Alternative compressed environments yielding improved regret bounds for Compressed-MAIDS

Construct compressed environments for Information-Directed Sampling in two-player zero-sum Markov games that satisfy either the expectation-based distortion constraint E[d_{Φ_A, Φ_B}(E, \tilde{E})] ≤ ε or the almost-sure distortion constraint P(d_{Φ_A, Φ_B}(E, \tilde{E}) > ε) = 0, and demonstrate that such constructions lead to Bayesian regret bounds strictly better than those obtained using the current hard-compression partition-based approach.

Background

The paper introduces Compressed-MAIDS, which leverages compressed environments as learning targets to improve sample efficiency. Two compression principles are presented: soft-compression (expectation-constrained distortion) and hard-compression (almost-sure distortion constraint). A regret bound is proved under a specific hard-compression construction based on partitioning the environment space by covering numbers.

The authors note that their particular hard-compression construction may not be optimal and conjecture the existence of alternative compressed environments—still meeting the defined distortion constraints—that yield better regret bounds. Establishing such constructions would refine the theoretical performance of IDS-based MARL and potentially reduce dependencies on state/action cardinalities and horizon.