Collaborative Research: CIF: Small: A Unified Framework of Distributional Optimization via Variational Transport

合作研究:CIF:小型:通过变分传输的分布式优化的统一框架

基本信息

  • 批准号:
    2008513
  • 负责人:
  • 金额:
    $ 25万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2020
  • 资助国家:
    美国
  • 起止时间:
    2020-10-01 至 2024-09-30
  • 项目状态:
    已结题

项目摘要

Distributional optimization refers to a class of mathematical problems where the optimizing variable in the objective function is a probability measure over some space. Because of its highly technical nature, distributional optimization has remained largely unexplored with advances made only on specific problem instances. This project proposes a unified framework to explore challenging distributional optimization problems in a wide range of important application domains. The main objective is to develop a comprehensive theory supporting the principled design of novel and efficient optimization algorithms. To do so, establishing connections between several mathematical disciplines will be required, including optimization theory, optimal transport, functional inequalities, and statistics. This will promote the cross-fertilization of ideas and lead to the creation of training material from an interdisciplinary perspective. The resulting open-source packages will be made available to support research efforts in related fields that our daily lives depend on. Problems in distributional optimization are infinite-dimensional optimization problems where the optimization variable is a probability measure. Many research problems fall into this class of problems; in particular, any non-convex optimization problem over Euclidean space can be cast as a convex distributional optimization problem. Traditionally, specific instances of these problems have been studied independently of each other. Formulating these seemingly different optimization problems into a single unified framework will allow more powerful mathematical techniques and tools to be used. This will lead to deeper insights into the structure of solutions, and to efficient algorithms tailored to large-scale applications in artificial intelligence and data science. The proposed framework is based on optimal transport theory that endows the space of distributions with a natural geometry. The proposed algorithm utilizes the gradient flow of the objective with respect to this geometry. To achieve scalability, the optimization variable is approximated by a collection of particles, with the algorithm now describing the collective dynamics of the particles. A novel variational approach will be used to approximate the gradient descent direction. The theoretical properties of this algorithm will be investigated thoroughly, including provable performance guarantees, convergence rates, and statistical properties. Case studies will be carried out by specializing this unified framework to applications such as Bayesian inference and distributionally robust learning. The acceleration of this algorithm will also be investigated by incorporating existing optimization techniques, such as momentum and variance reduction, as a way to improve convergence rates. Finally, the project will explore how to adapt this algorithm from minimization problems to min-max problems in order to deal with game-theoretic applications.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.
分布优化是指一类数学问题,其中目标函数中的优化变量是某个空间上的概率测度。由于其高度的技术性,分布式优化在很大程度上仍然是未开发的进展,只有在特定的问题实例。该项目提出了一个统一的框架,以探索具有挑战性的分布优化问题,在广泛的重要应用领域。其主要目标是发展一个全面的理论,支持新的和有效的优化算法的原则设计。要做到这一点,需要在几个数学学科之间建立联系,包括最优化理论、最优运输、函数不等式和统计学。这将促进思想交流,并导致从多学科角度编写培训材料。由此产生的开源软件包将可用于支持我们日常生活所依赖的相关领域的研究工作。分布优化问题是无限维优化问题,其中优化变量是概率测度。许多研究问题属于这类问题;特别是,任何非凸优化问题在欧几里德空间可以被铸造作为一个凸分布优化问题。传统上,这些问题的具体实例已经被彼此独立地研究。将这些看似不同的优化问题公式化到一个统一的框架中,将允许使用更强大的数学技术和工具。这将导致更深入地了解解决方案的结构,并为人工智能和数据科学中的大规模应用量身定制高效算法。所提出的框架是基于最优运输理论,赋予空间的分布与自然的几何形状。该算法利用梯度流的目标相对于这个几何形状。为了实现可扩展性,优化变量近似为粒子的集合,算法现在描述粒子的集体动态。一种新的变分方法将被用来近似梯度下降方向。该算法的理论特性将被彻底研究,包括可证明的性能保证,收敛速度和统计特性。案例研究将进行专门的统一框架,如贝叶斯推理和分布式鲁棒学习的应用。该算法的加速也将通过结合现有的优化技术,如动量和方差减少,作为一种提高收敛速度的方式进行研究。最后,该项目将探讨如何适应这种算法从最小化问题的最小-最大问题,以处理博弈论的应用程序。这个奖项反映了NSF的法定使命,并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

期刊论文数量(16)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Markov Chain Monte Carlo for Gaussian: A linear control perspective
高斯马尔可夫链蒙特卡罗:线性控制视角
  • DOI:
    10.1109/lcsys.2023.3285140
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    3
  • 作者:
    Yuan, Bo;Fan, Jiaojiao;Wang, Yuqing;Tao, Molei;Chen, Yongxin
  • 通讯作者:
    Chen, Yongxin
Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
  • DOI:
  • 发表时间:
    2020-07
  • 期刊:
  • 影响因子:
    0
  • 作者:
    JiaoJiao Fan;A. Taghvaei;Yongxin Chen
  • 通讯作者:
    JiaoJiao Fan;A. Taghvaei;Yongxin Chen
A Proximal Algorithm for Sampling from Non-Smooth Potentials
  • DOI:
    10.1109/wsc57314.2022.10015293
  • 发表时间:
    2021-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Jiaming Liang;Yongxin Chen
  • 通讯作者:
    Jiaming Liang;Yongxin Chen
Path Integral Sampler: a stochastic control approach for sampling
  • DOI:
  • 发表时间:
    2021-11
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Qinsheng Zhang;Yongxin Chen
  • 通讯作者:
    Qinsheng Zhang;Yongxin Chen
An optimal control approach to particle filtering
  • DOI:
    10.1016/j.automatica.2023.110894
  • 发表时间:
    2021-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Qinsheng Zhang;A. Taghvaei;Yongxin Chen
  • 通讯作者:
    Qinsheng Zhang;A. Taghvaei;Yongxin Chen
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Yongxin Chen其他文献

