Geometry Meets Incentives: Sample-Efficient Incentivized Exploration with Linear Contexts

TL;DR

This paper introduces a geometric approach to incentivized exploration in linear bandits, enabling efficient, incentive-compatible learning with polynomial sample complexity under mild conditions.

Contribution

It demonstrates that geometric conditions on action sets can eliminate exponential sample complexity barriers in incentivized exploration.

Findings

Sample complexity scales polynomially with dimension under geometric conditions.

Incentive-compatible algorithms achieve near-optimal regret efficiently.

Barriers to exploration are overcome with mild geometric assumptions.

Abstract

In the incentivized exploration model, a principal aims to explore and learn over time by interacting with a sequence of self-interested agents. It has been recently understood that the main challenge in designing incentive-compatible algorithms for this problem is to gather a moderate amount of initial data, after which one can obtain near-optimal regret via posterior sampling. With high-dimensional contexts, however, this \emph{initial exploration} phase requires exponential sample complexity in some cases, which prevents efficient learning unless initial data can be acquired exogenously. We show that these barriers to exploration disappear under mild geometric conditions on the set of available actions, in which case incentive-compatibility does not preclude regret-optimality. Namely, we consider the linear bandit model with actions in the Euclidean unit ball, and give an incentive-compatible exploration algorithm with sample complexity that scales polynomially with the dimension and other parameters.