Simulation-Efficient Analog Circuit Yield Optimization via Monte Carlo Zeroth-Order Gradient Estimation

Abstract

Yield optimization under process variation is expensive because each candidate design must be evaluated across many Monte Carlo SPICE samples. The resulting finite-sample yield is also piecewise constant in the design parameters, providing little local information for optimization. We introduce zeroth-order Monte Carlo stochastic gradient descent (ZO-MC-SGD), a black-box method that converts continuous specification margins into stochastic descent directions. Each update evaluates opposite design perturbations under shared process samples, allowing a small simulation batch to estimate a local direction without differentiating SPICE or fitting a global surrogate model. A Spearman rank-correlation test checks that the margin-based loss orders designs consistently with empirical yield. We prove that the estimator is unbiased for a Gaussian-smoothed surrogate and derive variance and sample-complexity bounds with no explicit dependence on process dimension. Across five analog circuit benchmarks with up to 30 design variables and 42 process variables, ZO-MC-SGD reaches a mean yield of 0.95 on four circuits within 50--200 simulations and the empirical yield ceiling on the fifth. Relative to the best of five black-box and learning-based baselines, it reduces the required simulation budget by up to a factor of eight.