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• W3204548006 abstract "Three Operator Splitting (TOS) (Davis & Yin, 2017) can minimize the sum of three convex functions effectively when an efficient gradient oracle or proximal operator is available for each term. This requirement often fails in machine learning applications: (i) instead of full gradients only stochastic gradients may be available; and (ii) instead of proximal operators, using subgradients to handle complex penalty functions may be more efficient and realistic. Motivated by these concerns, we analyze three potentially valuable extensions of TOS. The first two permit using subgradients and stochastic gradients, and are shown to ensure a $mathcal{O}(1/sqrt{t})$ convergence rate. The third extension AdapTOS endows TOS with adaptive step-sizes. For the important setting of optimizing a convex loss over the intersection of convex sets AdapTOS attains universal convergence rates, i.e., the rate adapts to the unknown smoothness degree of the objective. We compare our proposed methods with competing methods on various applications." @default.
• W3204548006 created "2021-10-11" @default.
• W3204548006 creator A5015106385 @default.
• W3204548006 creator A5043683448 @default.
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• W3204548006 date "2021-10-07" @default.
• W3204548006 modified "2023-09-27" @default.
• W3204548006 title "Three Operator Splitting with Subgradients, Stochastic Gradients, and Adaptive Learning Rates." @default.
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• W3204548006 hasPublicationYear "2021" @default.
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