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

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Title: A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers.
Authors: Menickelly, Matt1 (AUTHOR) mmenickelly@anl.gov, Wild, Stefan M.2 (AUTHOR) wild@lbl.gov, Xie, Miaolan3 (AUTHOR) miaolanx@purdue.edu
Source: Journal of Optimization Theory & Applications. Feb2026, Vol. 208 Issue 2, p1-32. 32p.
Subjects: Quasi-Newton methods, Random numbers, Mathematical optimization, Quantum chemistry, Computational complexity, Stochastic programming, Quantum computers
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Feb2026, Vol. 208 Issue 2, p1-32. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Quasi-Newton+methods%22">Quasi-Newton methods</searchLink><br /><searchLink fieldCode="DE" term="%22Random+numbers%22">Random numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+chemistry%22">Quantum chemistry</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+programming%22">Stochastic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+computers%22">Quantum computers</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10957-025-02914-y
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        Text: English
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        Type: general
      – SubjectFull: Random numbers
        Type: general
      – SubjectFull: Mathematical optimization
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      – SubjectFull: Quantum chemistry
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      – SubjectFull: Computational complexity
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      – SubjectFull: Stochastic programming
        Type: general
      – SubjectFull: Quantum computers
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      – TitleFull: A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers.
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              M: 02
              Text: Feb2026
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