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Stochastic ISTA/FISTA Adaptive Step Search Algorithms for Convex Composite Optimization
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We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms [Beck and Teboulle, 2009, Scheinberg et al., 2014] for composite optimization without the assumption that stochastic gradient is an unbiased estimator. This work extends analysis of inexact fixed step ISTA/FISTA in [Schmidt et al., 2011] to the case of stochastic gradient estimates and adaptive step-size parameter chosen by backtracking. It also extends the framework for analyzing stochastic line-search method in [Cartis and Scheinberg, 2018] to the proximal gradient framework as well as to the accelerated first order methods.
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On the Convergence and Complexity of Proximal Gradient and Accelerated Proximal Gradient Methods under Adaptive Gradient Estimation
Adaptive gradient accuracy yields optimal iteration complexity for (accelerated) proximal gradient methods with biased estimates, and query complexity claims for unbiased estimates.
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