Optimal dependence on S, A, and H in MAIL sample complexity

Characterize the optimal dependence on the state-space size S, action-space size(s) A (or A_max), and horizon H in the sample complexity guarantees of Multi-Agent Imitation Learning algorithms that learn ε-approximate Nash equilibria in finite-horizon two-player zero-sum Markov games.

Background

The paper establishes rate-optimal ε-dependence for both non-interactive and interactive MAIL, but leaves unanswered how other fundamental problem parameters influence optimal sample complexity.

Determining tight dependence on S, A, and H would refine theoretical guarantees and inform practical algorithm design, revealing whether current bounds are optimal or improvable along these dimensions.