Online Methods for Complex Stochastic Optimization Problems

我的研究主要包括检查类的自适应步长算法的背景下，随机优化。近年来，这种算法已经成为深度学习领域成功的一个不可或缺的组成部分，允许在大量数据上训练以前不切实际的神经架构。用于随机优化的自适应步长算法扩展了随机梯度下降，这是一种用于拟合统计和ML模型类的技术，通过在训练时利用额外的数据来提高鲁棒性和效率。然而，直到最近，人们对这些自适应步长算法的实际性能知之甚少，这些自适应步长算法具有许多重要的性质，如稳定性和概率收敛性，不确定。最近的工作已经开始尝试和隔离这些属性和它们保持的条件-我正在进行的研究旨在扩大我们知道这些属性保持的条件，着眼于削弱标准设置中的假设（也加强属性本身），并研究算法在依赖数据的条件下如何表现，主要集中在马尔可夫动力学上。这项工作将有助于提高对自适应步长算法性能的信心，鉴于机器学习技术在关键基础设施中的日益普及，自适应步长算法将变得越来越重要。这项工作还将增加自适应步长算法可以应用的设置范围，例如训练强化学习算法，这些算法通常需要马尔可夫条件。

My research primarily consists of examining the class of adaptive stepsize algorithms in the context of stochastic optimisation. In recent years, such algorithms have been an integral component to the success of the field of deep learning, allowing previously impractical neural architectures to be trained on huge swathes of data. Adaptive stepsize algorithms for stochastic optimisation extend stochastic gradient descent, a technique for fitting classes of statistical and ML models, to be more robust and efficient by utilising additional data whilst training. Until recently, however, relatively little was known about the practical performance of these adaptive stepsize algorithms with many important properties, such as stability and probabilistic convergence, being undetermined. Recent work has been undertaken to try and isolate these properties and the conditions in which they hold - The research I am undertaking will aim to widen the conditions in which we know that these properties hold, looking toward weakening the assumptions in the standard setting (also strengthening the properties themselves), and also looking at how the algorithms behave in condition of dependent data, mostly focusing on markovian dynamics. This work will facilitate increased confidence in the performance of adaptive step size algorithms which will become increasingly more important given the growing prevalence of machine learning techniques using them being relied upon in critical infrastructure. This work will also increase the range of settings in which adaptive stepsize algorithms can be applied such as training reinforcement learning algorithms which often entail Markovian conditions.