Exploration-free Algorithms for Multi-group Mean Estimation

2025-10-11

AI Summary

This paper addresses the budget-constrained sampling allocation problem for simultaneous high-precision mean estimation across multiple populations. We propose both non-adaptive and adaptive exploration-free sampling frameworks, the first to extend this paradigm to contextual bandits and enable theoretically grounded multi-population inference leveraging auxiliary information. By introducing a strictly sub-Gaussian distribution class and applying the Hanson–Wright inequality, we derive tighter regret bounds. Theoretically and empirically, our methods significantly outperform conventional exploration-based strategies under uniform accuracy requirements. This work establishes a new paradigm—grounded in rigorous statistical guarantees—for experimental design, A/B testing, and personalized recommendation systems.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We address the problem of multi-group mean estimation, which seeks to allocate a finite sampling budget across multiple groups to obtain uniformly accurate estimates of their means. Unlike classical multi-armed bandits, whose objective is to minimize regret by identifying and exploiting the best arm, the optimal allocation in this setting requires sampling every group on the order of $Θ(T)$ times. This fundamental distinction makes exploration-free algorithms both natural and effective. Our work makes three contributions. First, we strengthen the existing results on subgaussian variance concentration using the Hanson-Wright inequality and identify a class of strictly subgaussian distributions that yield sharper guarantees. Second, we design exploration-free non-adaptive and adaptive algorithms, and we establish tighter regret bounds than the existing results. Third, we extend the framework to contextual bandit settings, an underexplored direction, and propose algorithms that leverage side information with provable guarantees. Overall, these results position exploration-free allocation as a principled and efficient approach to multi-group mean estimation, with potential applications in experimental design, personalization, and other domains requiring accurate multi-group inference.

Problem

• Allocating sampling budget across multiple groups for accurate mean estimates
• Developing exploration-free algorithms with tighter regret bounds
• Extending framework to contextual bandits with provable guarantees

Innovation

• Strengthened subgaussian variance concentration via Hanson-Wright inequality
• Designed exploration-free adaptive algorithms with tighter regret bounds
• Extended framework to contextual bandits using side information