动态在线学习中时间变异性的进一步研究
A closer look at temporal variability in dynamic online learning
摘要：
本文研究了在信息充分的在线学习情境下，动态后悔的设置问题。特别是，我们分析的损失函数的时间变异性的遗憾界。通过假设序列的损失函数不随时间变化很大，我们表明，它是有可能招致改进的遗憾界相比，现有的结果。我们的方法的关键是在优化过程中使用损失函数（而不是它的梯度）。在隐式算法分析的最新进展的基础上，我们提出了一个适应的隐式版本的在线镜像下降的动态设置。我们所提出的算法不仅是自适应的损失函数的时间变化，但也比较器的序列的路径长度时，一个上限是已知的。此外，我们的分析表明，我们的结果是紧密的，不能得到改善，没有进一步的假设。接下来，我们将展示如何将我们的算法应用于专家建议的学习设置或复合损失函数的设置。最后，当路径长度的上限是不固定的事先，我们展示了如何结合贪婪的策略与现有的强自适应算法，以最佳的竞争对不同的序列的比较器同时进行。
英文摘要：
This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the sequence of loss functions does not vary much with time, we show that it is possible to incur improved regret bounds compared to existing results. The key to our approach is to use the loss function (and not its gradient) during the optimization process. Building on recent advances in the analysis of Implicit algorithms, we propose an adaptation of the Implicit version of Online Mirror Descent to the dynamic setting. Our proposed algorithm is adaptive not only to the temporal variability of the loss functions, but also to the path length of the sequence of comparators when an upper bound is known. Furthermore, our analysis reveals that our results are tight and cannot be improved without further assumptions. Next, we show how our algorithm can be applied to the setting of learning with expert advice or to settings with composite loss functions. Finally, when an upper bound to the path-length is not fixed beforehand we show how to combine a greedy strategy with existing strongly-adaptive algorithms to compete optimally against different sequences of comparators simultaneously.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
