A Point-Based Algorithm for Distributional Reinforcement Learning in Partially Observable Domains (2505.06518v1)

Abstract: 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 naturally enables 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.

A Point-Based Algorithm for Distributional Reinforcement Learning in Partially Observable Domains

The paper "A Point-Based Algorithm for Distributional Reinforcement Learning in Partially Observable Domains" presents a substantial contribution to the field of Reinforcement Learning (RL), extending the Distributional Reinforcement Learning (DistRL) framework to Partially Observable Markov Decision Processes (POMDPs). This research offers a sophisticated analysis and a proposed algorithm for handling both outcome variability and environmental uncertainty inherent in POMDPs.

Key Contributions

The paper delineates several key contributions that integrate distributional methods into the POMDP framework, as outlined below:

1. Contraction Properties of Distributional Operators: The authors prove that both the distributional partially observable evaluation operator and the optimality operator are $\gamma$-contractions under the supremum p-Wasserstein metric. This extends the existing DistRL results from fully observable Markov Decision Processes (MDPs) to POMDPs. The implication here is significant as it ensures convergence to a unique fixed point in risk-neutral settings, confirming the robustness of this extension.
2. Introduction of $\psi$-Vectors: In parallel to classical $\alpha$-vectors used in POMDPs, the authors introduce $\psi$-vectors as distributional analogs. They demonstrate that a finite set of these $\psi$-vectors is sufficient to represent the optimal distributional value function under risk-neutral objectives. This ensures that the computational complexity remains tractable while maintaining a piecewise linear and convex structure in the Wasserstein metric space.
3. Development of the Distributional Point-Based Value Iteration (DPBVI): The authors propose the DPBVI algorithm, which adapts the classical Point-Based Value Iteration (PBVI) by employing a distributional perspective. By substituting $\alpha$-vectors with $\psi$-vectors, DPBVI learns a finite representation of the optimal distributional value function while preserving the key aspects of the point-based backup structure. This novel approach unifies DistRL and POMDP planning, enabling a computationally feasible framework.
4. Risk-Neutral Policy Recovery: The paper asserts that in a risk-neutral setting, DPBVI's $\psi$-vectors are capable of recovering the same policy as classical PBVI by matching its value function in expectation. This argument is backed by releasing open-source code to facilitate reproducibility and further exploration of risk-aware decision-making in POMDPs.

Implications and Future Directions

The extension of DistRL into partially observable settings equips agents with enhanced capabilities to handle uncertainty and risk more effectively in complex real-world scenarios. By capturing the full distribution of potential returns rather than just the expectation, decision policies can be more robust, particularly when managing rare but high-impact events.

The theoretical implications presented in this paper, especially regarding the convergence properties of distributional operators, open new avenues for applying RL in domains where risk-sensitive control is paramount. In practical terms, this could be transformative for areas such as autonomous navigation, healthcare, and any domain requiring high-stakes decision-making under uncertainty.

Future research might focus on further optimizing DPBVI for efficiency, potentially developing risk-sensitive versions of the algorithm that accommodate diverse utility functions. Moreover, exploring practical applications and scalability in larger POMDP environments can test the robustness and general applicability of the proposed methods.

In conclusion, this paper contributes a vital theoretical and computational toolset for advancing RL in partially observable domains, setting the stage for future innovations in safer and more effective decision-making algorithms in uncertain environments.