Multi-armed Bandits with Cost Subsidy
This addresses cost-sensitive decision-making for online platforms, but it is incremental as it adapts a known framework to a specific variant.
The paper tackles the multi-armed bandit problem with cost subsidy, modeling real-world applications like SMS routing and ad audience optimization, and shows that naive extensions of existing algorithms perform poorly, while a simple variant of explore-then-commit achieves near-optimal regret bounds.
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.