Timezone: »
In online convex optimization (OCO), Lipschitz continuity of the functions is commonly assumed in order to obtain sublinear regret. Moreover, many algorithms have only logarithmic regret when these functions are also strongly convex. Recently, researchers from convex optimization proposed the notions of relative Lipschitz continuity'' and
relative strong convexity''. Both of the notions are generalizations of their classical counterparts. It has been shown that subgradient methods in the relative setting have performance analogous to their performance in the classical setting.
In this work, we consider OCO for relative Lipschitz and relative strongly convex functions. We extend the known regret bounds for classical OCO algorithms to the relative setting. Specifically, we show regret bounds for the follow the regularized leader algorithms and a variant of online mirror descent. Due to the generality of these methods, these results yield regret bounds for a wide variety of OCO algorithms. Furthermore, we further extend the results to algorithms with extra regularization such as regularized dual averaging.
Author Information
Yihan Zhou (University of British Columbia)
Victor Sanches Portella (University of British Columbia)
Mark Schmidt (University of British Columbia)
Nicholas Harvey (University of British Columbia)
More from the Same Authors
-
2021 : Heavy-tailed noise does not explain the gap between SGD and Adam on Transformers »
Jacques Chen · Frederik Kunstner · Mark Schmidt -
2021 : Heavy-tailed noise does not explain the gap between SGD and Adam on Transformers »
Jacques Chen · Frederik Kunstner · Mark Schmidt -
2021 : Faster Quasi-Newton Methods for Linear Composition Problems »
Betty Shea · Mark Schmidt -
2021 : A Closer Look at Gradient Estimators with Reinforcement Learning as Inference »
Jonathan Lavington · Michael Teng · Mark Schmidt · Frank Wood -
2021 : An Empirical Study of Non-Uniform Sampling in Off-Policy Reinforcement Learning for Continuous Control »
Nicholas Ioannidis · Jonathan Lavington · Mark Schmidt -
2022 : Target-based Surrogates for Stochastic Optimization »
Jonathan Lavington · Sharan Vaswani · Reza Babanezhad Harikandeh · Mark Schmidt · Nicolas Le Roux -
2022 : Fast Convergence of Greedy 2-Coordinate Updates for Optimizing with an Equality Constraint »
Amrutha Varshini Ramesh · Aaron Mishkin · Mark Schmidt -
2022 : Fast Convergence of Random Reshuffling under Interpolation and the Polyak-Łojasiewicz Condition »
Chen Fan · Christos Thrampoulidis · Mark Schmidt -
2022 : Practical Structured Riemannian Optimization with Momentum by using Generalized Normal Coordinates »
Wu Lin · Valentin Duruisseaux · Melvin Leok · Frank Nielsen · Mohammad Emtiyaz Khan · Mark Schmidt -
2020 : Closing remarks »
Quanquan Gu · Courtney Paquette · Mark Schmidt · Sebastian Stich · Martin Takac -
2020 : Live Q&A with Michael Friedlander (Zoom) »
Mark Schmidt -
2020 : Intro to Invited Speaker 8 »
Mark Schmidt -
2020 : Contributed talks in Session 3 (Zoom) »
Mark Schmidt · Zhan Gao · Wenjie Li · Preetum Nakkiran · Denny Wu · Chengrun Yang -
2020 : Live Q&A with Rachel Ward (Zoom) »
Mark Schmidt -
2020 : Live Q&A with Ashia Wilson (Zoom) »
Mark Schmidt -
2020 : Welcome remarks to Session 3 »
Mark Schmidt -
2020 Workshop: OPT2020: Optimization for Machine Learning »
Courtney Paquette · Mark Schmidt · Sebastian Stich · Quanquan Gu · Martin Takac -
2020 : Welcome event (gather.town) »
Quanquan Gu · Courtney Paquette · Mark Schmidt · Sebastian Stich · Martin Takac -
2020 Poster: Improved Algorithms for Online Submodular Maximization via First-order Regret Bounds »
Nicholas Harvey · Christopher Liaw · Tasuku Soma -
2019 Poster: Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates »
Sharan Vaswani · Aaron Mishkin · Issam Laradji · Mark Schmidt · Gauthier Gidel · Simon Lacoste-Julien -
2018 Poster: SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient »
Aaron Mishkin · Frederik Kunstner · Didrik Nielsen · Mark Schmidt · Mohammad Emtiyaz Khan -
2018 Poster: Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes »
Hassan Ashtiani · Shai Ben-David · Nicholas Harvey · Christopher Liaw · Abbas Mehrabian · Yaniv Plan -
2018 Oral: Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes »
Hassan Ashtiani · Shai Ben-David · Nicholas Harvey · Christopher Liaw · Abbas Mehrabian · Yaniv Plan -
2016 : Fast Patch-based Style Transfer of Arbitrary Style »
Tian Qi Chen · Mark Schmidt -
2015 Poster: StopWasting My Gradients: Practical SVRG »
Reza Babanezhad Harikandeh · Mohamed Osama Ahmed · Alim Virani · Mark Schmidt · Jakub Konečný · Scott Sallinen