Convergence Rates of Stochastic Zeroth-order Gradient Descent for \L ojasiewicz Functions

Zeroth order optimization is a central topic in optimization and related fields. Algorithms for zeroth order optimization find important real-world applications, since often times in practice, we cannot directly access the derivatives of the objective function. To optimize the function in such scenarios, one can estimate the gradient/Hessian first and deploy first/second order algorithms with the estimated derivatives. Previously, many authors have considered this problem. Yet stochastic zeroth order methods for Łojasiewicz functions have not been carefully investigated (See Section 2 for more discussion).