Data-Driven Optimal Control via Linear Transfer Operators: A Convex Approach
通过线性传递算子的数据驱动最优控制:凸方法
  • DOI:
    10.1016/j.automatica.2022.110841
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    J. Moyalan;Hyungjin Choi;Yongxin Chen;U. Vaidya
  • 通讯作者:
    U. Vaidya
Effects of neferine on TGF-β1 induced proliferation and gremlin expression in hepatic stellate cells
莲心碱对TGF-β1诱导的肝星状细胞增殖和gremlin表达的影响
  • DOI:
    10.3329/bjp.v7i3.11298
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    1.6
  • 作者:
    Xiaofei Li;L. Lou;Shuang Wu;Yongxin Chen;L. Jin
  • 通讯作者:
    L. Jin
I2-Catalyzed diamination of acetyl-compounds for the synthesis of multi-substituted imidazoles
I2-催化乙酰基化合物二胺化合成多取代咪唑
  • DOI:
    10.1039/c5nj00910c
  • 发表时间:
    2015-06
  • 期刊:
  • 影响因子:
    3.3
  • 作者:
    Jinpeng Qu;Ping Wu;Dong Tang;Xu Meng;Yongxin Chen;Shuaibo Guo;Baohua Chen
  • 通讯作者:
    Baohua Chen
Large eddy simulation of flow past a bluff body using immersed boundary method
采用浸入边界法对流经阻流体的大涡模拟
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Yongxin Chen;K. Djidjeli;Zheng
  • 通讯作者:
    Zheng
Navigation with Probabilistic Safety Constraints: A Convex Formulation
具有概率安全约束的导航:凸公式

Yongxin Chen的其他文献

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{{ truncateString('Yongxin Chen', 18)}}的其他基金

Graphical Optimal Transport: Theory, Algorithms, and Applications
图形优化传输:理论、算法和应用
  • 批准号:
    2206576
  • 财政年份:
    2022
  • 资助金额:
    $ 25万
  • 项目类别:
    Standard Grant
CAREER: Towards a Principled Framework for the Modeling and Control of Non-equilibrium Thermodynamic Systems
职业:建立非平衡热力学系统建模和控制的原则框架
  • 批准号:
    1942523
  • 财政年份:
    2020
  • 资助金额:
    $ 25万
  • 项目类别:
    Continuing Grant
COLLABORATIVE RESEARCH: DYNAMICS OF DENSITIES: MODELING, CONTROL AND ESTIMATION
合作研究:密度动态:建模、控制和估计
  • 批准号:
    1807677
  • 财政年份:
    2018
  • 资助金额:
    $ 25万
  • 项目类别:
    Standard Grant
COLLABORATIVE RESEARCH: DYNAMICS OF DENSITIES: MODELING, CONTROL AND ESTIMATION
合作研究:密度动态:建模、控制和估计
  • 批准号:
    1901599
  • 财政年份:
    2018
  • 资助金额:
    $ 25万
  • 项目类别:
    Standard Grant

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Collaborative Research: CIF: Medium: Snapshot Computational Imaging with Metaoptics
合作研究:CIF:Medium:Metaoptics 快照计算成像
  • 批准号:
    2403122
  • 财政年份:
    2024
  • 资助金额:
    $ 25万
  • 项目类别:
    Standard Grant
Collaborative Research: CIF-Medium: Privacy-preserving Machine Learning on Graphs
合作研究:CIF-Medium:图上的隐私保护机器学习
  • 批准号:
    2402815
  • 财政年份:
    2024
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    $ 25万
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Collaborative Research: CIF: Small: Mathematical and Algorithmic Foundations of Multi-Task Learning
协作研究:CIF:小型:多任务学习的数学和算法基础
  • 批准号:
    2343599
  • 财政年份:
    2024
  • 资助金额:
    $ 25万
  • 项目类别:
    Standard Grant
Collaborative Research: CIF: Small: Mathematical and Algorithmic Foundations of Multi-Task Learning
协作研究:CIF:小型:多任务学习的数学和算法基础
  • 批准号:
    2343600
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    $ 25万
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Collaborative Research: CIF-Medium: Privacy-preserving Machine Learning on Graphs
合作研究:CIF-Medium:图上的隐私保护机器学习
  • 批准号:
    2402817
  • 财政年份:
    2024
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    $ 25万
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Collaborative Research: NSF-AoF: CIF: Small: AI-assisted Waveform and Beamforming Design for Integrated Sensing and Communication
合作研究:NSF-AoF:CIF:小型:用于集成传感和通信的人工智能辅助波形和波束成形设计
  • 批准号:
    2326622
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Collaborative Research: CIF-Medium: Privacy-preserving Machine Learning on Graphs
合作研究:CIF-Medium:图上的隐私保护机器学习
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Collaborative Research: CIF: Medium: Snapshot Computational Imaging with Metaoptics
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  • 批准号:
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