Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input

What the math gives to ML

The paper identifies a useful variance-reduction principle for black-box optimization under input uncertainty: retain the realized phenotype or input and Rao-Blackwellize the evolutionary-strategy score estimator by replacing a latent perturbation with its conditional expectation given the observed input. The transferable asset is the exact conditional-expectation construction, which preserves unbiasedness and guarantees no larger estimator variance when the conditional model is correct. A practical neural-network adaptation is to train stochastic policies, routers, or noisy network inputs with ES while using the observed trajectory or phenotype to infer the posterior mean of the latent parameter perturbation. The extracted text does not include the paper's detailed PAES theorem, so the implementation below uses the general Rao-Blackwell identity and an explicit Gaussian realization model that can be tested independently.