Incentivized Lipschitz Bandits

TL;DR

This paper introduces incentivized exploration algorithms for continuous-armed bandits that balance regret minimization and compensation costs, extending to contextual settings with theoretical guarantees and simulations.

Contribution

It presents novel algorithms for incentivized exploration in infinite and contextual bandits, achieving sublinear regret and compensation bounds in continuous metric spaces.

Findings

Algorithms achieve sublinear regret and compensation.

Theoretical bounds depend on the metric space dimension.

Results extend to contextual bandit scenarios.

Abstract

We study incentivized exploration in multi-armed bandit (MAB) settings with infinitely many arms modeled as elements in continuous metric spaces. Unlike classical bandit models, we consider scenarios where the decision-maker (principal) incentivizes myopic agents to explore beyond their greedy choices through compensation, but with the complication of reward drift--biased feedback arising due to the incentives. We propose novel incentivized exploration algorithms that discretize the infinite arm space uniformly and demonstrate that these algorithms simultaneously achieve sublinear cumulative regret and sublinear total compensation. Specifically, we derive regret and compensation bounds of $\Tilde{O}(T^{d+1/d+2})$, with $d$ representing the covering dimension of the metric space. Furthermore, we generalize our results to contextual bandits, achieving comparable performance guarantees. We validate our theoretical findings through numerical simulations.