Randomized Quasi-Monte Carlo Methods for Risk-Averse Stochastic Optimization

Olena Melnikov () and Johannes Milz ()
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Olena Melnikov: Georgia Institute of Technology
Johannes Milz: Georgia Institute of Technology

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 14, 21 pages

Abstract: Abstract We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant composite risk functionals. These sample-based approximation schemes include Monte Carlo and certain randomized quasi-Monte Carlo integration methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that randomized quasi-Monte Carlo approaches based on scrambled Sobol’ sequences can yield smaller bias and root mean square error than Monte Carlo methods for risk-averse optimization.

Keywords: Quasi–Monte Carlo; Randomized quasi–Monte Carlo; Risk-averse optimization; Sample average approximation; 90C15; 90C59; 65C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02693-6

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