3 years ago

# Dynamic Online Gradient Descent with Improved Query Complexity: A Theoretical Revisit.

Yawei Zhao, En Zhu, Xinwang Liu, Jianping Yin

We provide a new theoretical analysis framework to investigate online gradient descent in the dynamic environment. Comparing with the previous work, the new framework recovers the state-of-the-art dynamic regret, but does not require extra gradient queries for every iteration. Specifically, when functions are $\alpha$ strongly convex and $\beta$ smooth, to achieve the state-of-the-art dynamic regret, the previous work requires $O(\kappa)$ with $\kappa = \frac{\beta}{\alpha}$ queries of gradients at every iteration. But, our framework shows that the query complexity can be improved to be $O(1)$, which does not depend on $\kappa$. The improvement is significant for ill-conditioned problems because that their objective function usually has a large $\kappa$.

Publisher URL: http://arxiv.org/abs/1812.10186

DOI: arXiv:1812.10186v3

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