Adversarial Network Optimization under Bandit Feedback: Maximizing Utility in Non-Stationary Multi-Hop Networks

Stochastic Network Optimization (SNO) concerns scheduling in stochastic queueing systems and has been widely studied in network theory. Classical SNO algorithms require network conditions to be stationary w.r.t. time, which fails to capture the non-stationary components in increasingly many real-world scenarios. Moreover, most existing algorithms in network optimization assume perfect knowledge of network conditions before decision, which again rules out applications where unpredictability in network conditions presents. Motivated by these issues, this paper considers Adversarial Network Optimization (ANO) under bandit feedback. Specifically, we consider the task of i) maximizing some unknown and time-varying utility function associated with scheduler's actions, where ii) the underlying network topology is a non-stationary multi-hop network whose conditions change arbitrarily with time, and iii) only bandit feedback (the effect of actually deployed actions) is revealed after decision-making. We propose the UMO2 algorithm, which does not require any pre-decision knowledge or counterfactual feedback, ensures network stability, and also matches the utility maximization performance of any ''mildly varying'' reference policy up to a polynomially decaying gap. To our knowledge, no previous algorithm can handle multi-hop networks or achieve utility maximization guarantees in ANO problems with bandit feedback, whereas ours is able to do both. Technically, our method builds upon a novel integration of online learning techniques into the Lyapunov drift-plus-penalty method. Specifically, we propose meticulous analytical techniques to jointly balance online learning and Lyapunov arguments, which is used to handle the complex inter-dependency among queues in multi-hop networks. To tackle the learning obstacles due to potentially unbounded queue sizes and negative queue differences, we design a new online linear optimization algorithm that automatically adapts to the unknown (potentially negative) loss magnitudes. Finally, we also propose a bandit convex optimization algorithm with novel queue-dependent learning rate scheduling that suites drastically varying queue lengths in utility maximization. Our new insights and techniques in online learning can also be of independent interest.