CMA-ES with Individual Adaptive Reevaluation for Black-Box Value-At-Risk Optimization

Noisy black-box continuous optimization using evolution strategies (ES) involves a trade-off between computational cost and estimation precision. While several approaches have been proposed to address this issue, most focus on optimizing the expected objective value, leaving Value-at-Risk (VaR) optimization largely unexplored. To address the trade-off problem in black-box VaR optimization, we propose an individual adaptive reevaluation mechanism that adjusts the number of reevaluations of the noisy objective function for each solution to estimate the VaR. This mechanism dynamically adapts the number of reevaluations for each solution by monitoring ranking deviations using bootstrapping. The proposed method is integrated into CMA-ES, named IR-CMA-ES, and evaluated against two baselines: CMA-ES with Monte Carlo VaR estimation using fixed reevaluation, and UH-CMA-ES modified for VaR optimization. Experiments under various noise settings demonstrate the competitive performance of IR-CMA-ES.