# Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyond

arXiv: https://arxiv.org/abs/2406.01386 · HTML: https://mlsanity.com/paper/2406.01386/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 37 of its 61 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 37)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Contextual Decision Processes with Low Bellman Rank are PAC-Learnable](https://mlsanity.com/paper/1610.09512/) (2016)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Tighter Problem-Dependent Regret Bounds in Reinforcement Learning without Domain Knowledge using Value Function Bounds](https://mlsanity.com/paper/1901.00210/) (2019)
- [Bilinear Classes: A Structural Framework for Provable Generalization in RL](https://mlsanity.com/paper/2103.10897/) (2021)
- [Unifying PAC and Regret: Uniform PAC Bounds for Episodic Reinforcement Learning](https://mlsanity.com/paper/1703.07710/) (2017)
- [Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs](https://mlsanity.com/paper/1905.03814/) (2019)
- [Is Reinforcement Learning More Difficult Than Bandits? A Near-optimal Algorithm Escaping the Curse of Horizon](https://mlsanity.com/paper/2009.13503/) (2020)
- [Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms](https://mlsanity.com/paper/1407.8339/) (2014)
- [Thompson Sampling for Combinatorial Semi-Bandits](https://mlsanity.com/paper/1803.04623/) (2018)
- [Cascading Bandits: Learning to Rank in the Cascade Model](https://mlsanity.com/paper/1502.02763/) (2015)
- [Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously](https://mlsanity.com/paper/1901.08779/) (2019)
- [Breaking the Sample Complexity Barrier to Regret-Optimal Model-Free Reinforcement Learning](https://mlsanity.com/paper/2110.04645/) (2021)
- [A Unifying View of Optimism in Episodic Reinforcement Learning](https://mlsanity.com/paper/2007.01891/) (2020)
- [UCB Momentum Q-learning: Correcting the bias without forgetting](https://mlsanity.com/paper/2103.01312/) (2021)
- [GEC: A Unified Framework for Interactive Decision Making in MDP, POMDP, and Beyond](https://mlsanity.com/paper/2211.01962/) (2022)
- [Improving Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms and Its Applications](https://mlsanity.com/paper/1703.01610/) (2017)
- [Settling the Sample Complexity of Online Reinforcement Learning](https://mlsanity.com/paper/2307.13586/) (2023)
- [Combinatorial Cascading Bandits](https://mlsanity.com/paper/1507.04208/) (2015)
- [Beyond Value-Function Gaps: Improved Instance-Dependent Regret Bounds for Episodic Reinforcement Learning](https://mlsanity.com/paper/2107.01264/) (2021)
- [Combinatorial semi-bandit with known covariance](https://mlsanity.com/paper/1612.01859/) (2016)
- [Maximize to Explore: One Objective Function Fusing Estimation, Planning, and Exploration](https://mlsanity.com/paper/2305.18258/) (2023)
- [Combinatorial Bandits with Relative Feedback](https://mlsanity.com/paper/1903.00543/) (2019)
- [A Framework for Adapting Offline Algorithms to Solve Combinatorial Multi-Armed Bandit Problems with Bandit Feedback](https://mlsanity.com/paper/2301.13326/) (2023)
- [Contextual Combinatorial Bandits with Probabilistically Triggered Arms](https://mlsanity.com/paper/2303.17110/) (2023)
- [Combinatorial Neural Bandits](https://mlsanity.com/paper/2306.00242/) (2023)
- [Batch-Size Independent Regret Bounds for Combinatorial Semi-Bandits with Probabilistically Triggered Arms or Independent Arms](https://mlsanity.com/paper/2208.14837/) (2022)

## Built on by (most cited first, 7 of 7)

- [Offline Learning for Combinatorial Multi-armed Bandits](https://mlsanity.com/paper/2501.19300/) (2025)
- [Near-Optimal Online Deployment and Routing for Streaming LLMs](https://mlsanity.com/paper/2506.17254/) (2025)
- [Hybrid Combinatorial Multi-armed Bandits with Probabilistically Triggered Arms](https://mlsanity.com/paper/2512.21925/) (2025)
- [Intelligent Channel Allocation for IEEE 802.11be Multi-Link Operation: When MAB Meets LLM](https://mlsanity.com/paper/2506.04594/) (2025)
- [DOPPLER: Dual-Policy Learning for Device Assignment in Asynchronous Dataflow Graphs](https://mlsanity.com/paper/2505.23131/) (2025)
- [Near-Optimal Regret for Efficient Stochastic Combinatorial Semi-Bandits](https://mlsanity.com/paper/2508.06247/) (2025)
- [ROAD: Adaptive Data Mixing for Offline-to-Online Reinforcement Learning via Bi-Level Optimization](https://mlsanity.com/paper/2605.14497/) (2026)

## Abstract (arXiv)

We introduce a novel framework of combinatorial multi-armed bandits (CMAB) with multivariant and probabilistically triggering arms (CMAB-MT), where the outcome of each arm is a d-dimensional multivariant random variable and the feedback follows a general arm triggering process. Compared with existing CMAB works, CMAB-MT not only enhances the modeling power but also allows improved results by leveraging distinct statistical properties for multivariant random variables. For CMAB-MT, we propose a general 1-norm multivariant and triggering probability-modulated smoothness condition, and an optimistic CUCB-MT algorithm built upon this condition. Our framework can include many important problems as applications, such as episodic reinforcement learning (RL) and probabilistic maximum coverage for goods distribution, all of which meet the above smoothness condition and achieve matching or improved regret bounds compared to existing works. Through our new framework, we build the first connection between the episodic RL and CMAB literature, by offering a new angle to solve the episodic RL through the lens of CMAB, which may encourage more interactions between these two important directions.