text: This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The search for policies is limited to over the space of finite state controllers, which leads to a tractable approach to determine policies. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. We relate the satisfaction of the specification in terms of reaching (a subset of) recurrent states of a Markov chain. We then present a procedure to determine a set of defender and adversary finite state controllers of given sizes that will satisfy the temporal logic specification. We illustrate our approach with an example.
  @cite_38: POMDPs and their decentralized multiagent counterparts, DEC-POMDPs, offer a rich framework for sequential decision making under uncertainty. Their high computational complexity, however, presents an important research challenge. One way to address the intractable memory requirements of current algorithms is based on representing agent policies as finite-state controllers. Using this representation, we propose a new approach that formulates the problem as a nonlinear program, which defines an optimal policy of a desired size for each agent. This new formulation 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 state-of-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.
  @cite_14: In the domain of decentralized Markov decision processes, we develop the first complete and optimal algorithm that is able to extract deterministic policy vectors based on finite state controllers for a cooperative team of agents. Our algorithm applies to the discounted infinite horizon case and extends best-first search methods to the domain of decentralized control theory. We prove the optimality of our approach and give some first experimental results for two small test problems. We believe this to be an important step forward in learning and planning in stochastic multi-agent systems.
  @cite_42: We present a bounded policy iteration algorithm for infinite-horizon decentralized POMDPs. Policies are represented as joint stochastic finite-state controllers, which consist of a local controller for each agent. We also let a joint controller include a correlation device that allows the agents to correlate their behavior without exchanging information during execution, and show that this leads to improved performance. The algorithm uses a fixed amount of memory, and each iteration is guaranteed to produce a controller with value at least as high as the previous one for all possible initial state distributions. For the case of a single agent, the algorithm reduces to Poupart and Boutilier's bounded policy iteration for POMDPs.
  @cite_39: This book introduces multiagent planning under uncertainty as formalized by decentralized partially observable Markov decision processes (Dec-POMDPs). The intended audience is researchers and graduate students working in the fields of artificial intelligence related to sequential decision making: reinforcement learning, decision-theoretic planning for single agents, classical multiagent planning, decentralized control, and operations research.
  @cite_15: We develop an exact dynamic programming algorithm for partially observable stochastic games (POSGs). The algorithm is a synthesis of dynamic programming for partially observable Markov decision processes (POMDPs) and iterated elimination or dominated strategies in normal form games. We prove that when applied to finite-horizon POSGs, the algorithm iteratively eliminates very weakly dominated strategies without first forming a normal form representation of the game. For the special case in which agents share the same payoffs, the algorithm can be used to find an optimal solution. We present preliminary empirical results and discuss ways to further exploit POMDP theory in solving POSGs.
summary: Dynamic programming (DP) for POSGs has been studied in @cite_15 , resulting in an algorithm that generalizes both DP for POMDPs and iterated elimination of dominated strategies for normal form games. This work, however, considered the finite horizon case, and all agents had to maximize their own expected rewards. When agents cooperate to earn rewards, the framework is called a decentralized-POMDP (Dec-POMDP). The infinite horizon case for Dec-POMDPs was studied in @cite_42 , where the authors proposed a bounded policy iteration algorithm for policies represented as joint FSCs. A complete and optimal algorithm for deterministic FSC policies for DecPOMDPs was presented in @cite_14 . Optimization techniques for fixed-size controllers' to solve Dec-POMDPs were investigated in @cite_38 . A survey of recent research in Dec- POMDPs is presented in @cite_39 .