Adversarial Bandit over Bandits: Hierarchical Bandits for Online Configuration Management

TL;DR

This paper introduces ABoB, a hierarchical adversarial bandit algorithm that clusters similar configurations to improve online parameter optimization, achieving better regret bounds and faster convergence in large action spaces.

Contribution

The paper proposes ABoB, a hierarchical bandit algorithm that leverages clustering to exploit local structure, providing improved regret bounds under favorable conditions.

Findings

ABoB achieves up to 50% lower regret than flat methods.

Theoretical regret bounds are maintained in worst-case scenarios.

Experimental results demonstrate faster convergence and better performance in real 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.