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

2025-06-02

AI Summary

This paper addresses incentive-compatible sequential exploration in high-dimensional linear environments with self-interested agents, aiming to overcome the exponential sample complexity bottleneck imposed by initial data collection. Conventional approaches face a fundamental tension between incentive compatibility and low regret, resulting in poor sample efficiency. We first identify the critical role of the action set’s geometric structure (e.g., the unit ball) and prove that it decouples the trade-off between incentive compatibility and optimal regret. Building on this insight, we propose the first algorithm that simultaneously achieves strict incentive compatibility and polynomial sample complexity—specifically, $O(mathrm{poly}(d))$—by integrating linear contextual bandits, posterior sampling, and geometry-driven mechanism design. Our method breaks the exponential lower bound barrier and provides the first computationally efficient, incentive-aware exploration framework for high-dimensional settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Incentivized exploration with self-interested agents in linear contexts
• Overcoming exponential sample complexity in high-dimensional initial exploration
• Achieving regret-optimality under mild geometric action set conditions

Innovation

• Incentive-compatible algorithm for linear bandits
• Polynomial sample complexity in high dimensions
• Geometric conditions enable efficient exploration