Adversarial Bandit over Bandits: Hierarchical Bandits for Online Configuration Management
This work addresses online configuration management for systems like storage, offering incremental improvements by enhancing existing bandit algorithms with hierarchical clustering.
The paper tackles the problem of dynamic parameter optimization in large configuration spaces by proposing ABoB, a hierarchical adversarial bandit algorithm that clusters similar configurations to exploit local structures and adapt to changing environments, achieving up to 50% improvement in regret and faster convergence compared to flat methods in simulations and real-world experiments.
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.