Are Bounded Contracts Learnable and Approximately Optimal?
Yurong Chen Zhaohua Chen Xiaotie Deng Zhiyi Huang
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.