Currently, large partially observable Markov decision processes (POMDPs) are often solved by sampling-based online methods which interleave planning and execution phases. However, a pre-computed offline policy is more desirable in POMDP applications with time or energy constraints. But previous offline algorithms are not able to scale up to large POMDPs. In this article, we propose a new sampling-based algorithm, the partially observable Monte-Carlo graph search (POMCGS) to solve large POMDPs offline. Different from many online POMDP methods, which progressively develop a tree while performing (Monte-Carlo) simulations, POMCGS folds this search tree on the fly to construct a policy graph, so that computations can be drastically reduced, and users can analyze and validate the policy prior to embedding and executing it. Moreover, POMCGS, together with action progressive widening and observation clustering methods provided in this article, is able to address certain continuous POMDPs. Through experiments, we demonstrate that POMCGS can generate policies on the most challenging POMDPs, which cannot be computed by previous offline algorithms, and these policies' values are competitive compared with the state-of-the-art online POMDP algorithms.

In human-robot collaboration, the objectives of the human are often unknown to the robot. Moreover, even assuming a known objective, the human behavior is also uncertain. In order to plan a robust robot behavior, a key preliminary question is then: How to derive realistic human behaviors given a known objective? A major issue is that such a human behavior should itself account for the robot behavior, otherwise collaboration cannot happen. In this paper, we rely on Markov decision models, representing the uncertainty over the human objective as a probability distribution over a finite set of objective functions (inducing a distribution over human behaviors). Based on this, we propose two contributions: 1) an approach to automatically generate an uncertain human behavior (a policy) for each given objective function while accounting for possible robot behaviors; and 2) a robot planning algorithm that is robust to the above-mentioned uncertainties and relies on solving a partially observable Markov decision process (POMDP) obtained by reasoning on a distribution over human behaviors. A co-working scenario allows conducting experiments and presenting qualitative and quantitative results to evaluate our approach.

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 existing Dec-POMDP solvers, even better than many offline methods using explicit models.

This paper looks at solving collaborative planning problems formalized as Decentralized POMDPs (Dec-POMDPs) by searching for Nash equilibria, i.e., situations where each agent’s policy is a best response to the other agents’ (fixed) policies. While the Joint Equilibrium-based Search for Policies (JESP) algorithm does this in the finite-horizon setting relying on policy trees, we propose here to adapt it to infinite-horizon Dec-POMDPs by using finite state controller (FSC) policy representations. In this article, we (1) explain how to turn a Dec-POMDP with N − 1 fixed FSCs into an infinite-horizon POMDP whose solution is an Nthagent best response; (2) propose a JESP variant, called Inf-JESP, using this to solve infinite-horizon Dec-POMDPs; (3) introduce heuristic initializations for JESP aiming at leading to good solutions; and (4) conduct experiments on state-of-the-art benchmark problems to evaluate our approach. This paper looks at solving collaborative planning problems formalized as Decentralized POMDPs (Dec-POMDPs) by searching for Nash equilibria, i.e., situations where each agent’s policy is a best response to the other agents’ (fixed) policies. While the Joint Equilibrium-based Search for Policies (JESP) algorithm does this in the finite-horizon setting relying on policy trees, we propose here to adapt it to infinite-horizon Dec-POMDPs by using finite state controller (FSC) policy representations. In this article, we (1) explain how to turn a Dec-POMDP with N 1 fixed FSCs into an infinite-horizon POMDP whose solution−is an Nthagent best response; (2) propose a JESP variant, called Inf-JESP, using this to solve infinite-horizon Dec-POMDPs; (3) introduce heuristic initializations for JESP aiming at leading to good solutions; and (4) conduct experiments on state-of-the-art benchmark problems to evaluate our approach.

