Bridging Adversarial and Nonstationary Multi-armed Bandit
This provides a theoretical foundation for handling time-varying rewards in bandit problems, which is incremental but clarifies connections between existing models.
The paper tackles the problem of unifying adversarial and nonstationary multi-armed bandit formulations by introducing a framework that bridges them as special cases, achieving optimal regret with matching lower bounds.
In the multi-armed bandit framework, there are two formulations that are commonly employed to handle time-varying reward distributions: adversarial bandit and nonstationary bandit. Although their oracles, algorithms, and regret analysis differ significantly, we provide a unified formulation in this paper that smoothly bridges the two as special cases. The formulation uses an oracle that takes the best-fixed arm within time windows. Depending on the window size, it turns into the oracle in hindsight in the adversarial bandit and dynamic oracle in the nonstationary bandit. We provide algorithms that attain the optimal regret with the matching lower bound.