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

Journal Article · Sun Feb 01 00:00:00 EST 2026 · Journal of Optimization Theory and Applications

DOI:https://doi.org/10.1007/s10957-025-02914-y· OSTI ID:3024984

Menickelly, Matt; Wild, Stefan M; Xie, Miaolan

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 3024984
• Journal Information: Journal of Optimization Theory and Applications, Journal Name: Journal of Optimization Theory and Applications Journal Issue: 2 Vol. 208
• Country of Publication: United States
• Language: English