The Limits of Pure Exploration in POMDPs: When the Observation Entropy is Enough
This work addresses a gap in pure exploration for POMDPs, relevant to domains like finance and robotics, but it is incremental as it adapts existing state entropy methods to partial observability.
The paper tackles state entropy maximization in partially observable Markov decision processes (POMDPs) by proposing to maximize observation entropy instead, providing theoretical bounds on the approximation error and a regularization method to improve performance.
The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.