Collaborative Research: TRIPODS Institute for Optimization and Learning

这个第一阶段项目形成了一个NSF TRIPODS研究所，位于利哈伊大学，与斯托尼布鲁克和西北大学合作，重点是机器学习应用工具的新进展。 机器学习的一个关键组成部分是数学优化，其中使用历史数据来训练工具，以进行未来的预测和决策。 传统上，机器学习的优化技术主要集中在简化的模型和算法上。 然而，最近机器学习工具的成功革命性飞跃-例如，在许多情况下，通过转向使用更复杂的技术（通常涉及深度神经网络），图像和语音识别成为可能。 这些技术的持续发展需要统计学家、计算机科学家和应用数学家共同努力，开发更复杂的模型和算法，沿着提供更全面的理论保证，以支持其使用。除了研究目标外，该研究所还培养博士。在统计学，计算机科学和应用数学的学生和博士后研究员，并举办跨学科研讨会和冬季/夏季学校。 第一阶段的研究工作是分析非凸机器学习模型，设计用于训练它们的优化算法，以及开发非参数模型和相关算法。 重点是深度神经网络（DNN），主要是一般性的，但也涉及感兴趣的特定架构。 该研究所的研究工作强调需要在最先进的DNN训练方法和统计性能保证（例如，关于泛化错误），目前还没有很好地理解。优化算法的发展集中在二阶导数类型的技术，包括（无海森）牛顿，拟牛顿，高斯牛顿，以及它们的有限内存变体。 在设计这些方法方面取得了最新进展; PI的工作建立在这些努力的基础上，他们在设计和实现（包括并行和分布式计算环境）这些方法方面拥有广泛的专业知识。 非参数模型的发展有望将机器学习方法从大量用户定义的参数（例如，定义网络结构或优化算法的学习速率）。 这些模型可能会导致机器学习的巨大进步，该研究所在这一领域的工作也借鉴了PI在无导数优化方法方面的专业知识，这是非参数设置培训所需的。在这个TRIPODS研究所，PI在统计学，计算机科学和应用数学三个学科中以统一的视角处理所有这些研究方向。 事实上，由于机器学习从这些领域中汲取了如此多的知识，未来的进步需要优化专家、学习理论家和统计学家之间的密切合作--这些研究人员社区迄今为止往往使用不同的术语和出版地点独立运作。 该研究所以深度学习为重点，旨在促进跨学院和跨学科的合作，克服这些障碍。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Phase I project forms an NSF TRIPODS Institute, based at Lehigh University and in collaboration with Stony Brook and Northwestern Universities, with a focus on new advances in tools for machine learning applications. A critical component for machine learning is mathematical optimization, where one uses historical data to train tools for making future predictions and decisions. Traditionally, optimization techniques for machine learning have focused on simplified models and algorithms. However, recent revolutionary leaps in the successes of machine learning tools---e.g., for image and speech recognition---have in many cases been made possible by a shift toward using more complicated techniques, often involving deep neural networks. Continued advances in the use of such techniques require combined efforts between statisticians, computer scientists, and applied mathematicians to develop more sophisticated models and algorithms along with more comprehensive theoretical guarantees that support their use. In addition to its research goals, the institute trains Ph.D. students and postdoctoral fellows in statistics, computer science, and applied mathematics, and hosts interdisciplinary workshops and Winter/Summer schools. The research efforts in Phase I are on the analysis of nonconvex machine learning models, the design of optimization algorithms for training them, and on the development of nonparametric models and associated algorithms. The focus is on deep neural networks (DNNs), mostly in general, but also with respect to specific architectures of interest. The institute's research efforts emphasize the need to develop connections between state-of-the-art approaches for training DNNs and statistical performance guarantees (e.g., on generalization errors), which are currently not well understood. Optimization algorithms development centers on second-order-derivative-type techniques, including (Hessian-free) Newton, quasi-Newton, Gauss-Newton, and their limited memory variants. Recent advances have been made in the design of such methods; the PIs' work builds upon these efforts with their broad expertise in the design and implementation (including in parallel and distributed computing environments) of such methods. The development of nonparametric models promises to free machine learning approaches from restrictions imposed by large numbers of user-defined parameters (e.g., defining a network structure or learning rate of an optimization algorithm). Such models could lead to great advances in machine learning, and the institute's work in this area also draws on the PIs expertise in derivative-free optimization methods, which are needed for training in nonparametric settings.In this TRIPODS institute, the PIs approach all of these research directions with a unified perspective in the three disciplines of statistics, computer science, and applied mathematics. Indeed, as machine learning draws so heavily from these areas, future progress requires close collaborations between optimization experts, learning theorists, and statisticians---communities of researchers that, as yet, have tended to operate separately with differing terminology and publication venues. With an emphasis on deep learning, this institute aims to foster intercollegiate and interdisciplinary collaborations that overcome these hindrances.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.