Depth over Fidelity in Fixed-Budget Noisy Evolution Strategies

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.

LLM-driven evolutionary search finds programs by launching seeds and iterating each one. Papers report a single budget setting, usually one seed run for a fixed number of iterations, and rank methods from that one point. We show this is not enough. We evaluate three evolutionary search strategies on five optimization tasks, commonly used by papers in the genre to report results. We run the analysis over a full grid of seeds and iterations. Our findings suggest that the best way to split a fixed budget between more seeds (width) and more iterations (depth) changes with the strategy, the task, and the total budget. Furthermore, we observe that the ranking of strategies also changes with the budget. On one task the strategy that looks worst at one seed is best at forty seeds. On another the best number of iterations is well below the value common in practice, so extra depth wastes budget that more seeds would turn into score. We provide a measurement protocol that reports the seeds-by-iterations frontier and practical guidance for using it.

LLM-guided evolutionary search (Evolve systems) has reached state-of-the-art results on mathematical and combinatorial tasks, yet most existing systems report only the best of many runs and leave the run-to-run distribution undocumented. We ask how a fixed budget of LLM calls should be allocated, and how reliably a single run reaches the reported numbers. Sweeping the depth-breadth grid over five models and three tasks, we identify two empirical regularities: a fitness-compute envelope along which capability ordering largely collapses on effective FLOPs, and a bilinear depth-breadth fit with task-specific interaction; both are gated by model-task capability. Motivated by these regularities, we propose BaSE (Bandit-based Self-Evolving), a multi-armed bandit that allocates LLM calls across parallel trajectories. Without changing the model, prompt, or evaluator, BaSE improves mean fitness by 12.3% over the strongest island-protocol baseline across 8 (model, task) cells, with the largest gains on high-variance settings: a reliability gain from allocation alone.