# Hybrid Combinatorial Multi-armed Bandits with Probabilistically Triggered Arms

arXiv: https://arxiv.org/abs/2512.21925 · HTML: https://mlsanity.com/paper/2512.21925/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Prompt Cache: Modular Attention Reuse for Low-Latency Inference](https://mlsanity.com/paper/2311.04934/) (2023)
- [Offline-to-Online Reinforcement Learning via Balanced Replay and Pessimistic Q-Ensemble](https://mlsanity.com/paper/2107.00591/) (2021)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Mobile Edge Intelligence for Large Language Models: A Contemporary Survey](https://mlsanity.com/paper/2407.18921/) (2024)
- [Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms](https://mlsanity.com/paper/1407.8339/) (2014)
- [Improving Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms and Its Applications](https://mlsanity.com/paper/1703.01610/) (2017)
- [Adaptive Policy Learning for Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2303.07693/) (2023)
- [Offline Neural Contextual Bandits: Pessimism, Optimization and Generalization](https://mlsanity.com/paper/2111.13807/) (2021)
- [Pessimism for Offline Linear Contextual Bandits using ℓp Confidence Sets](https://mlsanity.com/paper/2205.10671/) (2022)
- [Contextual Combinatorial Bandits with Probabilistically Triggered Arms](https://mlsanity.com/paper/2303.17110/) (2023)
- [Reward-agnostic Fine-tuning: Provable Statistical Benefits of Hybrid Reinforcement Learning](https://mlsanity.com/paper/2305.10282/) (2023)
- [Batch-Size Independent Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms or Independent Arms](https://mlsanity.com/paper/2208.14837/) (2022)
- [Online Pricing with Offline Data: Phase Transition and Inverse Square Law](https://mlsanity.com/paper/1910.08693/) (2019)
- [Hybrid Transfer Reinforcement Learning: Provable Sample Efficiency from Shifted-Dynamics Data](https://mlsanity.com/paper/2411.03810/) (2024)
- [Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyond](https://mlsanity.com/paper/2406.01386/) (2024)
- [Data-pooling Reinforcement Learning for Personalized Healthcare Intervention](https://mlsanity.com/paper/2211.08998/) (2022)
- [Online Bandit Learning with Offline Preference Data for Improved RLHF](https://mlsanity.com/paper/2406.09574/) (2024)
- [Balancing optimism and pessimism in offline-to-online learning](https://mlsanity.com/paper/2502.08259/) (2025)
- [Offline Learning for Combinatorial Multi-armed Bandits](https://mlsanity.com/paper/2501.19300/) (2025)
- [Online Influence Maximization under Decreasing Cascade Model](https://mlsanity.com/paper/2305.15428/) (2023)

## Built on by (most cited first, 2 of 2)

- [Direction-Aware Offline-to-Online Learning in Linear Contextual Bandits](https://mlsanity.com/paper/2604.24016/) (2026)
- [Sample-Mean Anchored Thompson Sampling for Offline-to-Online Learning with Distribution Shift](https://mlsanity.com/paper/2605.10289/) (2026)

## Abstract (arXiv)

The problem of combinatorial multi-armed bandits with probabilistically triggered arms (CMAB-T) has been extensively studied. Prior work primarily focuses on either the online setting where an agent learns about the unknown environment through iterative interactions, or the offline setting where a policy is learned solely from logged data. However, each of these paradigms has inherent limitations: online algorithms suffer from high interaction costs and slow adaptation, while offline methods are constrained by dataset quality and lack of exploration capabilities. To address these complementary weaknesses, we propose hybrid CMAB-T, a new framework that integrates offline data with online interaction in a principled manner. Our proposed hybrid CUCB algorithm leverages offline data to guide exploration and accelerate convergence, while strategically incorporating online interactions to mitigate the insufficient coverage or distributional bias of the offline dataset. We provide theoretical guarantees on the algorithm's regret, demonstrating that hybrid CUCB significantly outperforms purely online approaches when high-quality offline data is available, and effectively corrects the bias inherent in offline-only methods when the data is limited or misaligned. Empirical results further demonstrate the consistent advantage of our algorithm.