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We study primal-dual type stochastic optimization algorithms with non-uniformsampling. Our main theoretical contribution in this paper is to present aconvergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method witharbitrary sampling. Based on this theoretical framework, we propose OptimalityViolation-based Sampling SPDC (ovsSPDC), a non-uniform sampling method based onOptimality Violation. We also propose two efficient heuristic variants ofovsSPDC called ovsSDPC+ and ovsSDPC++. Through intensive numerical experiments,we demonstrate that the proposed method and its variants are faster than otherstate-of-the-art primal-dual type stochastic optimization methods.

Stochastic Primal Dual Coordinate Method with Non-Uniform Sampling Based on Optimality Violations