# Multi-armed Bandits with Cost Subsidy

arXiv: https://arxiv.org/abs/2011.01488 · HTML: https://mlsanity.com/paper/2011.01488/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

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

- [Cost Aware Best Arm Identification](https://mlsanity.com/paper/2402.16710/) (2024)
- [Confidence-Budget Matching for Sequential Budgeted Learning](https://mlsanity.com/paper/2102.03400/) (2021)
- [The Survival Bandit Problem](https://mlsanity.com/paper/2206.03019/) (2022)
- [Balancing Performance and Costs in Best Arm Identification](https://mlsanity.com/paper/2505.20583/) (2025)
- [Bayesian Optimization for Unknown Cost-Varying Variable Subsets with No-Regret Costs](https://mlsanity.com/paper/2412.15863/) (2024)
- [Budget-Constrained Causal Bandits: Bridging Uplift Modeling and Sequential Decision-Making](https://mlsanity.com/paper/2604.26169/) (2026)
- [Cost-Ordered Feasibility for Multi-Armed Bandits with Cost Subsidy](https://mlsanity.com/paper/2605.07171/) (2026)

## Abstract (arXiv)

In this paper, we consider a novel variant of the multi-armed bandit (MAB) problem, MAB with cost subsidy, which models many real-life applications where the learning agent has to pay to select an arm and is concerned about optimizing cumulative costs and rewards. We present two applications, intelligent SMS routing problem and ad audience optimization problem faced by several businesses (especially online platforms), and show how our problem uniquely captures key features of these applications. We show that naive generalizations of existing MAB algorithms like Upper Confidence Bound and Thompson Sampling do not perform well for this problem. We then establish a fundamental lower bound on the performance of any online learning algorithm for this problem, highlighting the hardness of our problem in comparison to the classical MAB problem. We also present a simple variant of explore-then-commit and establish near-optimal regret bounds for this algorithm. Lastly, we perform extensive numerical simulations to understand the behavior of a suite of algorithms for various instances and recommend a practical guide to employ different algorithms.