In sequential decision making, heuristic search algorithms allow exploiting both the initial situation and an admissible heuristic to efficiently search for an optimal solution, often for planning purposes. Such algorithms exist for problems with uncertain dynamics, partial observability, multiple criteria, or multiple collaborating agents. In this article, we look at two-player zero-sum stochastic games (zsSGs) with a discounted criterion, in a view to propose a solution tailored to the fully observable case, while solutions have been proposed for particular, though still more general, partially observable cases. This setting induces reasoning on both a lower and an upper bound of the value function, which leads us to proposing zsSG-HSVI, an algorithm based on heuristic search value iteration (HSVI), and which thus relies on generating trajectories. We demonstrate that, each player acting optimistically, and employing simple heuristic initializations, HSVI's convergence in finite time to an ∈-optimal solution is preserved. An empirical study of the resulting approach is conducted on benchmark problems of various sizes.

In this article, we discuss how to solve information-gathering problems expressed as rho-POMDPs, an extension of Partially Observable Markov Decision Processes (POMDPs) whose reward rho depends on the belief state. Point-based approaches used for solving POMDPs have been extended to solving rho-POMDPs as belief MDPs when its reward rho is convex in B or when it is Lipschitz-continuous. In the present paper, we build on the POMCP algorithm to propose a Monte Carlo Tree Search for rho-POMDPs, aiming for an efficient on-line planner which can be used for any rho function. Adaptations are required due to the belief-dependent rewards to (i) propagate more than one state at a time, and (ii) prevent biases in value estimates. An asymptotic convergence proof to epsilon-optimal values is given when rho is continuous. Experiments are conducted to analyze the algorithms at hand and show that they outperform myopic approaches.

Many state-of-the-art algorithms for solving Partially Observable Markov Decision Processes (POMDPs) rely on turning the problem into a “fully observable” problem—a belief MDP—and exploiting the piece-wise linearity and convexity (PWLC) of the optimal value function in this new state space (the belief simplex ∆). This approach has been extended to solving ρ-POMDPs—i.e., for information-oriented criteria—when the reward ρ is convex in ∆. General ρ-POMDPs can also be turned into “fully observable” problems, but with no means to exploit the PWLC property. In this paper, we focus on POMDPs and ρ-POMDPs with λ ρ -Lipschitz reward function, and demonstrate that, for finite horizons, the optimal value function is Lipschitz-continuous. Then, value function approximators are proposed for both upper- and lower-bounding the optimal value function, which are shown to provide uniformly improvable bounds. This allows proposing two algorithms derived from HSVI which are empirically evaluated on various benchmark problems.

Tracking and understanding moving pedestrian behaviors is of major concern for a growing number of applications. Classical approaches either consider both problems separately or treat them simultaneously on the basis of limited contextual graphical models. In this paper, we consider tackling both problems jointly based on richer contextual information issued from agent-based behavioral simulators designed for realistically reproducing human behaviors within complex environments. We focus on the single target case and experimentally show that the proposed approach keeps good performances even in case of long periods of occlusion.

The difficulties encountered in sequential decision-making problems under uncertainty are often linked to the large size of the state space. Exploiting the structure of the problem, for example by employing a factored representation, is usually an efficient approach but, in the case of partially observable Markov decision processes, the fact that some state variables may be visible has not been sufficiently appreciated. In this article, we present a complementary analysis and discussion about MOMDPs, a formalism that exploits the fact that the state space may be factored in one visible part and one hidden part. Starting from a POMDP description, we dig into the structure of the belief update, value function, and the consequences in value iteration, specifically how classical algorithms can be adapted to this factorization, and demonstrate the resulting benefits through an empirical evaluation.

Partially Observable Markov Decision Processes (POMDPs) model sequential decision-making problems under uncertainty and partial observability. Unfortunately, some problems cannot be modeled with state-dependent reward functions, e.g., problems whose objective explicitly implies reducing the uncertainty on the state. To that end, we introduce rho-POMDPs, an extension of POMDPs where the reward function rho depends on the belief state. We show that, under the common assumption that rho is convex, the value function is also convex, what makes it possible to (1) approximate rho arbitrarily well with a piecewise linear and convex (PWLC) function, and (2) use state-of-the-art exact or approximate solving algorithms with limited changes.