Multi-armed Bandits with Cost Subsidy

Abstract

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.

References in corpus (9)

• Unbiased Offline Evaluation of Contextual-bandit-based News Article Recommendation Algorithms
• Knapsack based Optimal Policies for Budget-Limited Multi-Armed Bandits
• Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits
• Conservative Contextual Linear Bandits
• A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations
• Conservative Bandits
• Bandits with concave rewards and convex knapsacks
• Nearly optimal Bernoulli factories for linear functions
• Thompson Sampling for Contextual Bandit Problems with Auxiliary Safety Constraints