Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universality
Yu-Hu Yan, Peng Zhao, Zhi-Hua Zhou

TL;DR
This paper introduces novel optimistic online-to-batch conversion methods that simplify algorithm design and achieve optimal accelerated convergence for smooth, strongly convex, and non-smooth objectives, unifying various optimization scenarios.
Contribution
It proposes new optimistic online-to-batch conversions that incorporate optimism into the analysis, achieving optimal accelerated convergence across multiple convex optimization settings.
Findings
Achieves optimal accelerated convergence with simple online gradient descent.
Extends to strongly convex objectives with optimal rates.
Provides universal methods applicable to smooth and non-smooth objectives without prior smoothness knowledge.
Abstract
In this work, we study offline convex optimization with smooth objectives, where the classical Nesterov's Accelerated Gradient (NAG) method achieves the optimal accelerated convergence. Extensive research has aimed to understand NAG from various perspectives, and a recent line of work approaches this from the viewpoint of online learning and online-to-batch conversion, emphasizing the role of optimistic online algorithms for acceleration. In this work, we contribute to this perspective by proposing novel optimistic online-to-batch conversions that incorporate optimism theoretically into the analysis, thereby significantly simplifying the online algorithm design while preserving the optimal convergence rates. Specifically, we demonstrate the effectiveness of our conversions through the following results: (i) when combined with simple online gradient descent, our optimistic conversion…
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Taxonomy
TopicsStochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques · Advanced Bandit Algorithms Research
