Combining Adversarial Guarantees and Stochastic Fast Rates in Online Learning
This work provides incremental improvements for researchers and practitioners in online learning by combining adversarial robustness with stochastic efficiency, though it builds on existing algorithms without introducing new methods.
The paper tackles the problem of designing online learning algorithms that guarantee robust performance in adversarial environments while also achieving fast convergence rates in favorable stochastic settings. The result shows that two existing algorithms, Squint and MetaGrad, automatically adapt to stochastic conditions defined by the Bernstein parameter, achieving fast rates in expectation and with high probability.
We consider online learning algorithms that guarantee worst-case regret rates in adversarial environments (so they can be deployed safely and will perform robustly), yet adapt optimally to favorable stochastic environments (so they will perform well in a variety of settings of practical importance). We quantify the friendliness of stochastic environments by means of the well-known Bernstein (a.k.a. generalized Tsybakov margin) condition. For two recent algorithms (Squint for the Hedge setting and MetaGrad for online convex optimization) we show that the particular form of their data-dependent individual-sequence regret guarantees implies that they adapt automatically to the Bernstein parameters of the stochastic environment. We prove that these algorithms attain fast rates in their respective settings both in expectation and with high probability.