Adaptive gradient accuracy yields optimal iteration complexity for (accelerated) proximal gradient methods with biased estimates, and query complexity claims for unbiased estimates.
Convex optimization algorithms
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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.