AF: Small: New Directions in Learning Theory

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This project is to develop core principles and technologies for systems that learn from observation and experience in order to better help their users. While there is already a significant body of work in the area of machine learning, today's interconnected world provides both new challenges and new opportunities that classic methods are not able to address or take advantage of. This project has three main thrusts. The first involves development of methods that can extract useful information from auxiliary sources in addition to traditional labeled data. This includes methods for quickly learning multiple related tasks by taking advantage of ways in which they relate to each other. The second involves approaches for learning about what different users or agents want by observing the results of their interactions. Finally, the third thrust involves development of new rigorous methods for quickly estimating the amount of resources that would be needed to solve a given learning task. Broader impacts of the project include the training of a diverse set of graduate students, improving undergraduate curricula with respect to machine learning technology, and developing a new book for advanced undergraduates on algorithms and analysis for data science.More specifically, the first main thrust of this work involves a combination of unsupervised, semi-supervised, and multi-task learning. This work will investigate problems of estimating error rates from unlabeled data, unifying co-training and topic models, learning multiple related tasks from limited supervision, and learning new representations of data using tools from high-dimensional geometry. The second main thrust will focus on reconstructing estimates of agent utilities from observing the outcomes of economic mechanisms such as combinatorial auctions. This thrust also includes problems of learning the rules of unknown mechanisms from experimentation. Finally, the last thrust focuses on development of the theory of property testing for machine learning problems, with the goal of quickly estimating natural formal measures of complexity of a given learning task.