论文标题
通过转移目标来提高一阶方法：最差速率速率更快的新方案
Boosting First-Order Methods by Shifting Objective: New Schemes with Faster Worst-Case Rates
论文作者
论文摘要
我们提出了一种新方法，以设计一阶方法，以解决不受限制的强烈凸出问题。具体而言，我们没有直接解决原始目标，而是构建了一个转移的目标函数，该目标函数具有与原始目标相同的最小化器，并在插值条件下编码原始目标的平滑度和强凸度。然后，我们提出了一个算法模板，以解决转移的目标，以利用这种情况。遵循此模板，我们为配备各种一阶甲壳的问题得出了几种新的加速方案，并表明插值条件使我们能够极大地简化和拧紧对派生方法的分析。特别是，所有派生的方法的最差收敛速率都比其现有同行更快。进行机器学习任务的实验以评估新方法。
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer as the original objective and encodes both the smoothness and strong convexity of the original objective in an interpolation condition. We then propose an algorithmic template for tackling the shifted objective, which can exploit such a condition. Following this template, we derive several new accelerated schemes for problems that are equipped with various first-order oracles and show that the interpolation condition allows us to vastly simplify and tighten the analysis of the derived methods. In particular, all the derived methods have faster worst-case convergence rates than their existing counterparts. Experiments on machine learning tasks are conducted to evaluate the new methods.
