# Depth over Fidelity in Fixed-Budget Noisy Evolution Strategies

arXiv: https://arxiv.org/abs/2606.06555 · HTML: https://mlsanity.com/paper/2606.06555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [CMA-ES with Learning Rate Adaptation](https://mlsanity.com/paper/2401.15876/) (2024)
- [CMA-ES with Adaptive Reevaluation for Multiplicative Noise](https://mlsanity.com/paper/2405.11471/) (2024)

## Abstract (arXiv)

Noisy evolution strategies under fixed evaluation budgets face a depth-fidelity trade-off: spending evaluations to denoise intra-generation rankings reduces the number of distribution updates the optimizer can execute. We argue for depth over fidelity and propose probabilistic elite membership (PEM), which replaces hard rank-based weights in evolution strategies with conditional expected rank weights that integrate over ranking uncertainty. PEM preserves the conditional mean update while reducing conditional update dispersion, a Rao-Blackwellization of the noisy rank-based step. We instantiate PEM via residual bootstrapping (RB-PEM) with capped per-generation overhead, complemented by an adaptive probe-and-switch mechanism for low-noise regimes. Across the COCO bbob-noisy suite and external tasks including RL policy search and hyperparameter optimization, RB-PEM achieves consistent gains in high-misranking, budget-constrained settings.