ZOAF: Towards Efficient Zeroth-Order Optimization for Analog/RF Circuit Design

2026-06-01

AI Summary

In analog and RF integrated circuit design, conventional gradient-based optimization fails due to the non-differentiability of simulators, while existing black-box methods suffer from high surrogate modeling costs, hyperparameter sensitivity, or slow convergence. This work proposes ZOAF, a zeroth-order optimization framework that eliminates the need for surrogate models by efficiently estimating gradients through a hybrid strategy combining random and coordinate-wise directional sampling. ZOAF further enhances performance via quasi-random multi-start initialization, a sliding-window early stopping criterion, and projected update mechanisms, effectively balancing exploration efficiency and convergence accuracy. Evaluated on three circuit design tasks, ZOAF achieves the best median performance across key metrics, delivers up to 10× improvement in peak performance, reduces simulation calls by 1.3–3.8×, and demonstrates strong robustness.

Abstract

Circuit optimization is an indispensable step in analog/RF IC design. Classical fast gradient-based optimization methods are typically infeasible due to lack of access to simulator source code and the technical barriers to implementing adjoint methods. Therefore, surrogate-based black-box optimization is widely used in practice; however, it can be costly to build and sensitive to hyperparameters, whereas population heuristics often suffer from slow convergence and large evaluation counts under tight simulator-call budgets. To address these limitations, we propose the Zeroth-Order Analog/RF Framework (ZOAF), which recovers gradient-descent directions from a small number of black-box circuit simulations, combining the benefits of both gradient-based optimization and black-box optimization. We also employ several surrogate-free techniques to improve the efficiency and accuracy, including (1) a hybrid ZO scheduling method that switches between random-direction ZO for budget-efficient exploration and coordinate-wise ZO for accurate late-stage refinement, (2) one-shot quasi-random multi-start to focus evaluations, and (3) a sliding-window monitor that triggers early stops and box-projected updates to maintain feasibility. Evaluated on three distinct schematics, ZOAF consistently outperforms state-of-the-art baselines, achieving the best median final value on every reported figure of merit -- with up to an order-of-magnitude advantage in median peaking on the 22-parameter two-stage amplifier -- together with the most robust worst-case behavior across seeds, while reducing simulator calls to convergence by $1.3$--$3.8\times$. Code is publicly available at https://github.com/LiyanTan111/ZOAF.

Problem

• Zeroth-Order Optimization
• Analog/RF Circuit Design
• Black-Box Optimization
• Gradient-Free Methods
• Simulator-Call Budget

Innovation

• Zeroth-Order Optimization
• Analog/RF Circuit Design
• Surrogate-Free
• Gradient Estimation
• Black-Box Optimization