An adaptive importance sampling algorithm for risk-averse optimization

doi:10.1016/j.jcp.2025.114548

An adaptive importance sampling algorithm for risk-averse optimization

2025-11-27

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DOI：10.1016/j.jcp.2025.114548

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Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge of accurately sampling from the tails of the underlying distribution of random inputs. This often leads to a much faster growth of the sample size compared to risk-neutral problems. In this work, we propose a novel adaptive sampling algorithm that adapts both the sample size and the sampling distribution at each iteration. The biasing distributions are constructed on the fly, leveraging a reduced-order model of the objective function to be minimized, and are designed to oversample a so-called risk region. As a result, a reduction of the variance of the gradients is achieved, which permits to use fewer samples per iteration compared to a standard algorithm, while still preserving the asymptotic convergence rate. Our focus is on the minimization of the Conditional Value-at-Risk (CVaR), and we establish the convergence of the proposed computational framework. Numerical experiments confirm the substantial computational savings achieved by our approach.

Keywords:

stochastic optimization

adaptive sampling

risk-averse minimization

PDE-constrained optimization under uncertainty

reduced order models

An adaptive importance sampling algorithm for risk-averse optimization

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