Tighter error bounds for representation learning and lifelong learning

机器学习算法的成功关键取决于使用哪些数值特征来表示数据。人类学习成功的很大一部分可以说是我们不仅学习表示来在预测任务中表现良好，而且我们还重用这些表示来更有效地学习新遇到的但类似的任务。我们现在处于一个“深度”机器学习方法实际上自动学习数据的有用表示的时代。这些深度学习方法对许多其他领域变得至关重要：只有少数成功的应用包括药物设计，计算机图形的3D渲染，以及在围棋等游戏中击败顶级人类玩家。尽管这些巨大的经验成功，我们的数学理解，为什么这些方法的工作以及如何最好地训练他们是缺乏的。** 我的研究的第一部分是开发新的理论，以了解深度模型在对新数据进行预测时的表现。我获得更好性能保证的策略是使用理论，该理论利用算法看到的实际数据的特定属性和算法本身的特定属性。通过考虑训练的这两个重要方面，我希望深度学习模型也能取得成功。我的分析的另一个重要部分是回答以下问题：如果深度学习模型对其输入的某些类型的转换不敏感，那么它是否可以使用更少的数据成功地进行训练？机器学习领域可以取得的最大进步之一是从孤立地学习每一个新事物转变为在学习新任务时重用过去学到的东西。这种在学习一系列无休止的任务时的持续迁移被称为终身学习。虽然在这一重要领域已经开始了一些研究，但缺乏算法如何进行终身学习的数学理论，特别是关于自适应算法，当它们遇到与过去任务高度相似的任务时，它们会从过去的经验中转移更多。** 我研究的第二部分是设计终身学习的算法，包括为这些算法开发数学保证。我的目标是回答这样的问题：如果一个学习代理遇到一系列缓慢变化的学习任务，我们是否可以从以前的任务中汇集数据，以便使用更少的数据学习新任务？我的策略将是从序列预测中采纳强有力的想法，这是终身学习工作中一个重要但以前尚未开发的资源。这项工作的两个部分都可以从根本上推动机器学习领域的发展，机器学习已经彻底改变了许多科学和行业。参加这项研究的学生将有能力在全球舞台上推动加拿大的技术贡献。

The success of machine learning algorithms crucially hinges on which numerical features are used to represent data. An arguably large part of the success of human learning is that we not only learn representations to perform well on prediction tasks, but we also reuse these representations to more efficiently learn newly encountered but similar tasks. We are now in an era where "deep" machine learning methods actually learn useful representations of data automatically. These deep learning methods are becoming vital to many other fields: just a few successful applications include drug design, 3D rendering for computer graphics, and beating top-level human players in games such as Go. Despite these great empirical successes, our mathematical understanding for why these methods work well and how to best train them is lacking. ******Part I of my research is to develop new theory to understand how well a deep model will perform when it makes predictions about new data. My strategy to obtain better performance guarantees is to use theory that leverages specific properties of the actual data an algorithm sees and specific properties of the algorithm itself. By considering both of these important aspects of training, I expect to achieve success for deep learning models as well. Another important part of my analysis is to answer the following question: If a deep learning model is insensitive to certain types of transformations of its input, can it successfully be trained using less data as a result?******One of the greatest advancements the field of machine learning can make is to shift from learning each new thing in isolation to reusing what has been learned in the past when learning new tasks. This continual transfer when learning an endless sequence of tasks is known as lifelong learning. While some research has begun in this important area, the mathematical theory for how well algorithms can perform lifelong learning is lacking, especially with regards to adaptive algorithms that transfer much more from their past experiences when they encounter tasks that are highly similar to past tasks. ******Part II of my research is to design algorithms for lifelong learning, including developing mathematical guarantees for these algorithms. I aim to answer questions like the following: If a learning agent encounters a series of slowly changing learning tasks, can we pool the data from previous tasks in order to learn new tasks using much less data? My strategy will be to adapt powerful ideas from sequential prediction, a vital yet previously untapped resource for work in lifelong learning.******Both parts of this work can fundamentally advance the field of machine learning, which already is revolutionizing a number of sciences and industries. The students participating in this research will be excellently-equipped to fuel Canada's technological contributions at the global stage.