🤖 AI Summary
This work addresses the challenges in black-box optimization posed by heteroscedastic noise—namely, uncertain fitness evaluations, inaccurate solution ranking, and excessive computational cost—by introducing a confidence-driven dynamic sampling mechanism. The proposed approach integrates adaptive budget allocation and explicit averaging strategies within both CMA-ES and genetic algorithm frameworks. It further presents the first systematically constructed benchmark suite for heteroscedastic noise, thereby overcoming the conventional reliance on homoscedasticity and function smoothness assumptions. Experimental results demonstrate that the method consistently outperforms state-of-the-art algorithms under both homoscedastic and heteroscedastic noise conditions, achieving superior robustness and computational efficiency.
📝 Abstract
Real-world optimization problems often involve black-box functions and uncertainties in their evaluation, widely referred to as noisy optimization problems (NOPs). Evolutionary algorithms (EA), including Evolutionary Strategies (ES) and genetic algorithms (GA) have been commonly adopted to solve these problems in the contemporary literature. An ongoing challenge is the computational expense involved, given the number of evaluations required for good fitness estimation and ranking. Two fundamental methods commonly used for fitness estimation for NOPs are implicit averaging and explicit averaging. Explicit averaging uses resampling of solutions to improve the estimates, while implicit averaging typically uses a large population size with low resampling. Implicit averaging has been shown to have theoretical advantages for certain cases, which has motivated some recent approaches to use them. However, a recent study demonstrated that its performance is highly dependent on certain assumptions about the function, such as steepness and constant noise level, which may not apply for majority of the real world problems. Moreover, most existing algorithms have only considered homoscedastic noise, where the amplitude of variation is uniform across the entire search space, as opposed to more generic case of heteroscedastic noise. To address these issues, we introduce a set of heteroscedastic test problems and propose a novel confidence ranking method that employs a computationally efficient explicit averaging strategy with sampling budget adaptation. It is implemented within the Covariance Matrix Adaptation ES (CMA-ES) and GA frameworks to demonstrate its effectiveness and versatility. The resulting algorithm is evaluated on a range of problems with both homoscedastic and heteroscedastic noise, and it demonstrates superior performance compared to state-of-the-art approaches.