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We consider unconstrained stochastic optimization problems with no availablegradient information. Such problems arise in settings from derivative-freesimulation optimization to reinforcement learning. We propose an adaptivesampling quasi-Newton method where we estimate the gradients of a stochasticfunction using finite differences within a common random number framework. Wedevelop modified versions of a norm test and an inner product quasi-Newton testto control the sample sizes used in the stochastic approximations and provideglobal convergence results to the neighborhood of the optimal solution. Wepresent numerical experiments on simulation optimization problems to illustratethe performance of the proposed algorithm. When compared with classicalzeroth-order stochastic gradient methods, we observe that our strategies ofadapting the sample sizes significantly improve performance in terms of thenumber of stochastic function evaluations required.

Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization