Multi-objective decision making.

在真实的世界中做决定是困难的，因为通常有许多观点和选择需要同时考虑。这些问题中的许多可以在数学上形式化为一种类型的多目标决策问题，其目标是确定一组决策，这些决策在决策者设定的不同目标之间提供最佳折衷。该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数学科学研究领域的福尔斯，该领域涵盖了“运筹学”和“统计学和应用概率”等相关领域。该项目还得到了跨国化学公司巴斯夫的支持，他们的合作将有助于推动有效和实用的工具的开发和测试。该项目的核心部分是集中在多目标黑箱优化问题上，目标是优化一个向量值函数，该函数的评估成本很高，并且会受到噪声的影响。例如，化学制造中的一个常见问题是找到控制输入的组合，从而导致一些期望的性能结果，例如高产率和低经济成本。在这种情况下，我们可能无法完全了解可能发生的化学反应，因此我们只能依赖技术人员进行化学实验收集的数据。贝叶斯优化已在文献中被证明是一个很有前途的策略，以解决这类问题。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连续性。特别是，一个实际的扩展到现有的工作是提高样本效率的优化过程中，有效地和高效地将目标和动态的顺序选择procedure.The另一个方向的工作考虑更一般的问题，其中福尔斯属于多目标马尔可夫决策过程的主题。这些过程通常用于模拟顺序决策问题，其中决策者通过选择动作按顺序与系统进行交互。用户采取的行动会影响他们从系统收到的反馈以及他们将来可能收到的反馈。现有的大部分工作的多目标反馈设置依赖于标量化框架，在那里我们将多目标问题转化为一组可以使用标准技术解决的单目标问题。解决这些多目标问题的理论成果的发展与不标量化仍然是一个持续的努力。本项目将通过在可行的情况下查明和解决文献中的空白，为这一努力作出贡献。希望这项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由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.