Interface of Statistical Learning and Optimal Decisions

在生物、自然、社会科学和工程领域，大量数据集被常规收集，并对统计分析、个性化治疗和决策产生了巨大影响。这些成功背后的驱动引擎是深度学习的表示能力和马尔可夫决策过程的动态策略优化框架，以及大数据的可用性。然而，训练算法仍然需要大量的时间和计算能力，而统计和算法效率也仍然知之甚少。该项目的目的是理解和改进用于深度学习、强化学习和大数据分析的统计方法，重点是统计建模和最优策略学习之间的接口。它旨在推进人工智能研究、自动驾驶和控制、电子商务、分子机制、生物过程、遗传关联、大脑功能以及经济和金融风险方面的知识。本项目将通过与本科生、研究生和博士后的紧密合作，将研究与教育结合起来，并开发具有良好理论支持的公开计算机软件。该项目旨在开发和理解深度学习中使用的各种新的统计方法，引入统计建模和学习技术来增强强化学习中的策略优化，并解决大数据分析中的几个重要问题。第一个目标是提供对深度学习中使用的各种技术的理论理解。研究者将研究过度参数化在非线性模型和低秩矩阵恢复中的作用，理解最小范数插值并阐明神经网络模型与数据分布尾部之间的相互作用。第二个目标是研究统计建模和最优决策之间的接口。研究者计划使用半参数模型和结构化非参数模型研究上下文动态定价，并从自适应函数近似的角度使用分层组合模型揭示支撑深度强化学习成功的统计理论。研究者还将为政策学习引入新的降维技术和理论，以提高统计和算法效率。第三个目标是解决大数据分析中的几个风格化问题。这些包括马尔可夫依赖性、缺失数据、高度相关的测量、删减的响应和分布式数据等。该奖项反映了美国国家科学基金会的法定使命，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。

Massive datasets are routinely collected in the fields of biological, natural, and social sciences, and engineering and have had a huge impact on statistical analysis, personalized treatments, and decision-making. The driving engines behind these successes are the representation power of deep learning and the dynamic policy optimization framework of Markov decision processes, in addition to the availability of big data. However, training algorithms still take enormous amounts of time and computing power, while statistical and algorithmic efficiencies are also still poorly understood. The aim of this project is to understand and improve statistical methods used in deep learning, reinforcement learning, and big data analysis, with an emphasis on the interfaces between statistical modeling and optimal policy learning. It aims to advance knowledge in AI research, automatic driving and control, e-commerce, molecular mechanisms, biological processes, genetic associations, brain functions, and economic and financial risks. The project will integrate research and education by working closely with undergraduate students, graduate students, and postdoctoral fellows, and develop publicly available computer software with sound theoretical support.The project aims at developing and understanding various new statistical methods used in deep learning, introducing statistical modeling and learning techniques to enhance policy optimization in reinforcement learning, and addressing several important issues in the analysis of big data. The first aim is to provide a theoretical understanding of various techniques used in deep learning. The investigator will study the role of over-parametrization in nonlinear models and low-rank matrix recoveries, understanding minimum norm interpolation and elucidating the interactions between neural network models and the tails of the data distribution. The second aim is to study the interface between statistical modeling and optimal decision. The investigator plans to study contextual dynamic pricing using semiparametric models and structured nonparametric models and to unveil the statistical theory that underpins the success of deep reinforcement learning from an adaptive function approximation point of view using hierarchical composition models. The investigator will also introduce new dimensionality reduction techniques and theories for policy learning to improve both statistical and algorithmic efficiencies. The third aim is to address several stylized issues in big data analytics. These include Markovian dependence, missing data, highly correlated measurements, censored responses, and distributed data, among others.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.