A Lyapunov-Based Methodology for Constrained Optimization with Bandit Feedback
This work addresses constrained decision-making problems in applications like online advertising and wireless scheduling, offering a novel algorithmic approach with theoretical guarantees.
The authors tackled the problem of constrained optimization with bandit feedback, where a decision-maker aims to maximize total reward under budget and stochastic constraints, by proposing a low-complexity Lyapunov-based algorithm named LyOn, which achieves O(√(K B log B)) regret and zero constraint-violation for sufficiently large B.
In a wide variety of applications including online advertising, contractual hiring, and wireless scheduling, the controller is constrained by a stringent budget constraint on the available resources, which are consumed in a random amount by each action, and a stochastic feasibility constraint that may impose important operational limitations on decision-making. In this work, we consider a general model to address such problems, where each action returns a random reward, cost, and penalty from an unknown joint distribution, and the decision-maker aims to maximize the total reward under a budget constraint $B$ on the total cost and a stochastic constraint on the time-average penalty. We propose a novel low-complexity algorithm based on Lyapunov optimization methodology, named ${\tt LyOn}$, and prove that for $K$ arms it achieves $O(\sqrt{K B\log B})$ regret and zero constraint-violation when $B$ is sufficiently large. The low computational cost and sharp performance bounds of ${\tt LyOn}$ suggest that Lyapunov-based algorithm design methodology can be effective in solving constrained bandit optimization problems.