English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Consider an online convex optimization problem where the loss functions areself-concordant barriers, smooth relative to a convex function $h$, andpossibly non-Lipschitz. We analyze the regret of online mirror descent with$h$. Then, based on the result, we prove the following in a unified manner.Denote by $T$ the time horizon and $d$ the parameter dimension. 1. For onlineportfolio selection, the regret of $\widetilde{\text{EG}}$, a variant ofexponentiated gradient due to Helmbold et al., is $\tilde{O} ( T^{2/3} d^{1/3})$ when $T > 4 d / \log d$. This improves on the original $\tilde{O} ( T^{3/4}d^{1/2} )$ regret bound for $\widetilde{\text{EG}}$. 2. For online portfolioselection, the regret of online mirror descent with the logarithmic barrier is$\tilde{O}(\sqrt{T d})$. The regret bound is the same as that of Soft-Bayes dueto Orseau et al. up to logarithmic terms. 3. For online learning quantum stateswith the logarithmic loss, the regret of online mirror descent with thelog-determinant function is also $\tilde{O} ( \sqrt{T d} )$. Its per-iterationtime is shorter than all existing algorithms we know.

Online Self-Concordant and Relatively Smooth Minimization, With Applications to Online Portfolio Selection and Learning Quantum States