We study a repeated Principal Agent problem between a long lived Principal and Agent pair in a prior free setting. In our setting, the sequence of realized states of nature may be adversarially chosen, the Agent is non-myopic, and the Principal aims for a strong form of policy regret. Following Camara, Hartline, and Johnson, we model the Agent's long-run behavior with behavioral assumptions that relax the common prior assumption (for example, that the Agent has no swap regret). Within this framework, we revisit the mechanism proposed by Camara et al., which informally uses calibrated forecasts of the unknown states of nature in place of a common prior. We give two main improvements. First, we give a mechanism that has an exponentially improved dependence (in terms of both running time and regret bounds) on the number of distinct states of nature. To do this, we show that our mechanism does not require truly calibrated forecasts, but rather forecasts that are unbiased subject to only a polynomially sized collection of events -- which can be produced with polynomial overhead. Second, in several important special cases -- including the focal linear contracting setting -- we show how to remove strong ``Alignment'' assumptions (which informally require that near-ties are always broken in favor of the Principal) by specifically deploying ``stable'' policies that do not have any near ties that are payoff relevant to the Principal. Taken together, our new mechanism makes the compelling framework proposed by Camara et al. much more powerful, now able to be realized over polynomially sized state spaces, and while requiring only mild assumptions on Agent behavior.

翻译：本文研究长期委托人与代理人之间在无先验设定下的重复委托代理问题。在该设定中，自然状态序列可由对抗性方式选择，代理人具有非短视特性，而委托人追求强形式的策略后悔最小化。遵循Camara、Hartline和Johnson的研究方法，我们采用放松公共先验假设的行为假设（例如代理人无交换后悔）来建模代理人的长期行为。在此框架下，我们重新审视了Camara等人提出的机制——该机制非正式地使用未知自然状态的校准预测来替代公共先验。我们提出两项主要改进：第一，我们给出一种新机制，在自然状态数目维度上实现了指数级依赖关系改进（包括运行时间与后悔界）。为此，我们证明该机制无需真正校准的预测，而仅需对多项式规模事件集合保持无偏性——此类预测可通过多项式开销生成。第二，在若干重要特例中（包括焦点线性契约设定），我们展示了如何通过专门部署无接近平局状态（即对委托人收益无影响的接近平局情况）的"稳定"策略，移除强"对齐"假设（该假设非正式要求接近平局始终以委托人优先解决）。综合而言，新机制显著增强了Camara等人提出的框架能力，现在可在多项式规模状态空间中实现，且仅需对代理人行为施加温和假设。