Decentralized control of cooperative systems captures the operation of a group of decision-makers that share a single global objective. The difficulty in solving optimally such problems arises when the agents lack full observability of the global state of the system when they operate. The general problem has been shown to be NEXP-complete. In this paper, we identify classes of decentralized control problems whose complexity ranges between NEXP and P. In particular, we study problems characterized by independent transitions, independent observations, and goal-oriented objective functions. Two algorithms are shown to solve optimally useful classes of goal-oriented decentralized processes in polynomial time. This paper also studies information sharing among the decision-makers, which can improve their performance. We distinguish between three ways in which agents can exchange information: indirect communication, direct communication and sharing state features that are not controlled by the agents. Our analysis shows that for every class of problems we consider, introducing direct or indirect communication does not change the worst-case complexity. The results provide a better understanding of the complexity of decentralized control problems that arise in practice and facilitate the development of planning algorithms for these problems. 1.

Formal treatment of collaborative multi-agent systems has been lagging behind the rapid progress in sequential decision making by individual agents. Recent work in the area of decentralized Markov Decision Processes (MDPs) has contributed to closing this gap, but the computational complexity of these models remains a serious obstacle. To overcome this complexity barrier, we identify a specific class of decentralized MDPs in which the agents ’ transitions are independent. The class consists of independent collaborating agents that are tied together through a structured global reward function that depends on all of their histories of states and actions. We present a novel algorithm for solving this class of problems and examine its properties, both as an optimal algorithm and as an anytime algorithm. To the best of our knowledge, this is the first algorithm to optimally solve a non-trivial subclass of decentralized MDPs. It lays the foundation for further work in this area on both exact and approximate algorithms. 1.

In this article we describe a set of scalable techniques for learning the behavior of a group of agents in a collaborative multiagent setting. As a basis we use the framework of coordination graphs of Guestrin, Koller, and Parr (2002a) which exploits the dependencies between agents to decompose the global payoff function into a sum of local terms. First, we deal with the single-state case and describe a payoff propagation algorithm that computes the individual actions that approximately maximize the global payoff function. The method can be viewed as the decision-making analogue of belief propagation in Bayesian networks. Second, we focus on learning the behavior of the agents in sequential decision-making tasks. We introduce different model-free reinforcementlearning techniques, unitedly called Sparse Cooperative Q-learning, which approximate the global action-value function based on the topology of a coordination graph, and perform updates using the contribution of the individual agents to the maximal global action value. The combined use of an edge-based decomposition of the action-value function and the payoff propagation algorithm for efficient action selection, result in an approach that scales only linearly in the problem size. We provide experimental evidence that our method outperforms related multiagent reinforcement-learning methods based on temporal differences.

Many current large-scale multiagent team implementations can be characterized as following the “belief-desire-intention” (BDI) paradigm, with explicit representation of team plans. Despite their promise, current BDI team approaches lack tools for quantitative performance analysis under uncertainty. Distributed partially observable Markov decision problems (POMDPs) are well suited for such analysis, but the complexity of finding optimal policies in such models is highly intractable. The key contribution of this article is a hybrid BDI-POMDP approach, where BDI team plans are exploited to improve POMDP tractability and POMDP analysis improves BDI team plan performance. Concretely, we focus on role allocation, a fundamental problem in BDI teams: which agents to allocate to the different roles in the team. The article provides three key con- tributions. First, we describe a role allocation technique that takes into account future uncertainties in the domain; prior work in multiagent role allocation has failed to address such uncertainties. To that end, we introduce RMTDP (Role-based Markov Team De- cision Problem), a new distributed POMDP model for analysis of role allocations. Our technique gains in tractability by significantly curtailing RMTDP policy search; in partic- ular, BDI team plans provide incomplete RMTDP policies, and the RMTDP policy search fills the gaps in such incomplete policies by searching for the best role allocation. Our second key contribution is a novel decomposition technique to further improve RMTDP policy search efficiency. Even though limited to searching role allocations, there are still combinatorially many role allocations, and evaluating each in RMTDP to identify the best is extremely difficult. Our decomposition technique exploits the structure in the BDI team plans to significantly prune the search space of role allocations. Our third key contribution is a significantly faster policy evaluation algorithm suited for our BDI-POMDP hybrid ap- proach. Finally, we also present experimental results from two domains: mission rehearsal simulation and RoboCupRescue disaster rescue simulation.

