A Systematic Approach to Lyapunov Analyses of Continuous-Time Models in Convex Optimization
本文提出一种系统方法，用于寻找和验证常微分与随机微分方程的Lyapunov函数，扩展了性能估计框架到连续时间模型，在更少假设下得到与离散方法相当的收敛结果，并为随机加速梯度流提供了新结论。
First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and verify Lyapunov functions for classes of ordinary and stochastic differential equations. More precisely, we extend the performance estimation framework, originally proposed by Drori and Teboulle [10], to continuous-time models. We retrieve convergence results comparable to those of discrete methods using fewer assumptions and convexity inequalities, and provide new results for stochastic accelerated gradient flows.