Scieur, DamienLiu, LewisPumir, ThomasBoumal, Nicolas2021-08-282021-08-282021-08-282021-01-01https://infoscience.epfl.ch/handle/20.500.14299/180985WOS:000659893800062Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees.Computer Science, Artificial IntelligenceMathematics, AppliedStatistics & ProbabilityComputer ScienceMathematicsconvergencebfgstext::conference output::conference proceedings::conference paper