生成器梯度估计器是随机微分方程的伴随状态方法
The generator gradient estimator is an adjoint state method for stochastic differential equations
AI总结：
本文证明针对过参数化 SDEs 的生成器梯度估计器本质上是一种伴随状态方法，且与用于随机化学反应网络的精确 eIPA 估计器高度相似。
摘要：
受 Neural SDEs 等过参数化 Stochastic Differential Equations (SDEs) 日益普及的启发，Wang, Blanchet 和 Glynn 最近提出了生成器梯度估计器，这是一种用于 SDEs 的新型无偏随机梯度估计器，其计算时间在参数数量增加时保持稳定。在本文中，我们证明该估计器实际上是一种伴随状态方法，在 Ordinary Differential Equations (ODEs) 情形下，已知该方法随状态数而非参数数进行扩展。此外，我们表明生成器梯度估计器与由 Gupta, Rathinam 和 Khammash 为被称为随机化学反应网络的 Continuous-Time Markov Chains (CTMCs) 类所引入的精确 Integral Path Algorithm (eIPA) 估计器高度相似。
英文摘要：
Motivated by the increasing popularity of overparameterized Stochastic Differential Equations (SDEs) like Neural SDEs, Wang, Blanchet and Glynn recently introduced the generator gradient estimator, a novel unbiased stochastic gradient estimator for SDEs whose computation time remains stable in the number of parameters. In this note, we demonstrate that this estimator is in fact an adjoint state method, an approach which is known to scale with the number of states and not the number of parameters in the case of Ordinary Differential Equations (ODEs). In addition, we show that the generator gradient estimator is a close analogue to the exact Integral Path Algorithm (eIPA) estimator which was introduced by Gupta, Rathinam and Khammash for a class of Continuous-Time Markov Chains (CTMCs) known as stochastic chemical reactions networks (CRNs).
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