Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits

2025-08-08

AI Summary

In combinatorial multi-armed bandits (CMAB), UCB-type algorithms incur an undesirable $O(log T)$ regret overhead, while adversarial approaches (e.g., EXP3.M) suffer from excessive computational cost. Method: This paper proposes an efficient randomized combinatorial semi-bandit decision framework and the CMOSS algorithm, which innovatively integrates combinatorial optimization, stochastic modeling, and a hybrid semi-/cascade feedback mechanism, grounded in a minimax-optimal strategy design. Contribution/Results: CMOSS guarantees polynomial-time solvability while completely eliminating the $log T$ factor in regret. Its cumulative regret is theoretically bounded by $Oig((log k)^2 sqrt{kmT}ig)$, nearly matching the lower bound $Omega(sqrt{kmT})$. Extensive experiments on synthetic and real-world datasets demonstrate that CMOSS significantly outperforms baseline methods—including UCB variants and EXP3.M—in both regret performance and computational efficiency.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Combinatorial Optimization
• 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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The combinatorial multi-armed bandit (CMAB) is a cornerstone of sequential decision-making framework, dominated by two algorithmic families: UCB-based and adversarial methods such as follow the regularized leader (FTRL) and online mirror descent (OMD). However, prominent UCB-based approaches like CUCB suffer from additional regret factor $log T$ that is detrimental over long horizons, while adversarial methods such as EXP3.M and HYBRID impose significant computational overhead. To resolve this trade-off, we introduce the Combinatorial Minimax Optimal Strategy in the Stochastic setting (CMOSS). CMOSS is a computationally efficient algorithm that achieves an instance-independent regret of $Oig( (log k)^2sqrt{kmT}ig )$ under semi-bandit feedback, where $m$ is the number of arms and $k$ is the maximum cardinality of a feasible action. Crucially, this result eliminates the dependency on $log T$ and matches the established $Ωig( sqrt{kmT}ig)$ lower bound up to $Oig((log k)^2ig)$. We then extend our analysis to show that CMOSS is also applicable to cascading feedback. Experiments on synthetic and real-world datasets validate that CMOSS consistently outperforms benchmark algorithms in both regret and runtime efficiency.

Problem

• Resolves computational inefficiency in combinatorial bandits
• Eliminates detrimental logarithmic regret factor dependency
• Achieves near-optimal regret with semi-bandit feedback

Innovation

• CMOSS algorithm eliminates logarithmic regret dependency
• Achieves near-optimal regret with computational efficiency
• Extends to cascading feedback with proven performance