The Sample Complexity of Stackelberg Games

TL;DR

This paper investigates the sample complexity of learning optimal strategies in Stackelberg games, introducing a novel algorithm that manages trade-offs between sample size and strategy precision without restrictive assumptions.

Contribution

It presents a new algorithm for learning in Stackelberg games that handles finite precision trade-offs and relaxes previous assumptions, advancing practical applicability.

Findings

The algorithm avoids exponential sample complexity under finite precision.

It introduces techniques to balance sample size and strategy accuracy.

The approach generalizes to other commitment-based models.

Abstract

Stackelberg games (SGs) constitute the most fundamental and acclaimed models of strategic interactions involving some form of commitment. Moreover, they form the basis of more elaborate models of this kind, such as, e.g., Bayesian persuasion and principal-agent problems. Addressing learning tasks in SGs and related models is crucial to operationalize them in practice, where model parameters are usually unknown. In this paper, we revise the sample complexity of learning an optimal strategy to commit to in SGs. We provide a novel algorithm that (i) does not require any of the limiting assumptions made by state-of-the-art approaches and (ii) deals with a trade-off between sample complexity and termination probability arising when leader's strategies representation has finite precision. Such a trade-off has been completely neglected by existing algorithms and, if not properly managed, it may result in them using exponentially-many samples. Our algorithm requires novel techniques, which also pave the way to addressing learning problems in other models with commitment ubiquitous in the real world.