Many high-level multi-agent planning problems, including multi-robot navigation and path planning, can be effectively modeled using deterministic actions and observations. In this work, we focus on such domains and introduce the class of Deterministic Decentralized POMDPs (Det-Dec-POMDPs). This is a subclass of Dec-POMDPs characterized by deterministic transitions and observations conditioned on the state and joint actions. We then propose a practical solver called Iterative Deterministic POMDP Planning (IDPP). This method builds on the classic Joint Equilibrium Search for Policies framework and is specifically optimized to handle large-scale Det-Dec-POMDPs that current Dec-POMDP solvers are unable to address efficiently.

Decentralized partially observable Markov decision processes with communication (Dec-POMDP-Com) provide a framework for multiagent decision making under uncertainty, but the NEXP-complete complexity renders solutions intractable in general. While sharing actions and observations can reduce the complexity to PSPACE-complete, we propose an approach that bridges POMDPs and Dec-POMDPs by communicating only suggested joint actions, eliminating the need to share observations while maintaining performance comparable to fully centralized planning and execution. Our algorithm estimates joint beliefs using shared actions to prune infeasible beliefs. Each agent maintains possible belief sets for other agents, pruning them based on suggested actions to form an estimated joint belief usable with any centralized policy. This approach requires solving a POMDP for each agent, reducing computational complexity while preserving performance. We demonstrate its effectiveness on several Dec-POMDP benchmarks showing performance comparable to centralized methods when shared actions enable effective belief pruning. This action-based communication framework offers a natural avenue for integrating human-agent cooperation, opening new directions for scalable multiagent planning under uncertainty, with applications in both autonomous systems and human-agent teams.

Applications such as robot control and wireless communication require planning under uncertainty. Partially observable Markov decision processes (POMDPs) plan policies for single agents under uncertainty and their decentralized versions (DEC-POMDPs) find a policy for multiple agents. The policy in infinite-horizon POMDP and DEC-POMDP problems has been represented as finite state controllers(FSCs). We introduce a novel class of periodic FSCs, composed of layers connected only to the previous and next layer. Our periodic FSC method finds a deterministic finite-horizon policy and converts it to an initial periodic infinitehorizon policy. This policy is optimized by a new infinite-horizon algorithm to yield deterministic periodic policies, and by a new expectation maximization algorithm to yield stochastic periodic policies. Our method yields better results than earlier planning methods and can compute larger solutions than with regular FSCs.

Decentralized partially observable Markov decision processes (Dec-POMDPs) formalize the problem of designing individual controllers for a group of collaborative agents under stochastic dynamics and partial observability. Seeking a global optimum is difficult (NEXP complete), but seeking a Nash equilibrium -- each agent policy being a best response to the other agents -- is more accessible, and allowed addressing infinite-horizon problems with solutions in the form of finite state controllers. In this paper, we show that this approach can be adapted to cases where only a generative model (a simulator) of the Dec-POMDP is available. This requires relying on a simulation-based POMDP solver to construct an agent's FSC node by node. A related process is used to heuristically derive initial FSCs. Experiment with benchmarks shows that MC-JESP is competitive with exisiting Dec-POMDP solvers, even better than many offline methods using explicit models.

Decentralized partially observable Markov decision processes (Dec-POMDPs) are general models for decentralized multi-agent decision making under uncertainty. However, they typically model a problem at a low level of granularity, where each agent's actions are primitive operations lasting exactly one time step. We address the case where each agent has macro-actions: temporally extended actions that may require different amounts of time to execute. We model macro-actions as options in a Dec-POMDP, focusing on actions that depend only on information directly available to the agent during execution. Therefore, we model systems where coordination decisions only occur at the level of deciding which macro-actions to execute. The core technical difficulty in this setting is that the options chosen by each agent no longer terminate at the same time. We extend three leading Dec-POMDP algorithms for policy generation to the macro-action case, and demonstrate their effectiveness in both standard benchmarks and a multi-robot coordination problem. The results show that our new algorithms retain agent coordination while allowing high-quality solutions to be generated for significantly longer horizons and larger state-spaces than previous Dec-POMDP methods. Furthermore, in the multi-robot domain, we show that, in contrast to most existing methods that are specialized to a particular problem class, our approach can synthesize control policies that exploit opportunities for coordination while balancing uncertainty, sensor information, and information about other agents.

We present a new algorithm called PIEM to approximately solve for the policy of an infinite-horizon decentralized partially observable Markov decision process (DEC-POMDP). The algorithm uses expectation maximization (EM) only in the step of policy improvement, with policy evaluation achieved by solving the Bellman's equation in terms of finite state controllers (FSCs). This marks a key distinction of PIEM from the previous EM algorithm of (Kumar and Zilberstein, 2010), i.e., PIEM directly operates on a DEC-POMDP without transforming it into a mixture of dynamic Bayes nets. Thus, PIEM precisely maximizes the value function, avoiding complicated forward/backward message passing and the corresponding computational and memory cost. To overcome local optima, we follow (Pajarinen and Peltonen, 2011) to solve the DEC-POMDP for a finite length horizon and use the resulting policy graph to initialize the FSCs. We solve the finite-horizon problem using a modified point-based policy generation (PBPG) algorithm, in which a closed-form solution is provided which was previously found by linear programming in the original PBPG. Experimental results on benchmark problems show that the proposed algorithms compare favorably to state-of-the-art methods.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called \emph{decentralized stick-breaking policy representation} (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.

This article describes the MultiAgent Decision Process (MADP) toolbox, a software library to support planning and learning for intelligent agents and multiagent systems in uncertain environments. Some of its key features are that it supports partially observable environments and stochastic transition models; has unified support for single- and multiagent systems; provides a large number of models for decision-theoretic decision making, including one-shot decision making (e.g., Bayesian games) and sequential decision making under various assumptions of observability and cooperation, such as Dec-POMDPs and POSGs; provides tools and parsers to quickly prototype new problems; provides an extensive range of planning and learning algorithms for single-and multiagent systems; and is written in C++ and designed to be extensible via the object-oriented paradigm.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from the optimal value. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called decentralized stick-breaking policy representation (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.

This paper presents four major results towards solving decentralized partially observable Markov decision problems (DecPOMDPs) culminating in an algorithm that outperforms all existing algorithms on all but one standard infinite-horizon benchmark problems. (1) We give an integer program that solves collaborative Bayesian games (CBGs). The program is notable because its linear relaxation is very often integral. (2) We show that a DecPOMDP with bounded belief can be converted to a POMDP (albeit with actions exponential in the number of beliefs). These actions correspond to strategies of a CBG. (3) We present a method to transform any DecPOMDP into a DecPOMDP with bounded beliefs (the number of beliefs is a free parameter) using optimal (not lossless) belief compression. (4) We show that the combination of these results opens the door for new classes of DecPOMDP algorithms based on previous POMDP algorithms. We choose one such algorithm, point-based valued iteration, and modify it to produce the first tractable value iteration method for DecPOMDPs which outperforms existing algorithms.