Structured Blackbox Optimization

结构化黑盒优化

• 批准号: RGPIN-2018-03865
• 负责人: Hare, Warren
• 金额: $ 3.13万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=761809
• 关键词: Structured; Blackbox; Optimization

Optimization, the study of minimizing or maximizing a function, arises naturally in virtually every area of science. In some applications the use of optimization is obvious, such as minimizing the cost when designing a new road. In other applications the use of optimization is more subtle, such as denoising in medical imaging.In optimization, a blackbox is any function that is not analytically available. When evaluated at a point, a blackbox returns an objective function value. In addition, some blackboxes return a (sub)gradient vector. A blackbox optimization problem is any optimization problem where some, or all, of the functions defining the problem are given by blackboxes.One common occurrences of blackbox functions is the output of a computer simulation. Given some input parameters, the simulation executes and returns a function value. If the simulation is implemented in an open source language, then automated differentiation could be employed to further obtain a (sub-)gradient vector. As computer simulations have become ubiquitous in modern research, blackbox optimization represents one of the most important areas of research for solving future real-world applications.In some applications, the blackbox has some visible structure. A structured blackbox optimization problem is any optimization problem where some, or all, of the underlying functions are given by blackboxes, but the problem itself has some visible mathematical structure. A simple example of structured blackbox optimization is minimizing the `worst-case outcome'. In this case, each scenario is provided through a blackbox, and the final objective is to minimize the maximum of all the blackbox functions. This can be (and often has been) approached by considering the maximum of all the blackbox functions as a single blackbox function. However, if we recognize the structure of the max function, we can design algorithms that are faster and more accurate for this problem.My research focuses on structured blackbox optimization. My work includes the development of novel algorithms for structured blackbox optimization, the application of algorithms to solve real-world optimization problems, and the advancement of knowledge in the mathematics behind structured blackbox optimization.HQP interested in working in algorithm design will be trained in developing convergence analysis, implementing algorithms, and numerical testing of algorithms. HQP interested in working in optimization applications will be trained in determining the structures within optimization problems, considering methods to exploit this structure, and selecting the appropriate algorithm to solve problems while considering solution time and quality. HQP interested in working theoretical analysis will be trained in the broad field of optimization theory, including strong foundations in functional analysis and variational analysis.

优化，即对功能的最小化或最大化的研究，在几乎每个科学领域都很自然地出现。在某些应用中，优化的使用是显而易见的，例如在设计一条新道路时最小化成本。在其他应用中，优化的使用更为微妙，例如医学成像中的去噪。在优化中，黑盒是任何无法分析的函数。当在某一点求值时，黑盒返回目标函数值。此外，一些黑盒返回（子）梯度向量。黑箱优化问题是定义问题的部分或全部函数由黑箱给出的任何优化问题。黑箱函数的一个常见现象是计算机模拟的输出。给定一些输入参数，模拟执行并返回一个函数值。如果模拟是用开源语言实现的，那么可以使用自动微分来进一步获得（子）梯度向量。随着计算机模拟在现代研究中变得无处不在，黑盒优化代表了解决未来现实世界应用的最重要研究领域之一。在某些应用程序中，黑盒具有一些可见的结构。结构化黑箱优化问题是一些或全部底层函数由黑箱给出的优化问题，但问题本身具有一些可见的数学结构。结构化黑盒优化的一个简单例子是最小化“最坏结果”。在这种情况下，每个场景都是通过一个黑盒提供的，最终目标是最小化所有黑盒函数的最大值。这可以（并且经常）通过将所有黑盒函数的最大值视为单个黑盒函数来解决。然而，如果我们认识到max函数的结构，我们就可以设计出更快、更准确的算法来解决这个问题。我的研究重点是结构化黑盒优化。我的工作包括开发结构化黑盒优化的新算法，应用算法来解决现实世界的优化问题，以及结构化黑盒优化背后的数学知识的进步。对算法设计工作感兴趣的HQP将接受开发收敛分析，实现算法和算法数值测试的培训。对优化应用感兴趣的HQP将被训练确定优化问题中的结构，考虑利用这种结构的方法，并在考虑解决时间和质量的情况下选择适当的算法来解决问题。对理论分析感兴趣的HQP将接受广泛的优化理论领域的培训，包括泛函分析和变分分析的坚实基础。