Pessimistic Minimax Learning for Public-Private Information Games under Unilateral Coverage

2026-10-04

AI Summary

This study addresses the absence of a theoretical framework for offline equilibrium learning in zero-sum games with public and private information. To this end, it introduces the concept of one-sided coverability and constructs a Pessimistic Policy Mirror Descent (PPA-PMD) framework based on pessimistic estimation and function approximation to achieve no-regret policy updates. This work establishes the first theory for offline equilibrium learning under asymmetric information constraints, revealing how such asymmetry influences data coverage mechanisms. Furthermore, it demonstrates that the proposed method attains an exploitability rate of $\tilde{O}(1/\sqrt{n})$, matching the convergence speed of fully observable games and thereby unifying the theoretical bounds.

Abstract

We study offline learning in two-player zero-sum contextual games with public and private information, motivated by strategic settings such as auctions and negotiations with private valuations. We introduce unilateral prescriptive concentrability and show that asymmetric information can change offline coverage through its effect on equilibrium behavior. For finite state-action spaces, we develop a pessimistic algorithm with an $\tilde{O}(1/\sqrt{n})$ exploitability rate, matching the standard sample-size dependence for fully observed minimax games. We further develop a pessimistic policy mirror descent framework, PPA-PMD, for general function approximation and obtain a unified $\tilde{O}(1/\sqrt{n} + 1/\sqrt{T})$ exploitability rate with no-regret actor updates. Together, these results provide the first theoretical framework for offline equilibrium learning under public-private information constraints.

Problem

• offline learning
• zero-sum contextual games
• public-private information
• asymmetric information
• equilibrium learning

Innovation

• Offline Learning
• Pessimistic Minimax
• Public-Private Information Games
• Policy Mirror Descent
• Unilateral Prescriptive Concentrability