Identifying All ε-Best Arms in (Misspecified) Linear Bandits

2025-09-29

AI Summary

In high-cost exploration settings—such as drug discovery—efficiently identifying all ε-optimal arms in linear stochastic bandits is critical yet challenging. Method: We propose LinFACT, the first algorithm for ε-optimal arm identification in linear bandits that achieves instance optimality. It establishes a novel information-theoretic lower bound on sample complexity under the linear bandit model and integrates this bound into an adaptive sampling framework. The resulting algorithm yields a matching upper bound on sample complexity, accommodates model misspecification, and extends naturally to generalized linear models. Results: LinFACT’s termination time is governed by an information bottleneck, achieving sample complexity optimal up to logarithmic factors. Experiments on synthetic benchmarks and real-world drug discovery datasets demonstrate that LinFACT identifies more high-quality candidates at significantly lower sampling cost, substantially improving early-stage exploration efficiency.

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

Problem

• Identifying near-optimal arms in linear bandits efficiently
• Optimizing sample complexity for multi-candidate selection tasks
• Addressing model misspecification in generalized linear bandits

Innovation

• LinFACT algorithm identifies near-optimal arms efficiently
• Matches information-theoretic lower bound for sample complexity
• Extends analysis to misspecified and generalized linear models