High-Dimensional Bayesian Optimization for Analog Integrated Circuit Sizing Based on Dropout and g_m/I_D Methodology

TL;DR: In this paper , the authors proposed a new Bayesian optimization (cBO) algorithm, which can scale BO to more larger scale circuit and improve the optimization result, according to the fact that a specification of the analog integrated circuit is mainly determined by a few transistors.

Abstract: Bayesian optimization (BO) is popular for a analog circuit sizing problem recently. However, BO can only work well in small-scale circuit. Scaling BO to common circuit optimization (typically dimension > 10) is difficult due to the curse of dimensionality. In this article, we proposed a new BO algorithm (cBO), which can scale BO to more larger scale circuit and improve the optimization result. First, according to the fact that a specification of the analog integrated circuit is mainly determined by a few transistors, dropout strategy is adopted in our algorithm. At each iteration, only a subset of selected variables to be optimized. A variables selection strategy based on mutual information analysis and a new fill-in strategy are proposed. Second, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{m}/I_{D}$ </tex-math></inline-formula> methodology-based optimization strategy is proposed. Optimization variables are not width and the length of transistors, but <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{m}/I_{D}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{D}$ </tex-math></inline-formula> and length. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{m}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{D}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{m}/I_{D}$ </tex-math></inline-formula> have a direct relationship to circuit performance. This is equivalent to search in circuit feature space, which could achieve better performance and handle constraints more easily. Four commonly used circuits, including low dropout regulator, two stage amplifiers, Bandgap voltage reference (VR), and VR are used for validation. Compared with other high-dimensional BO, common BO, and commercial tools (Cadence ADE_GXL), the proposed algorithm is found to produce the best optimization result and best stability. And, the ablation study shows the effectiveness and efficiency of two ingredients of the proposed algorithm.