Are Bounded Contracts Learnable and Approximately Optimal?
This work addresses contract design in economics and AI, providing efficient learning methods for bounded contracts, though it is incremental as it builds on existing assumptions and models.
The paper tackles the problem of learning bounded contracts in the principal-agent hidden-action model, showing that under standard assumptions, two algorithms can find a nearly optimal bounded contract with polynomial query complexity, achieving an exponential improvement over known lower bounds.
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.