Improving Thompson Sampling via Information Relaxation for Budgeted Multi-armed Bandits
This work addresses resource allocation under budget constraints, offering incremental enhancements for applications like online advertising or clinical trials.
The paper tackled the budgeted multi-armed bandit problem by proposing algorithms that incorporate remaining budget information into Thompson Sampling, resulting in incremental improvements over existing methods across various settings, including a real-world example.
We consider a Bayesian budgeted multi-armed bandit problem, in which each arm consumes a different amount of resources when selected and there is a budget constraint on the total amount of resources that can be used. Budgeted Thompson Sampling (BTS) offers a very effective heuristic to this problem, but its arm-selection rule does not take into account the remaining budget information. We adopt \textit{Information Relaxation Sampling} framework that generalizes Thompson Sampling for classical $K$-armed bandit problems, and propose a series of algorithms that are randomized like BTS but more carefully optimize their decisions with respect to the budget constraint. In a one-to-one correspondence with these algorithms, a series of performance benchmarks that improve the conventional benchmark are also suggested. Our theoretical analysis and simulation results show that our algorithms (and our benchmarks) make incremental improvements over BTS (respectively, the conventional benchmark) across various settings including a real-world example.