# Budgeted Combinatorial Multi-Armed Bandits

arXiv: https://arxiv.org/abs/2202.03704 · HTML: https://mlsanity.com/paper/2202.03704/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Thompson Sampling for Combinatorial Semi-Bandits](https://mlsanity.com/paper/1803.04623/) (2018)
- [Efficient Learning in Large-Scale Combinatorial Semi-Bandits](https://mlsanity.com/paper/1406.7443/) (2014)
- [Budget-Constrained Multi-Armed Bandits with Multiple Plays](https://mlsanity.com/paper/1711.05928/) (2017)
- [An Optimal Bidimensional Multi-Armed Bandit Auction for Multi-unit Procurement](https://mlsanity.com/paper/1502.06934/) (2015)
- [A Multi-Arm Bandit Approach To Subset Selection Under Constraints](https://mlsanity.com/paper/2102.04824/) (2021)
- [Bandit-Based Task Assignment for Heterogeneous Crowdsourcing](https://mlsanity.com/paper/1507.05800/) (2015)
- [Bandit Data-Driven Optimization](https://mlsanity.com/paper/2008.11707/) (2020)

## Built on by (most cited first, 6 of 6)

- [Learning to Schedule Online Tasks with Bandit Feedback](https://mlsanity.com/paper/2402.16463/) (2024)
- [Balancing Risk and Reward: An Automated Phased Release Strategy](https://mlsanity.com/paper/2305.09626/) (2023)
- [Stochastic Multi-round Submodular Optimization with Budget](https://mlsanity.com/paper/2404.13737/) (2024)
- [Finite-Time Guarantees for Multi-Agent Combinatorial Bandits with Nonstationary Rewards](https://mlsanity.com/paper/2508.20923/) (2025)
- [DARTS: Targeting Prognostic Covariates in Budget-Constrained Sequential Experiments](https://mlsanity.com/paper/2605.06608/) (2026)
- [Cost of Structural Learning Under Censored Feedback: A Threshold-Bandit Approach](https://mlsanity.com/paper/2605.27076/) (2026)

## Abstract (arXiv)

We consider a budgeted combinatorial multi-armed bandit setting where, in every round, the algorithm selects a super-arm consisting of one or more arms. The goal is to minimize the total expected regret after all rounds within a limited budget. Existing techniques in this literature either fix the budget per round or fix the number of arms pulled in each round. Our setting is more general where based on the remaining budget and remaining number of rounds, the algorithm can decide how many arms to be pulled in each round. First, we propose CBwK-Greedy-UCB algorithm, which uses a greedy technique, CBwK-Greedy, to allocate the arms to the rounds. Next, we propose a reduction of this problem to Bandits with Knapsacks (BwK) with a single pull. With this reduction, we propose CBwK-LPUCB that uses PrimalDualBwK ingeniously. We rigorously prove regret bounds for CBwK-LP-UCB. We experimentally compare the two algorithms and observe that CBwK-Greedy-UCB performs incrementally better than CBwK-LP-UCB. We also show that for very high budgets, the regret goes to zero.