Fixed-Budget Constrained Best Arm Identification in Grouped Bandits

2026-03-04

AI Summary

This study addresses the fixed-budget best-arm identification problem in grouped multi-armed bandits under feasibility constraints: each arm is characterized by multiple independent attributes, and it is deemed feasible only if the mean of every attribute exceeds a given threshold. The goal is to identify, within a finite budget, the feasible arm with the highest overall mean reward. The authors establish the first information-theoretic lower bound on the error probability for this problem and propose the Feasibility Constrained Successive Rejects (FCSR) algorithm. FCSR integrates a successive-rejects strategy with rigorous feasibility testing, achieving optimal dependence on problem parameters as dictated by the lower bound. Empirical evaluations demonstrate that FCSR significantly outperforms existing baselines while strictly guaranteeing the feasibility of the selected arm.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study fixed budget constrained best-arm identification in grouped bandits, where each arm consists of multiple independent attributes with stochastic rewards. An arm is considered feasible only if all its attributes' means are above a given threshold. The aim is to find the feasible arm with the largest overall mean. We first derive a lower bound on the error probability for any algorithm on this setting. We then propose Feasibility Constrained Successive Rejects (FCSR), a novel algorithm that identifies the best arm while ensuring feasibility. We show it attains optimal dependence on problem parameters up to constant factors in the exponent. Empirically, FCSR outperforms natural baselines while preserving feasibility guarantees.

Problem

• best-arm identification
• grouped bandits
• fixed budget
• feasibility constraints
• stochastic rewards

Innovation

• Grouped Bandits
• Best Arm Identification
• Fixed Budget
• Feasibility Constraints
• Successive Rejects