论文标题
无启示录和启用启示录的一阶低级优化算法的比较
Comparison of an Apocalypse-Free and an Apocalypse-Prone First-Order Low-Rank Optimization Algorithm
论文作者
论文摘要
我们比较了两种一阶低排名优化算法，即$ \ text {p}^2 \ text {gd} $（Schneider和Uschmajew，2015年），已证明已被证明是apocalypse-prone（Levin et al。，2021），及其apocalypse-fext $ fext $ fext $ \ gert text^2^2^2^2^2 {p {p {p}为$ \ text {p}^2 \ text {gd} $配备合适的等级降低机制（Olikier等，2022）。在这里，启示录指的是平稳度度沿收敛序列为零的情况，而在极限下为nonger。比较是在两个启示录的简单示例上进行的，即原始的示例（Levin等，2021）和一个新的。我们还提出了$ \ text {p}^2 \ text {gdr} $的等级降低机制的潜在副作用，并讨论了等级降低参数的选择。
We compare two first-order low-rank optimization algorithms, namely $\text{P}^2\text{GD}$ (Schneider and Uschmajew, 2015), which has been proven to be apocalypse-prone (Levin et al., 2021), and its apocalypse-free version $\text{P}^2\text{GDR}$ obtained by equipping $\text{P}^2\text{GD}$ with a suitable rank reduction mechanism (Olikier et al., 2022). Here an apocalypse refers to the situation where the stationarity measure goes to zero along a convergent sequence whereas it is nonzero at the limit. The comparison is conducted on two simple examples of apocalypses, the original one (Levin et al., 2021) and a new one. We also present a potential side effect of the rank reduction mechanism of $\text{P}^2\text{GDR}$ and discuss the choice of the rank reduction parameter.
