Adversarial Bandit over Bandits: Hierarchical Bandits for Online Configuration Management

TL;DR

The paper tackles online configuration management in large, metric action spaces under adversarial rewards by introducing ABoB, a hierarchical Adversarial Bandit over Bandits framework that clusters similar configurations to exploit local structure while adapting to changing environments. The method integrates an $\epsilon$-net discretization and Lipschitz continuity to preserve worst-case guarantees, achieving $O(k^{1/2}T^{1/2})$ regret in general and potentially $O(k^{1/4}T^{1/2})$ under favorable conditions; it also demonstrates substantial empirical gains on a real storage system, with up to 50% faster convergence than flat baselines using base algorithms like $EXP3$ and $Tsallis-INF$ in both stochastic and nonstochastic settings. Theoretical results are complemented by practical evaluations showing improved regret and convergence, highlighting the value of hierarchical clustering for scalable online configuration in complex action spaces. Overall, the work provides a principled approach to leverage structure in action spaces without sacrificing robust worst-case performance, with direct implications for dynamic parameter optimization in large-scale systems.

Abstract

Motivated by dynamic parameter optimization in finite, but large action (configurations) spaces, this work studies the nonstochastic multi-armed bandit (MAB) problem in metric action spaces with oblivious Lipschitz adversaries. We propose ABoB, a hierarchical Adversarial Bandit over Bandits algorithm that can use state-of-the-art existing "flat" algorithms, but additionally clusters similar configurations to exploit local structures and adapt to changing environments. We prove that in the worst-case scenario, such clustering approach cannot hurt too much and ABoB guarantees a standard worst-case regret bound of $O\left(k^{\frac{1}{2}}T^{\frac{1}{2}}\right)$, where $T$ is the number of rounds and $k$ is the number of arms, matching the traditional flat approach. However, under favorable conditions related to the algorithm properties, clusters properties, and certain Lipschitz conditions, the regret bound can be improved to $O\left(k^{\frac{1}{4}}T^{\frac{1}{2}}\right)$. Simulations and experiments on a real storage system demonstrate that ABoB, using standard algorithms like EXP3 and Tsallis-INF, achieves lower regret and faster convergence than the flat method, up to 50% improvement in known previous setups, nonstochastic and stochastic, as well as in our settings.

Theorems & Definitions (2)

• Theorem 3.1: Regret for Uniform Discretization
• Theorem 3.2: EXP3 with Uniform Discretization