Principal-agent problems model scenarios where a principal incentivizes an agent to take costly, unobservable actions through the provision of payments. Such problems are ubiquitous in several real-world applications, ranging from blockchain to the delegation of machine learning tasks. In this paper, we initiate the study of hidden-action principal-agent problems under approximate best responses, in which the agent may select any action that is not too much suboptimal given the principal's payment scheme (a.k.a. contract). Our main result is a polynomial-time algorithm to compute an optimal contract under approximate best responses. This positive result is perhaps surprising, since, in Stackelberg games, computing an optimal commitment under approximate best responses is computationally intractable. We also investigate the learnability of contracts under approximate best responses, by providing a no-regret learning algorithm for a natural application scenario where the principal has no prior knowledge about the environment.

翻译：委托代理问题模拟了委托人通过提供报酬激励代理人采取代价高昂且不可观察行为的场景。此类问题在从区块链到机器学习任务委托的多个现实应用中普遍存在。本文首次研究了近似最优响应下的隐藏行动委托代理问题，其中代理人可在给定委托人支付方案（即契约）下选择任何非过度次优的行动。我们的主要成果是提出了一个计算近似最优响应下最优契约的多项式时间算法。这一积极结果或许令人惊讶，因为在斯塔克尔伯格博弈中，计算近似最优响应下的最优承诺在计算上是不可行的。我们还通过为委托人缺乏环境先验知识的自然应用场景提供无遗憾学习算法，探讨了近似最优响应下契约的可学习性。