Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction

In this paper we study the lower complexity bounds for finite-sum optimization problems, where the objective is the average of $n$ individual component functions. We consider a so-called proximal incremental first-order oracle (PIFO) algorithm, which employs the individual component function's gradient and proximal information provided by PIFO to update the variable. To incorporate loopless methods, we also allow the PIFO algorithm to obtain the full gradient infrequently. We develop a novel approach to constructing the hard instances, which partitions the …

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