Adaptive gradient accuracy yields optimal iteration complexity for (accelerated) proximal gradient methods with biased estimates, and query complexity claims for unbiased estimates.
Fixed-point algorithms for inverse problems in science and engineering , volume 49
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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.