs, where agents can only affect their local state, while their value may depend on the state of others. We decompose the returns into local returns per agent that we represent compactly in a conditional return graph (CRG). Using CRGs the value of a joint policy as well as bounds on the value of partially specified joint policies can be efficiently computed. We propose CoRe, a novel branch-and-bound policy search algorithm building on CRGs. CoRe typically requires less runtime than the available alternatives and is able to find solutions to problems previously considered unsolvable.