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• W3033376635 abstract "The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth functions, , Zhang et al. establish the squared path-length of the minimizer sequence ($C^*_{2,T}$) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. We first show that a preconditioned variant of OGD achieves $O(C^*_{2,T})$ with one gradient query per round. We then propose online optimistic Newton (OON) method for the case when the first and second order information of the function sequence is predictable. The regret bound of OON is captured via the quartic path-length of the minimizer sequence ($C^*_{4,T}$), which can be much smaller than $C^*_{2,T}$. We finally show that by using multiple gradients for OGD, we can achieve an upper bound of $O(min{C^*_{2,T},V_T})$ on regret." @default.
• W3033376635 created "2020-06-12" @default.
• W3033376635 creator A5040922600 @default.
• W3033376635 creator A5087313193 @default.
• W3033376635 date "2020-06-06" @default.
• W3033376635 modified "2023-09-25" @default.
• W3033376635 title "Unconstrained Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems" @default.
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• W3033376635 doi "https://doi.org/10.48550/arxiv.2006.03912" @default.
• W3033376635 hasPublicationYear "2020" @default.
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