A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

Abstract We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.