论文标题
优化出现的普通微分方程的基本收敛速率
Essential convergence rate of ordinary differential equations appearing in optimization
论文作者
论文摘要
通过采用连续限制，可以将某些连续的优化方法连接到普通的微分方程（OD），并且它们的收敛速率可以用ODE来解释。但是，由于这样的ODE可以按时间缩放达到任何收敛速率，因此对应关系并不像通常预期的那样简单，并且通过ODES衍生新方法并不完全直接。在这封信中，我们注意离散ODE的稳定性限制，并表明按时间缩放的加速基本上意味着离散化的减速。它们平衡了，以便我们可以定义可实现的独特收敛速率，我们称之为“基本融合率”。
Some continuous optimization methods can be connected to ordinary differential equations (ODEs) by taking continuous limits, and their convergence rates can be explained by the ODEs. However, since such ODEs can achieve any convergence rate by time scaling, the correspondence is not as straightforward as usually expected, and deriving new methods through ODEs is not quite direct. In this letter, we pay attention to stability restriction in discretizing ODEs and show that acceleration by time scaling basically implies deceleration in discretization; they balance out so that we can define an attainable unique convergence rate which we call an "essential convergence rate".
