Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918264857165824 |
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| author | Ye, Zichun Wang, Runqi Liu, Xutong Li, Shuai |
| author_facet | Ye, Zichun Wang, Runqi Liu, Xutong Li, Shuai |
| contents | 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 $O\big( (\log k)\sqrt{kmT}\big )$ when $k\leq \frac{m}{2}$ and $O\big((m-k)\sqrt{\log k\log(m-k)T}\big )$ when $k>\frac{m}{2}$ 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 lower bounds of $Ω\big(\sqrt{kmT}\big)$ when $k\leq \frac{m}{2}$ and $Ω\big((m-k)\sqrt{\log (\frac{m}{m-k}) T}\big)$ when $k>\frac{m}{2}$ up to logarithmic terms of $k$ and $m$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits Ye, Zichun Wang, Runqi Liu, Xutong Li, Shuai Machine Learning Data Structures and Algorithms 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 $O\big( (\log k)\sqrt{kmT}\big )$ when $k\leq \frac{m}{2}$ and $O\big((m-k)\sqrt{\log k\log(m-k)T}\big )$ when $k>\frac{m}{2}$ 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 lower bounds of $Ω\big(\sqrt{kmT}\big)$ when $k\leq \frac{m}{2}$ and $Ω\big((m-k)\sqrt{\log (\frac{m}{m-k}) T}\big)$ when $k>\frac{m}{2}$ up to logarithmic terms of $k$ and $m$. 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. |
| title | Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2508.06247 |