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.
Scalability is a major issue in multi-agent planning under uncertainty. In response to this challenge, two important lines of work have been developed. One line of work proposed approximate solutions by imposing and exploiting an additive structure in the value function @cite_20 . This approach has been applied in a range of stochastic planning settings, fully and partially observable alike, both from a single-agent perspective @cite_13 @cite_6 and multi-agent @cite_16 @cite_4 @cite_9 @cite_21 . The drawback of such methods is that typically no bounds on the efficiency loss can be given. We focus on optimal solutions, required to deal with strategic behaviour in a mechanism @cite_2 @cite_19 .
@cite_4 @cite_9 @cite_21 @cite_6 @cite_19 @cite_2 @cite_16 @cite_13 @cite_20
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Loosely coupled multi-agent systems are perceived as easier to plan for because they require less coordination between agent sub-plans. In this paper we set out to formalize this intuition. We establish an upper bound on the complexity of multi-agent planning problems that depends exponentially on two parameters quantifying the level of agents' coupling, and on these parameters only. The first parameter is problem-independent, and it measures the inherent level of coupling within the system. The second is problem-specific and it has to do with the minmax number of action-commitments per agent required to solve the problem. Most importantly, the direct dependence on the number of agents, on the overall size of the problem, and on the length of the agents' plans, is only polynomial. This result is obtained using a new algorithmic methodology which we call "planning as CSP+planning". We believe this to be one of the first formal results to both quantify the notion of agents' coupling, and to demonstrate a multi-agent planning algorithm that, for fixed coupling levels, scales polynomially with the size of the problem. Multiagent planning has seen much progress with the development of formal models such as Dec-POMDPs. However, the complexity of these models--NEXP-Complete even for two agents-- has limited scalability. We identify certain mild conditions that are sufficient to make multiagent planning amenable to a scalable approximation w.r.t. the number of agents. This is achieved by constructing a graphical model in which likelihood maximization is equivalent to plan optimization. Using the Expectation-Maximization framework for likelihood maximization, we show that the necessary inference can be decomposed into processes that often involve a small subset of agents, thereby facilitating scalability. We derive a global update rule that combines these local inferences to monotonically increase the overall solution quality. Experiments on a large multiagent planning benchmark confirm the benefits of the new approach in terms of runtime and scalability. Scaling decision theoretic planning to large multiagent systems is challenging due to uncertainty and partial observability in the environment. We focus on a multiagent planning model subclass, relevant to urban settings, where agent interactions are dependent on their collective influence'' on each other, rather than their identities. Unlike previous work, we address a general setting where system reward is not decomposable among agents. We develop collective actor-critic RL approaches for this setting, and address the problem of multiagent credit assignment, and computing low variance policy gradient estimates that result in faster convergence to high quality solutions. We also develop difference rewards based credit assignment methods for the collective setting. Empirically our new approaches provide significantly better solutions than previous methods in the presence of global rewards on two real world problems modeling taxi fleet optimization and multiagent patrolling, and a synthetic grid navigation domain. Planning under uncertainty faces a scalability problem when considering multi-robot teams, as the information space scales exponentially with the number of robots. To address this issue, this paper proposes to decentralize multi-robot partially observable Markov decision processes (POMDPs) while maintaining cooperation between robots by using POMDP policy auctions. Auctions provide a flexible way of coordinating individual policies modeled by POMDPs and have low communication requirements. In addition, communication models in the multi-agent POMDP literature severely mismatch with real inter-robot communication. We address this issue by exploiting a decentralized data fusion method in order to efficiently maintain a joint belief state among the robots. The paper presents two different applications: environmental monitoring with unmanned aerial vehicles (UAVs); and cooperative tracking, in which several robots have to jointly track a moving target of interest. The first one is used as a proof of concept and illustrates the proposed ideas through different simulations. The second one adds real multi-robot experiments, showcasing the flexibility and robust coordination that our techniques can provide.