Efficient algorithms for optimal designs - a unifying approach

在学术界和工业界的许多研究领域，实验是建立新的科学成果的一种手段。例如，进行临床试验以评估新疗法的功效，或测试新发动机的原型以评估其燃料效率。众所周知，以统计学上最优/有效的方式设计这样的实验将从数据中得出准确的结论，同时节省资源，因为需要更少的实验运行。这不仅节省了实验者的成本，还节省了时间，并可能导致新的治疗/技术更快地进入市场。多年来，实验最优设计领域主要关注理论进展，其特征在于最优设计，并且在某些特殊情况下允许通过分析找到最优设计。通常，这些结果是在逐个案例的基础上获得的，分别针对每个模型和最优性标准。近年来，一些统一的方法被开发出来，这导致了该领域的重大理论进展。然而，在实践中，大多数优化设计问题太复杂，无法解析求解，需要有效的数值设计搜索算法。特别是，虽然最佳设计的好处已经在各个应用领域得到了很好的确立，但从业人员不能使用最佳设计，除非他们随时可用。因此，有必要开发有效的算法，并将其纳入一个易于使用的软件包，它可以找到最佳的设计快速和良好的精度。目前关于最优设计算法的文献类似于几十年前的理论设计文献，因为算法通常是针对具体问题逐个找到的，目前尚不清楚哪种算法/算法的构造方法在哪种情况下最有效。似乎运筹学和计算机科学等领域已经开发出许多必要的工具，在一般情况下的优化问题，现在需要对设计优化进行调整。现在是时候弥合统计优化设计社区和优化领域研究人员之间的差距了。最终目标是在优化设计和优化研究人员与优化设计用户之间的大型合作项目中，开发新算法/定制现有算法进行设计搜索。我们计划评估这些算法，并在软件包中实现最好的算法。拟议的研究将是实现这一目标的第一步。PI将访问来自所有领域的领先专家，以启动对话。在项目期间，PI将发展国际合作，学习新技术，会见潜在的进一步合作者和研究用户，并协调整个合作者团队，以找到最佳的前进方向。然后，她将带头撰写一份涉及所有国际合作者的大规模赠款提案，以访问和研究成果的未来用户。拟议的研究的成果将是提交一个大规模的合作赠款提案，以及一个方法的短名单，这似乎是最有希望的设计搜索。这个候选名单本身对优化设计的研究人员很有用，因为它提供了一些关于使用哪些算法的指导。这可能会导致更快或更准确地找到最佳/有效的设计，这反过来又有利于学术界和工业界的科学家，他们可以进行更好的实验。优化领域的研究人员将受益于其研究成果的新应用领域。

In many research areas in both academia and industry, experimentation is performed as a means to establish new scientific results. For example, clinical trials are conducted to assess the efficacy of new treatments, or prototypes of new engines are tested to assess their fuel efficiency. It is well established that designing such experiments in a statistically optimal/efficient way will result in accurate conclusions from the data while at the same time saving resources since fewer runs of the experiment are needed. This not only saves the experimenters' costs, but also time, and may result in new treatments/technology reaching the market faster. For many years, the field of optimal design of experiments was mostly concerned with theoretical advances, which characterised optimal designs, and in some special cases allowed finding optimal designs analytically. Usually these results were obtained on a case-by-case basis, for each model and optimality criterion separately. More recently, some unifying approaches were developed, which led to significant theoretical advances in the field.However, in practice, most optimal design problems are too complicated to be solved analytically, and efficient algorithms for numerical design search are required. In particular, while the benefits of optimal designs have been well established in various application areas, practitioners cannot use optimal designs unless they are readily available to them. Therefore, it is essential to develop efficient algorithms and to incorporate them into an easy-to-use software package, which can find optimal designs quickly and to a good accuracy. The current literature on algorithms for optimal designs resembles the theoretical design literature from decades ago in the sense that algorithms are usually found for specific problems on a case-by-case basis, and it is not clear which type of algorithm/construction method for algorithms will work best in which situation.It seems that areas such as operational research and computer science have already developed many of the necessary tools for optimisation problems in a general context, which now need to be tailored towards design optimisation. It is time to bridge the gap between the statistical optimal design community and researchers working in the field of optimisation. The ultimate goal is to develop new algorithms/tailor existing algorithms towards design search, within a large collaborative project between researchers in optimal design and in optimisation and users of optimal designs. We plan to assess these algorithms, and to implement the best ones in a software package available to users. The proposed research will be a first step towards this goal. The PI will visit leading experts from all areas to start the dialogue. During the project, the PI will develop international collaborations, learn new techniques, meet potential further collaborators and users of the research, and co-ordinate the whole team of collaborators to find the best way forward. She will then take the lead on writing a large scale grant proposal involving all international collaborators to be visited and future users of the research outputs. Deliverables of the proposed research will be the submission of a large scale collaborative grant proposal, and a shortlist of methods, which appear to be most promising for design search. This shortlist will in itself be useful to researchers in optimal design, since it gives some guidance on which algorithms to use. This may lead to finding optimal/efficient designs faster or with greater accuracy, which in turn benefits scientists in academia and industry who can conduct better experiments. Researchers in optimisation will benefit from a new application area for their research outputs.