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Optimistic Online Mirror Descent for Bridging Stochastic and Adversarial Online Convex Optimization
March 19, 2024, 4:44 a.m. | Sijia Chen, Yu-Jie Zhang, Wei-Wei Tu, Peng Zhao, Lijun Zhang
cs.LG updates on arXiv.org arxiv.org
Abstract: Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance $\sigma_{1:T}^2$ and the cumulative adversarial variation $\Sigma_{1:T}^2$ for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance $\sigma_{\max}^2$ and the maximal adversarial variation $\Sigma_{\max}^2$ for strongly convex …
abstract adversarial arxiv cs.lg leader optimization stat.ml stochastic type variance
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