Game-Theoretic Bandits for Network Optimization With High-Probability Swap-Regret Upper Bounds

In this paper, we study a multi-agent bandit problem in an unknown general-sum game repeated for a number of rounds (i.e., learning in a black-box game with bandit feedback), where a set of agents have no information about the underlying game structure and cannot observe each other’s actions and rewards. In each round, each agent needs to play an arm (i.e., action) from a (possibly different) arm set (i.e., action set), and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> receives the reward of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">played</i> arm that is affected by other agents’ actions. The objective of each agent is to minimize her own cumulative swap regret, where the swap regret is a generic performance measure for online learning algorithms. Many network optimization problems can be cast with the framework of this multi-agent bandit problem, such as wireless medium access control and end-to-end congestion control. We propose an online-mirror-descent-based algorithm and provide near-optimal high-probability swap-regret upper bounds based on refined martingale analyses, which can further bound the expected swap regret instead of the pseudo-regret studied in the literature. Moreover, the high-probability bounds guarantee that correlated equilibria can be achieved in a polynomial number of rounds if the algorithms are played by all agents. To assess the performance of the studied algorithm, we conducted numerical experiments in the context of wireless medium access control, and we performed emulation experiments by implementing the studied algorithms through the Linux Kernel for the end-to-end congestion control.