Multi-objective decision making.

在现实世界中做决定是困难的，因为通常要同时考虑许多观点和选择。这些问题中的许多都可以在数学上形式化为一种多目标决策问题，其目标是在决策者设定的不同目标之间确定一组提供最佳折衷的决策。这个项目的重点是开发理论上合理的算法来解决不同类型的多目标决策问题。该项目属于EPSRC数学科学研究领域，涵盖了“运筹学”和“统计与应用概率”等相关领域。该项目也得到了跨国化工公司巴斯夫的支持，他们的合作将有助于推动有效和实用工具的开发和测试。该项目的核心部分集中在多目标黑盒优化问题上，其目标是优化一个评估成本高且受噪声影响的矢量值函数。例如，化学制造中的一个常见问题是找到控制输入的组合，从而产生一些理想的性能结果，如高产量和低经济成本。在这样的环境下，我们可能无法完全了解可能发生的化学反应，因此我们只能依靠进行化学实验的技术人员收集的数据。贝叶斯优化已经在文献中被证明是解决这类问题的一个有前途的策略。这项工作将建立在现有文献的基础上，重点是建立有效的模型和效用函数，考虑到问题的多目标和顺序性质。特别是，对现有工作的一个实际扩展是通过有效和高效地结合目标和顺序选择过程的动态之间的相关性来提高优化过程的样本效率。这项工作的另一个方向考虑了更一般的问题，它属于多目标马尔可夫决策过程的主题。这些过程通常用于对顺序决策问题进行建模，其中决策者通过选择操作及时地与系统进行顺序交互。用户采取的操作会影响他们从系统接收到的反馈以及他们将来可能收到的反馈。多目标反馈设置的大部分现有工作依赖于标量化框架，其中我们将多目标问题转换为一组可以使用标准技术解决的单目标问题。在有或没有标量化的情况下，解决这些多目标问题的理论结果的发展仍然是一个持续的努力。在可行的情况下，本项目将通过识别和解决文献中的差距来促进这一努力。希望这一系列的工作能够揭示一些有用的见解，然后可以利用这些见解来创建有理论保证支持的多目标算法。

Making decisions in the real world is difficult because there are usually many perspectives and options to consider simultaneously. Many of these problem can be formalised mathematically as a type of multi-objective decision making problem, where the goal is to identify a set of decisions that offer the best compromise among the different objectives set by the decision maker. The focus of this project is to develop theoretically justified algorithms to solve different types of multi-objective decision making problems. This project falls within the EPSRC Mathematical Sciences research area, which covers relevant areas such as "operational research" and "statistics and applied probability". This project is also supported by the multinational chemical company BASF, whose collaboration will help drive the development and testing of tools that are both effective and practical in purpose.A central part of this project is focussed on the multi-objective black-box optimization problem, where the goal is to optimize a vector valued function that is expensive to evaluate and subject to noise. For example, a common problem in chemical manufacturing is to find the combination of controls inputs that lead to some desirable performance outcomes such as high yield and low economical cost. In such a setting, we might not fully understand the possible chemical reactions that can take place and hence we rely solely on the data collected by the technicians performing the chemical experiments. Bayesian optimization has been shown in the literature to be a promising strategy to address these sorts of problems. This work will build on top the existing literature and focus on building effective models and utility functions that take into consideration the multi-objective and sequential nature of the problem. In particular, a practical extension to the existing work is to improve sample efficiency of the optimization procedure by effectively and efficiently incorporating correlation between the objectives and the dynamics of the sequential selection procedure.The other direction of this work considers the more general problem, which falls under the topic of multi-objective Markov decision processes. These processes are commonly used to model a sequential decision making problem, where a decision maker interacts with a system sequentially in time by selecting actions. The actions that a user takes influences the feedback they receive from the system and the potential feedback they will receive in the future. A large portion of the existing work for the multi-objective feedback setting relies on the scalarization framework, where we transform the multi-objective problem into a set of single objective problems that can be solved using standard techniques. The development of theoretical results for solving these multi-objective problems with and without scalarization is still an ongoing endeavour. This project will contribute to this effort by identifying and addressing gaps in the literature where feasible. The hope is that this stream of work will uncover some useful insight, which can then be exploited to create multi-objective algorithms that are supported by theoretical guarantees.