We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the conditional number, Varag exhibits the unified optimal rates of convergence for solving smooth convex finite-sum problems directly regardless of their strong convexity. Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence. It also establishes an optimal linear rate of convergence for solving a wide class of problems only satisfying a certain error bound condition rather than strong convexity. Varag can also be extended to solve stochastic finite-sum problems.
Guanghui Lan (Georgia Tech)
Zhize Li (Tsinghua University, and KAUST)
Zhize Li is a Postdoc at the King Abdullah University of Science and Technology (KAUST) advised by Prof. Peter Richtárik. He got his PhD in Computer Science from Tsinghua University (Advisor: Prof. Jian Li) in July 2019.
Yi Zhou (IBM Almaden Research Center)
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