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Stochastic variance reduced optimization methods are known to be globallyconvergent while they suffer from slow local convergence, especially whenmoderate or high accuracy is needed. To alleviate this problem, we propose anoptimization algorithm -- which we refer to as a hybrid acceleration scheme --for a class of proximal variance reduced stochastic optimization algorithms.The proposed optimization scheme combines a fast locally convergent algorithm,such as a quasi--Newton method, with a globally convergent variance reducedstochastic algorithm, for instance SAGA or L--SVRG. Our global convergenceresult of the hybrid acceleration method is based on specific safeguardconditions that need to be satisfied for a step of the locally fast convergentmethod to be accepted.  We prove that the sequence of the iterates generated by the hybridacceleration scheme converges almost surely to a solution of the underlyingoptimization problem. We also provide numerical experiments that showsignificantly improved convergence of the hybrid acceleration scheme comparedto the basic stochastic variance reduced optimization algorithm.

Hybrid Acceleration Scheme for Variance Reduced Stochastic Optimization Algorithms