mlsanityData to 14 Oct 2026

Batch-Size Independent Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms or Independent Arms

arXiv 2208.14837 ↗First posted 31 Aug 2022cs.LG cs.AI stat.MLcited by 15

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Abstract (arXiv)

In this paper, we study the combinatorial semi-bandits (CMAB) and focus on reducing the dependency of the batch-size K in the regret bound, where K is the total number of arms that can be pulled or triggered in each round. First, for the setting of CMAB with probabilistically triggered arms (CMAB-T), we discover a novel (directional) triggering probability and variance modulated (TPVM) condition that can replace the previously-used smoothness condition for various applications, such as cascading bandits, online network exploration and online influence maximization. Under this new condition, we propose a BCUCB-T algorithm with variance-aware confidence intervals and conduct regret analysis which reduces the O(K) factor to O(log K) or O(log2 K) in the regret bound, significantly improving the regret bounds for the above applications. Second, for the setting of non-triggering CMAB with independent arms, we propose a SESCB algorithm which leverages on the non-triggering version of the TPVM condition and completely removes the dependency on K in the leading regret. As a valuable by-product, the regret analysis used in this paper can improve several existing results by a factor of O(log K). Finally, experimental evaluations show our superior performance compared with benchmark algorithms in different applications.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 15 of its 35 references that are in the map. First posted on arXiv 31 Aug 2022.

Builds on

15 of 35 references.

References · 15

  1. 2020Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processescited by 200
  2. 2014Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Armscited by 79
  3. 2018Thompson Sampling for Combinatorial Semi-Banditscited by 78
  4. 2015Cascading Bandits: Learning to Rank in the Cascade Modelcited by 77
  5. 2017Improving Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms and Its Applicationscited by 45
  6. 2021Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDPcited by 45
  7. 2015Combinatorial Cascading Banditscited by 40
  8. 2016Combinatorial semi-bandit with known covariancecited by 24
  9. 2020Online Influence Maximization under Linear Threshold Modelcited by 17
  10. 2020Tight Lower Bounds for Combinatorial Multi-Armed Banditscited by 15
  11. 2019Batch-Size Independent Regret Bounds for the Combinatorial Multi-Armed Bandit Problemcited by 14
  12. 2020Statistically Efficient, Polynomial Time Algorithms for Combinatorial Semi Banditscited by 11
3 more
  1. 2022Minimax Regret for Cascading Banditscited by 10
  2. 2021Multi-layered Network Exploration via Random Walks: From Offline Optimization to Online Learningcited by 6
  3. 2014Tight Regret Bounds for Stochastic Combinatorial Semi-Banditscited by 2

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Citing papers per year: 2023: 3; 2024: 5; 2025: 7.

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  1. 2024Cost-Effective Online Multi-LLM Selection with Versatile Reward Modelscited by 39
  2. 2023Contextual Combinatorial Bandits with Probabilistically Triggered Armscited by 18
  3. 2025Semantic Caching for Low-Cost LLM Serving: From Offline Learning to Online Adaptationcited by 13
  4. 2024Effective Off-Policy Evaluation and Learning in Contextual Combinatorial Banditscited by 8
  5. 2024Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyondcited by 7
  6. 2024Federated Contextual Cascading Bandits with Asynchronous Communication and Heterogeneous Userscited by 6
  7. 2025Offline Learning for Combinatorial Multi-armed Banditscited by 5
  8. 2023Online Corrupted User Detection and Regret Minimizationcited by 3
  9. 2024Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Banditscited by 3
  10. 2025Hybrid Combinatorial Multi-armed Bandits with Probabilistically Triggered Armscited by 2
  11. 2025A Unified Online-Offline Framework for Co-Branding Campaign Recommendationscited by 1
  12. 2025LLM Cache Bandit Revisited: Addressing Query Heterogeneity for Cost-Effective LLM Inferencecited by 1
3 more
  1. 2023Online Influence Maximization: Concept and Algorithmcited by 0
  2. 2025Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Banditscited by 0
  3. 2025Online Learning to Rank under Corruption: A Robust Cascading Bandits Approachcited by 0