Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

We consider unconstrained stochastic optimization problems with no available gradient information. Such arise in settings from derivative-free simulation to reinforcement learning. propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of function evaluations within a common random number framework. develop modified versions norm test and inner product control sample sizes used approximations provide global convergence results neighborhood locally optimal solution. present numerical experiments on illustrate performance proposed algorithm. When compared classical zeroth-order methods, observe that our strategies adapting significantly improve terms required.