A Simpler Approach to Accelerated Stochastic Optimization

Jul 12, 2020



Recently there have been several attempts to improve the rates of convergence achievable for smooth objectives. In particular, several recent papers have attempted to extend Nesterov's accelerated algorithm to stochastic and variance-reduced optimization. In this paper, we show that there is a simpler approach to obtaining accelerated rates: applying generic, well-known optimistic online learning algorithms and using the online average of their predictions to query the (deterministic or stochastic) first-order optimization oracle at each time step. In particular, we tighten the recent results of Cutkosky (2019) to demonstrate theoretically that online averaging results in a reduced optimization gap, independently of the algorithm involved. Then, we show that a simple tuning of existing generic optimistic online learning algorithms (e.g., Joulani et al [2017]), when combined with the reduced error quantified above, naturally results in optimal accelerated rates. what would you consider unnatural? get rid of this word? Importantly, the smooth objective may or may not be strongly-convex, and the rates are nevertheless optimal for both stochastic and deterministic first-order oracles. We further show that the same ideas transfer to variance-reduced optimization. In each case, the proofs are much simpler than the previous work, such as the new derivations of accelerated algorithms based on a primal-dual view (Wang and Abernethy, 2018) or the ideas based on linear coupling (Allen-Zhu and Orecchia, 2017). Importantly, we also provide algorithms that maintain the “universality” property, meaning that the same algorithm achieves the optimal rate for smooth and non-smooth objectives without further prior knowledge, generalizing the results of Kavis et al (2019) and solving a number of their open problems.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

Store presentation

Should this presentation be stored for 1000 years?

How do we store presentations

Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%


Recommended Videos

Presentations on similar topic, category or speaker