In the real world, planning is often challenged by distribution shifts. As such, a model of the environment obtained under one set of conditions may no longer remain valid as the distribution of states or the environment dynamics change, which in turn causes previously learned strategies to fail. In this work, we propose a theoretical framework for planning under partial observability using Partially Observable Markov Decision Processes (POMDPs) formulated using causal knowledge. By representing shifts in the environment as interventions on this causal POMDP, the framework enables evaluating plans under hypothesized changes and actively identifying which components of the environment have been altered. We show how to maintain and update a belief over both the latent state and the underlying domain, and we prove that the value function remains piecewise linear and convex (PWLC) in this augmented belief space. Preservation of PWLC under distribution shifts has the advantage of maintaining the tractability of planning via α-vector-based POMDP methods.
Figures & tables
Figure 1: On the left is an example of a non–time-homogeneous causal POMDP. If the causal model is faithful, that is, every edge in the causal graph corresponds to an actual direct dependency between two variables, then any change in the graph structure across timesteps implies a change in the transition function. In the center is a CID that is compatible with a time-homogeneous causal POMDP. On the right is a compact representation of a time-homogeneous causal POMDP compatible with the CID shown in the center.
In many real-world planning tasks, agents must tackle uncertainty about the environment's state and variability in the outcomes of any chosen policy. We address both forms of uncertainty as a first step toward safer algorithms in partially observable settings. Specifically, we extend Distributional Reinforcement Learning (DistRL)-which models the entire return distribution for fully observable domains-to Partially Observable Markov Decision Processes (POMDPs), allowing an agent to learn the distribution of returns for each conditional plan. Concretely, we introduce new distributional Bellman operators for partial observability and prove their convergence under the supremum p-Wasserstein metric. We also propose a finite representation of these return distributions via psi-vectors, generalizing the classical alpha-vectors in POMDP solvers. Building on this, we develop Distributional Point-Based Value Iteration (DPBVI), which integrates psi-vectors into a standard point-based backup procedure-bridging DistRL and POMDP planning. By tracking return distributions, DPBVI lays the foundation for future risk-sensitive control in domains where rare, high-impact events must be carefully managed. We provide source code to foster further research in robust decision-making under partial observability.
Larry Preuett, Qiuyi Zhang, Muhammad Aurangzeb Ahmad
University of Washington, Tacoma, USA · Google DeepMind, California, USA · University of Washington, Bothell, USA
Partially observable Markov decision processes (POMDPs) offer a principled formalism for planning under state and transition uncertainty. Despite advances made towards solving large POMDPs, obtaining performant policies under limited planning time remains a major challenge due to the curse of dimensionality and the curse of history. For many POMDP problems, the value of information (VOI) - the expected performance gain from reasoning about observations - varies over the belief space. We introduce a dynamic programming framework that exploits this structure by conditionally processing observations based on the value of information at each belief. Building on this framework, we propose Value of Information Monte Carlo planning (VOIMCP), a Monte Carlo Tree Search algorithm that allocates computational effort more efficiently by selectively disregarding observation information when the VOI is low, avoiding unnecessary branching of observations. We provide theoretical guarantees on the near-optimality of our VOI reasoning framework and derive non-asymptotic convergence bounds for VOIMCP. Simulation evaluations demonstrate that VOIMCP outperforms baselines on several POMDP benchmarks.
Zakariya Laouar, Qi Heng Ho, Zachary Sunberg
Department of Aerospace Engineering Sciences, University of Colorado Boulder · Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech
Planning under uncertainty is an essential capability for autonomous robots. The Partially Observable Markov Decision Process (POMDP) provides a powerful framework for such a capability. Although POMDP-based planning has advanced significantly, its application to real-world problems is often limited by the difficulty of obtaining faithful POMDP models. We present Vectorized Online planning wIth Learned diffusion model for POMDP Agents (VOiLA), a framework that learns task-agnostic POMDP world models for online planning under uncertainty. Specifically, VOiLA learns transition and observation samplers using conditional diffusion models and observation-likelihood models for particle-based belief updates. To enable efficient online planning, the diffusion samplers are distilled into compact feedforward generators and integrated with Vectorized Online POMDP Planner (VOPP), an online POMDP planner designed to leverage GPU parallelization. Experimental results indicate the distillation strategy reduces sampling cost by up to nearly three orders of magnitude, making learned generative POMDP models practical for online planning. Evaluation of VOiLA on three benchmark problems indicates that VOiLA achieves equal or better performance than current reinforcement learning (RL) methods for POMDPs, such as Recurrent Soft Actor Critic and DreamerV3, while using less than 10% of the training data, and generalizes much better to unseen environment configurations. In a physical robot experiment, VOiLA accomplishes the task in 10 of 10 runs while using models learned purely from simulated data for online planning.
Marcus Hoerger, Rishikesh Joshi, Rahul Shome +2
Australian National University, Canberra, ACT, Australia · The University of Sydney, Sydney, NSW, Australia.