Zeroth-Order Langevin Monte Carlo via SPSA under Noisy Function Measurements

What the math gives to ML

The paper provides a practical two-query estimator for Langevin drift when the target potential can only be evaluated through noisy function values. Its transferable asset is the SPSA perturbation identity: a full-dimensional gradient estimate costs only two oracle calls, while paired evaluations reduce the effect of additive measurement noise. The direct neural-network use is sampling latent variables or parameters from an energy-based posterior whose energy is supplied by a simulator, black-box scorer, or nondifferentiable evaluation pipeline. Diminishing perturbation and step-size schedules are useful when stable long-run sampling matters more than rapid transient exploration.