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arXiv2026

Contracting with an Agent under Model Mismatch

In the classical principal-agent setting, the principal delegates some task to the agent, who receives a payment conditioned on the outcome of the task, which in turn benefits the principal. To align their objectives, the principal designs a contract that incentivizes the agent to take actions beneficial to the principal. In practice, however, the agent may act under misspecified beliefs about the underlying environment, leading to systematically suboptimal decisions. In this work, we study this problem through a principal-agent Markov Decision Process (PAMDP), in which the principal repeatedly interacts with an agent whose transition model may differ from the true environment dynamics. The principal has access to the true transition model and designs contracts that account for the agent's belief and incentives. We characterize contract design under model mismatch and develop a framework that enables the principal to induce desirable long-term benefits even though the agent has a potentially inaccurate understanding of the environment.

cs.LG↗

arXiv2026

Two-Player Zero-Sum Games with Bandit Feedback

We study a two-player zero-sum game in which the row player aims to maximize their payoff against a competing column player, under an unknown payoff matrix estimated through bandit feedback. We propose three algorithms based on the Explore-Then-Commit (ETC) and action pair elimination frameworks. The first adapts it to zero-sum games, the second incorporates adaptive elimination that leverages the $\varepsilon$-Nash Equilibrium property to efficiently select the optimal action pair, and the third extends the elimination algorithm by employing non-uniform exploration. Our objective is to demonstrate the applicability of ETC and action pair elimination algorithms in a zero-sum game setting by focusing on learning pure strategy Nash Equilibria. A key contribution of our work is a derivation of instance-dependent upper bounds on the expected regret of our proposed algorithms, which has received limited attention in the literature on zero-sum games. Particularly, after $T$ rounds, we achieve an instance-dependent regret upper bounds of $O(Δ+ \sqrt{T})$ for ETC in zero-sum game setting and $O\left(\frac{\log (T Δ^2)}Δ\right)$ for the adaptive elimination algorithm and its variant with non-uniform exploration, where $Δ$ denotes the suboptimality gap. Therefore, our results indicate that the ETC and action pair elimination algorithms perform effectively in zero-sum game settings, achieving regret bounds comparable to existing methods while providing insight through instance-dependent analysis.

cs.LG↗