CIF: Small: Efficient and Secure Federated Structure Learning from Bad Data

该项目开发安全的分布式算法，用于有效解决医学成像和机器学习中出现的大量优化问题。重要的例子包括加速磁共振成像（MRI）、产品推荐系统、计算机视觉（例如，遮挡去除或视频编辑）和生物信息学（未标记数据分组）。重点是快速的算法，只需要少量的数据通信，并且在数据稀缺的情况下工作良好。算法速度在所有现代应用中都是一个重要的问题。在MRI中，它对于（近）实时应用至关重要，例如介入性MRI或动态识别和纠正伪影，例如，如果患者在第一次扫描期间咳嗽，则重新扫描。样本效率对于加速MRI扫描，或者从很少的可用产品中了解用户对产品的评级至关重要。该项目还通过CyMath项目支持早期数学教育，该项目由热爱数学的研究生为小至三年级的学生提供课后数学辅导支持。该项目引入了一种新的解决方案框架，称为交替梯度下降（GD）和最小化，它为许多优化问题提供了更快、更高效的通信解决方案，其中交替最小化（AltMin）是一种流行的解决方案。特别地，它对于在一组变量上求最小值比在另一组变量上求最小值快得多的问题很有用。从谨慎地初始化一个集合开始，AltGDmin交替地更新变量，对较快的集合使用最小化，对另一个集合使用梯度下降（GD）。通常，对某些变量的最小化之所以快速，是因为优化问题与这些变量解耦了。这种解耦还有助于在联邦设置中保证每次迭代的通信效率和隐私。对一组变量的最小化使用也有助于确保在每次算法迭代中有足够的误差衰减。这意味着，对于某些问题，例如低秩列感知，AltGDmin几乎与（分解的）GD一样快，每次迭代的通信效率也一样高，而收敛速度几乎与AltMin一样快。这使得它比两种解决方案都要快。导出了特定于问题的正确性保证。这决定了迭代复杂度和样本复杂度的理论界限。获得这些结果需要新的证明技术的发展，这可能是独立的兴趣。原因是AltGDmin既不是AltMin方法，也不是任何变量子集的标准GD算法。设计和分析拜占庭弹性（安全）AltGDmin算法正在研究各种低秩，以及其他结构，恢复问题。该项目由计算机和信息科学理事会（CISE）的计算和通信基金会（CCF）部门以及促进竞争研究的既定计划（EPSCoR）共同资助。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。

This project develops secure distributed algorithms for efficiently solving a large class of optimization problems that occur in medical imaging and machine learning. Important examples include accelerated magnetic resonance imaging (MRI), product recommender systems, computer vision (e.g., occlusion removal or video editing), and bioinformatics (grouping of unlabeled data). The focus is on algorithms that are fast, require communicating only small amounts of data, and work well in the data-scarce regime. Algorithm speed is an important concern in all modern applications. Within MRI, it is essential for (near) real-time applications such as interventional MRI or on the fly identification and correction of artifacts, e.g., re-scanning if the patient coughs during the first scan. Sample efficiency is critical for accelerating the MRI scan, or for learning user ratings of products from very few available ones. The project also supports Early Math education via the CyMath program, a program in which Math-loving graduate students provide after-school Math tutoring support for students as young as third graders. This project introduces a novel solution framework called alternating gradient descent (GD) and minimization that provides a faster and more communication-efficient solution for many optimization problems for which alternating minimization (AltMin) is a popular solution. In particular, it is useful for any problem for which the minimization over one set of variables is much quicker than that over the other set. Starting with a careful initialization for one set, AltGDmin alternately updates the variables using minimization for the quicker set and gradient descent (GD) for the other set. Often, the reason that the minimization is fast over some variables is that the optimization problem is decoupled with respect to these variables. This decoupling also helps guarantee per-iteration communication-efficiency and privacy in federated settings. The use of minimization for one set of the variables is also what helps ensure sufficient error decay in each algorithm iteration. This implies that, for certain problems such as low rank column-wise sensing, AltGDmin is almost as fast and as communication-efficient per iteration as (factorized) GD, while converging almost as quickly as AltMin. This makes it faster overall than both types of solutions. Problem-specific correctness guarantees are derived. These determine the theoretical bounds on the iteration complexity and the sample complexity. Obtaining these results requires the development of novel proof techniques that may be of independent interest. The reason is AltGDmin is neither an AltMin approach nor a a standard GD algorithm for any subset of variables. The design and analysis Byzantine resilient (secure) AltGDmin algorithms is being studied for various low rank, and other structure, recovery problems.This project is jointly funded by the Computing and Communications Foundations (CCF) division of the Computer and Information Sciences Directorate (CISE) and the Established Program to Stimulate Competitive Research (EPSCoR).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.