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

arXiv: https://arxiv.org/abs/2610.04997 · HTML: https://mlsanity.com/paper/2610.04997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 30 of 35)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism](https://mlsanity.com/paper/2203.05804/) (2022)
- [Plan Better Amid Conservatism: Offline Multi-Agent Reinforcement Learning with Actor Rectification](https://mlsanity.com/paper/2111.11188/) (2021)
- [Contrasting Centralized and Decentralized Critics in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2102.04402/) (2021)
- [Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets](https://mlsanity.com/paper/2202.07511/) (2022)
- [Provably Efficient Offline Multi-agent Reinforcement Learning via Strategy-wise Bonus](https://mlsanity.com/paper/2206.00159/) (2022)
- [The ODE Method for Stochastic Approximation and Reinforcement Learning with Markovian Noise](https://mlsanity.com/paper/2401.07844/) (2024)
- [Offline Learning in Markov Games with General Function Approximation](https://mlsanity.com/paper/2302.02571/) (2023)
- [Efficient Policy Evaluation with Offline Data Informed Behavior Policy Design](https://mlsanity.com/paper/2301.13734/) (2023)
- [Sample Complexity of Posted Pricing for a Single Item](https://mlsanity.com/paper/2406.00819/) (2024)
- [Beyond Pessimism: Offline Learning in KL-regularized Games](https://mlsanity.com/paper/2604.06738/) (2026)
- [Efficient Multi-Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/2408.08706/) (2024)
- [Off-the-Grid MARL: Datasets with Baselines for Offline Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2302.00521/) (2023)
- [Doubly Optimal Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/2410.02226/) (2024)
- [Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2604.09855/) (2026)
- [Efficient Policy Evaluation with Safety Constraint for Reinforcement Learning](https://mlsanity.com/paper/2410.05655/) (2024)
- [Offline Two-Player Zero-Sum Markov Games with KL Regularization](https://mlsanity.com/paper/2605.13025/) (2026)
- [Pessimism-Free Offline Learning in General-Sum Games via KL Regularization](https://mlsanity.com/paper/2605.00264/) (2026)
- [Fast Rates in α-Potential Games via Regularized Mirror Descent](https://mlsanity.com/paper/2605.00268/) (2026)
- [Beyond Linear Attention: Softmax Transformers Implement In-Context Reinforcement Learning](https://mlsanity.com/paper/2605.07333/) (2026)

## Abstract (arXiv)

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 tildeO(1/√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 tildeO(1/√n + 1/√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.