This paper considers the hidden-action model of the principal-agent problem, in which a principal incentivizes an agent to work on a project using a contract. We investigate whether contracts with bounded payments are learnable and approximately optimal. Our main results are two learning algorithms that can find a nearly optimal bounded contract using a polynomial number of queries, under two standard assumptions in the literature: a costlier action for the agent leads to a better outcome distribution for the principal, and the agent's cost/effort has diminishing returns. Our polynomial query complexity upper bound shows that standard assumptions are sufficient for achieving an exponential improvement upon the known lower bound for general instances. Unlike the existing algorithms, which relied on discretizing the contract space, our algorithms directly learn the underlying outcome distributions. As for the approximate optimality of bounded contracts, we find that they could be far from optimal in terms of multiplicative or additive approximation, but satisfy a notion of mixed approximation.

翻译：本文考虑委托-代理问题的隐藏行动模型，其中委托人通过合同激励代理人执行项目。我们研究具有支付上限的合同是否可学习且近似最优。主要贡献是提出了两种学习算法，在文献中的两个标准假设下（即代理人的成本更高行为会导致委托人收益分布更优，以及代理人成本/努力呈现边际递减效应），这些算法能够通过多项式次数的查询找到近乎最优的有界合同。我们的多项式查询复杂度上界表明，标准假设足以在一般实例中将已知下界实现指数级改进。与依赖合同空间离散化的现有算法不同，我们的算法直接学习底层收益分布。关于有界合同的近似最优性，我们发现其在乘法或加法近似方面可能远非最优，但满足一种混合近似概念。