In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical 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 transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and the bounds on 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 finds solutions to problems previously unsolvable.
There has been substantial progress with formal models for sequential decision making by individual agents using the Markov decision process (MDP). However, similar treatment of multi-agent systems is lacking. A recent complexity result, showing that solving decentralized MDPs is NEXP-hard, provides a partial explanation. To overcome this complexity barrier, we identify a general class of transition-independent decentralized MDPs that is widely applicable. The class consists of independent collaborating agents that are tied together through a global reward function that depends upon both of their histories. We present a novel algorithm for solving this class of problems and examine its properties. The result is the first effective technique to solve optimally a class of decentralized MDPs. This lays the foundation for further work in this area on both exact and approximate solutions. Creating coordinated multiagent policies in environments with uncertainty is a challenging problem, which can be greatly simplified if the coordination needs are known to be limited to specific parts of the state space. In this work, we explore how such local interactions can simplify coordination in multiagent systems. We focus on problems in which the interaction between the agents is sparse and contribute a new decision-theoretic model for decentralized sparse-interaction multiagent systems, Dec-SIMDPs, that explicitly distinguishes the situations in which the agents in the team must coordinate from those in which they can act independently. We relate our new model to other existing models such as MMDPs and Dec-MDPs. We then propose a solution method that takes advantage of the particular structure of Dec-SIMDPs and provide theoretical error bounds on the quality of the obtained solution. Finally, we show a reinforcement learning algorithm in which independent agents learn both individual policies and when and how to coordinate. We illustrate the application of the algorithms throughout the paper in several multiagent navigation scenarios. Decentralized partially observable Markov decision processes (DEC-POMDPs) form a general framework for planning for groups of cooperating agents that inhabit a stochastic and partially observable environment. Unfortunately, computing optimal plans in a DEC-POMDP has been shown to be intractable (NEXP-complete), and approximate algorithms for specific subclasses have been proposed. Many of these algorithms rely on an (approximate) solution of the centralized planning problem (i.e., treating the whole team as a single agent). We take a more decentralized approach, in which each agent only reasons over its own local state and some uncontrollable state features, which are shared by all team members. In contrast to other approaches, we model communication as an integral part of the agent's reasoning, in which the meaning of a message is directly encoded in the policy of the communicating agent. We explore iterative methods for approximately solving such models, and we conclude with some encouraging preliminary experimental results. There has been substantial progress on algorithms for single-agent sequential decision making using partially observable Markov decision processes (POMDPs). A number of efficient algorithms for solving POMDPs share two desirable properties: error-bounds and fast convergence rates. Despite significant efforts, no algorithms for solving decentralized POMDPs benefit from these properties, leading to either poor solution quality or limited scalability. This paper presents the first approach for solving transition independent decentralized Markov decision processes (Dec-MDPs), that inherits these properties. Two related algorithms illustrate this approach. The first recasts the original problem as a deterministic and completely observable Markov decision process. In this form, the original problem is solved by combining heuristic search with constraint optimization to quickly converge into a near-optimal policy. This algorithm also provides the foundation for the first algorithm for solving infinite-horizon transition independent decentralized MDPs. We demonstrate that both methods outperform state-of-the-art algorithms by multiple orders of magnitude, and for infinite-horizon decentralized MDPs, the algorithm is able to construct more concise policies by searching cyclic policy graphs.