Efficient Matroid Bandit Linear Optimization Leveraging Unimodality

2025-11-29

AI Summary

For combinatorial semi-bandit problems under matroid constraints, state-of-the-art optimal-regret algorithms suffer from high computational complexity due to frequent membership oracle calls—rendering them impractical for large-scale or costly matroids (e.g., diversity-driven online recommendation). This work is the first to identify and exploit an inherent unimodal structure in the problem, proposing a novel learning framework based on unimodal search. Our approach reduces membership oracle queries to $O(log log T)$ while preserving near-optimal regret of $ ilde{O}(sqrt{T})$, matching the information-theoretic lower bound up to logarithmic factors. By integrating ideas from combinatorial optimization and stochastic optimization, the method significantly alleviates reliance on expensive oracle evaluations. Experiments demonstrate that our algorithm achieves regret comparable to the best existing methods, yet with drastically reduced oracle query overhead and runtime.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• 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
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We study the combinatorial semi-bandit problem under matroid constraints. The regret achieved by recent approaches is optimal, in the sense that it matches the lower bound. Yet, time complexity remains an issue for large matroids or for matroids with costly membership oracles (e.g. online recommendation that ensures diversity). This paper sheds a new light on the matroid semi-bandit problem by exploiting its underlying unimodal structure. We demonstrate that, with negligible loss in regret, the number of iterations involving the membership oracle can be limited to mathcal{O}(log log T)$. This results in an overall improved time complexity of the learning process. Experiments conducted on various matroid benchmarks show (i) no loss in regret compared to state-of-the-art approaches; and (ii) reduced time complexity and number of calls to the membership oracle.

Problem

• Optimizes combinatorial semi-bandit learning under matroid constraints
• Reduces time complexity by limiting membership oracle calls
• Exploits unimodal structure to maintain near-optimal regret performance

Innovation

• Exploits unimodal structure for efficiency
• Limits oracle calls to log-log scale
• Maintains optimal regret with reduced complexity