Optimization and Learning Algorithms for Stochastic and Adversarial Power Control

Power control in wireless networks is a well-studied problem. However, recently it has been demonstrated that significant throughput gains can be achieved using data-driven online learning algorithms, supported by a cloud computing infrastructure. In this paper, we provide theoretical guarantees for such algorithms. In particular, we consider two variants of the problem: one which emphasizes long-term throughput and the other which emphasizes robust short-term throughput. The first problem reduces to solving a convex optimization problem with noisy, stochastic measurements while the second one is an online optimization problem where an adversary chooses the reward functions. We provide stochastic and online gradient descent methods customized for the power control problem and establish their convergence analysis. We show that in both cases, the total regret over a time horizon $T$ grows sublinearly at rate $O(\sqrt{T})$ for suitable choices of algorithms and algorithm parameters.