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，最小化或最大化功能的研究自然而然地在科学的每个领域都产生。在某些应用中，优化的使用是显而易见的，例如在设计新道路时最小化成本。在其他应用程序中，优化的使用更加微妙，例如在医学成像中deNO.。在优化中，黑框是任何在分析上可用的函数。当在某个点进行评估时，黑框将返回目标函数值。另外，一些黑框返回（子）梯度向量。黑框优化问题是任何优化问题，其中某些或全部定义问题的功能由黑框提供。黑框函数的一种常见出现是计算机模拟的输出。给定一些输入参数，模拟执行并返回函数值。如果以开源语言实施模拟，则可以使用自动化分化来进一步获得（子）梯度向量。随着计算机模拟在现代研究中的普遍存在，BlackBox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。在某些应用中，BlackBox具有一定的可见结构。结构化的黑框优化问题是任何优化问题，其中某些或全部基础函数由黑盒给出，但是该问题本身具有一些可见的数学结构。 结构化黑框优化的一个简单示例是最大程度地减少“最坏情况结果”。在这种情况下，每种情况都是通过BlackBox提供的，最终目标是最大程度地减少所有BlackBox函数的最大值。通过将所有BlackBox函数的最大功能视为单个BlackBox函数，可以（并且经常被）接近。但是，如果我们识别最大函数的结构，我们可以设计为此问题更快，更准确的算法。我的研究专注于结构化的黑框优化。我的工作包括开发用于结构化黑盒优化的新型算法，算法在解决现实世界中的优化问题方面的应用以及结构化的黑盒优化背后的数学知识的进步。有兴趣从事算法设计工作的HQP将在开发融合分析，实施算法测试和数字测试和数字测试和数字测试中。 有兴趣从事优化应用程序的HQP将接受培训，以确定优化问题中的结构，考虑利用此结构的方法，并选择适当的算法来解决问题，同时考虑解决方案时间和质量。 对工作理论分析感兴趣的HQP将在优化理论的广泛领域进行培训，包括功能分析和变分分析中的强大基础。