论文标题
凸优化中连续时间模型的Lyapunov分析的系统方法
A systematic approach to Lyapunov analyses of continuous-time models in convex optimization
论文作者
论文摘要
通常通过其连续时间模型分析一阶方法，其中通常通过Lyapunov函数接近其最坏情况的收敛属性。在这项工作中，我们提供了一种系统和原则的方法，以找到和验证Lyapunov的函数，以适用于普通和随机微分方程的类别。更确切地说，我们将最初由Drori和Teboulle [10]提出的绩效估计框架扩展到连续的时间模型。我们检索收敛结果与使用更少的假设和凸性不等式相媲美的收敛结果，并为随机加速梯度流提供了新的结果。
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.
