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Indefinite-Horizon Reachability in Goal-DEC-POMDPs

AAAI Conferences

DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost.We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new and novel method to solve the problem that extends methods for finite-horizon DEC-POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show that our approach presents promising results.


An Investigation into Mathematical Programming for Finite Horizon Decentralized POMDPs

Journal of Artificial Intelligence Research

Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, solving them is a task with an overwhelming complexity that can be doubly exponential. In this paper, we study an alternate formulation of DEC-POMDPs relying on a sequence-form representation of policies. From this formulation, we show how to derive Mixed Integer Linear Programming (MILP) problems that, once solved, give exact optimal solutions to the DEC-POMDPs. We show that these MILPs can be derived either by using some combinatorial characteristics of the optimal solutions of the DEC-POMDPs or by using concepts borrowed from game theory. Through an experimental validation on classical test problems from the DEC-POMDP literature, we compare our approach to existing algorithms. Results show that mathematical programming outperforms dynamic programming but is less efficient than forward search, except for some particular problems. The main contributions of this work are the use of mathematical programming for DEC-POMDPs and a better understanding of DEC-POMDPs and of their solutions. Besides, we argue that our alternate representation of DEC-POMDPs could be helpful for designing novel algorithms looking for approximate solutions to DEC-POMDPs.


Efficient Planning for Factored Infinite-Horizon DEC-POMDPs

AAAI Conferences

Decentralized partially observable Markov decision processes (DEC-POMDPs) are used to plan policies for multiple agents that must maximize a joint reward function but do not communicate with each other. The agents act under uncertainty about each other and the environment. This planning task arises in optimization of wireless networks, and other scenarios where communication between agents is restricted by costs or physical limits. DEC-POMDPs are a promising solution, but optimizing policies quickly becomes computationally intractable when problem size grows. Factored DEC-POMDPs allow large problems to be described in compact form, but have the same worst case complexity as non-factored DEC-POMDPs. We propose an efficient optimization algorithm for large factored infinite-horizon DEC-POMDPs. We formulate expectation-maximization based optimization into a new form, where complexity can be kept tractable by factored approximations. Our method performs well, and it can solve problems with more agents and larger state spaces than state of the art DEC-POMDP methods. We give results for factored infinite-horizon DEC-POMDP problems with up to 10 agents.


Three New Algorithms to Solve N-POMDPs

AAAI Conferences

In many fields in computational sustainability, applications of POMDPs are inhibited by the complexity of the optimal solution. One way of delivering simple solutions is to represent the policy with a small number of alpha-vectors. We would like to find the best possible policy that can be expressed using a fixed number N of alpha-vectors. We call this the N-POMDP problem. The existing solver alpha-min approximately solves finite-horizon POMDPs with a controllable number of alpha-vectors. However alpha-min is a greedy algorithm without performance guarantees, and it is rather slow. This paper proposes three new algorithms, based on a general approach that we call alpha-min-2. These three algorithms are able to approximately solve N-POMDPs. Alpha-min-2-fast (heuristic) and alpha-min-2-p (with performance guarantees) are designed to complement an existing POMDP solver, while alpha-min-2-solve (heuristic) is a solver itself. Complexity results are provided for each of the algorithms, and they are tested on well-known benchmarks. These new algorithms will help users to interpret solutions to POMDP problems in computational sustainability.


Point-Based Value Iteration for Finite-Horizon POMDPs

Journal of Artificial Intelligence Research

Partially Observable Markov Decision Processes (POMDPs) are a popular formalism for sequential decision making in partially observable environments. Since solving POMDPs to optimality is a difficult task, point-based value iteration methods are widely used. These methods compute an approximate POMDP solution, and in some cases they even provide guarantees on the solution quality, but these algorithms have been designed for problems with an infinite planning horizon. In this paper we discuss why state-of-the-art point-based algorithms cannot be easily applied to finite-horizon problems that do not include discounting. Subsequently, we present a general point-based value iteration algorithm for finite-horizon problems which provides solutions with guarantees on solution quality.