# Incentivized Lipschitz Bandits

arXiv: https://arxiv.org/abs/2508.19466 · HTML: https://mlsanity.com/paper/2508.19466/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Stochastic bandits robust to adversarial corruptions](https://mlsanity.com/paper/1803.09353/) (2018)
- [Bandits and Experts in Metric Spaces](https://mlsanity.com/paper/1312.1277/) (2013)
- [Bayesian Incentive-Compatible Bandit Exploration](https://mlsanity.com/paper/1502.04147/) (2015)
- [The Price of Incentivizing Exploration: A Characterization via Thompson Sampling and Sample Complexity](https://mlsanity.com/paper/2002.00558/) (2020)
- [The Intrinsic Robustness of Stochastic Bandits to Strategic Manipulation](https://mlsanity.com/paper/1906.01528/) (2019)
- [Multi-armed Bandits with Compensation](https://mlsanity.com/paper/1811.01715/) (2018)
- [Bayesian Exploration with Heterogeneous Agents](https://mlsanity.com/paper/1902.07119/) (2019)
- [Incentivizing Exploration with Heterogeneous Value of Money](https://mlsanity.com/paper/1512.08427/) (2015)
- [Optimal Algorithm for Bayesian Incentive-Compatible Exploration](https://mlsanity.com/paper/1810.10304/) (2018)
- [Incentivized Exploration for Multi-Armed Bandits under Reward Drift](https://mlsanity.com/paper/1911.05142/) (2019)
- [Learning User Preferences to Incentivize Exploration in the Sharing Economy](https://mlsanity.com/paper/1711.08331/) (2017)
- [Incentivized Exploration of Non-Stationary Stochastic Bandits](https://mlsanity.com/paper/2403.10819/) (2024)

## Built on by (most cited first, 2 of 2)

- [Multi-Agent Lipschitz Bandits](https://mlsanity.com/paper/2602.16965/) (2026)
- [Learning from Local Walks on Dynamic Graphs with Bandit Feedback](https://mlsanity.com/paper/2607.10571/) (2026)

## Abstract (arXiv)

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 TildeO(Td+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.