POMDPs and their decentralized multiagent counterparts, DEC-POMDPs, offer a rich framework for sequential decision making under uncertainty. Their computational complexity, however, presents an important research challenge. One approach that effectively addresses the intractable memory requirements of current algorithms is based on representing agent policies as finite-state controllers. In this paper, we propose a new approach that uses this representation and formulates the problem as a nonlinear program (NLP). The NLP defines an optimal policy of a desired size for each agent. This new representation allows a wide range of powerful nonlinear programming algorithms to be used to solve POMDPs and DEC-POMDPs. Although solving the NLP optimally is often intractable, the results we obtain using an off-the-shelf optimization method are competitive with stateof-the-art POMDP algorithms and outperform state-of-the-art DEC-POMDP algorithms. Our approach is easy to implement and it opens up promising research directions for solving POMDPs and DEC-POMDPs using nonlinear programming methods. 1.

Despite the significant progress to extend Markov Decision Processes (MDP) to cooperative multi-agent systems, developing approaches that can deal with realistic problems remains a serious challenge. Existing approaches that solve Decentralized Markov Decision Processes (DEC-MDPs) suffer from the fact that they can only solve relatively small problems without complex constraints on task execution. OC-DEC-MDP has been introduced to deal with large DEC-MDPs under resource and temporal constraints. However, the algorithm developed to solve this class of DEC-MDPs has some limits: it suffers from overestimation of opportunity cost and restricts policy improvement. In this paper, we propose to overcome these limits by first introducing the notion of Expected Opportunity Cost to better assess the influence of a decision on the others. We then describe an iterative version of the algorithm that can be used to iterate the improvement process leading to higher quality solutions in some settings. 1

Although the presence of free communication reduces the complexity of multi-agent POMDPs to that of single-agent POMDPs, in practice, communication is not free and reducing the frequency of communication is often desirable. We present a novel approach for using centralized "single-agent" policies in decentralized multi-agent systems by maintaining and reasoning over the collection of possible joint beliefs of the team. We describe how communication can be used to integrate local observations into the team belief as needed to improve performance, and show both experimentally and through a detailed example how our approach minimizes communication while improving the performance of distributed execution.

Coordination of multiple agents under uncertainty in the decentralized POMDP model is known to be NEXP-complete, even when the agents have a joint set of goals. Nevertheless, we show that the existence of goals can help develop effective planning algorithms. We examine an approach to model these problems as indefinite-horizon decentralized POMDPs, suitable for many practical problems that terminate after some unspecified number of steps. Our algorithm for solving these problems is optimal under some common assumptions – that terminal actions exist for each agent and rewards for non-terminal actions are negative. We also propose an infinite-horizon approximation method that allows us to relax these assumptions while maintaining goal conditions. An optimality bound is developed for this samplebased approach and experimental results show that it is able to exploit the goal structure effectively. Compared with the state-of-the-art, our approach can solve larger problems and produce significantly better solutions. 1.

In this article we consider the issue of optimal control in collaborative multi-agent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part factorizes over the agents. Full observation of the global state is assumed. The goal is to minimize the accumulated joint cost, which consists of integrated instantaneous costs and a joint end cost. The joint end cost expresses the joint task of the agents. The instantaneous costs are quadratic in the control and factorize over the agents. The optimal control is given as a weighted linear combination of single-agent to single-target controls. The single-agent to single-target controls are expressed in terms of diffusion processes. These controls, when not closed form expressions, are formulated in terms of path integrals, which are calculated approximately by Metropolis-Hastings sampling. The weights in the control are interpreted as marginals of a joint distribution over agent to target assignments. The structure of the latter is represented by a graphical model, and the marginals are obtained by graphical model inference. Exact inference of the graphical model will break down in large systems, and so approximate inference methods are needed. We use naive mean field approximation and belief propagation to approximate the optimal control in systems with linear dynamics. We compare the approximate inference methods with the exact solution, and we show that they can accurately compute the optimal control. Finally, we demonstrate the control method in multi-agent systems with nonlinear dynamics consisting of up to 80 agents that have to reach an equal number of target states. 1.

We address the problem of how to play optimally against a fixed opponent in a twoplayer card game with partial information like poker. A game theoretic approach to this problem would specify a pair of stochastic policies that are best-responses to each other, i.e., a Nash equilibrium. Although such a Nash-optimal policy guarantees a lower bound to the attainable payo# against any opponent, it may not necessarily be optimal against a fixed opponent. We show here that if the opponent's policy is fixed (either known or estimated by repeated play), then we can model the problem as a partially observable Markov decision process (POMDP) from the perspective of one agent, and solve it by dynamic programming. In particular, for a large class of card games including poker, the derived POMDP consists of a finite number of belief states and it can be solved exactly.