Robust Optimization using Machine Learning for Uncertainty Sets
Robust Optimization using Machine Learning for Uncertainty Sets
复制标题
使用机器学习对不确定性集进行鲁棒优化
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
C. Rudin
中科院分区：
文献类型：
--
作者：
Theja Tulabandhula;C. Rudin
我们的目标是建立强大的优化问题，根据过去的复杂数据做出决策。在鲁棒优化（RO）中，目标通常是创建一个决策策略，该策略对我们对未来的不确定性具有鲁棒性。特别是，我们希望我们的政策能够最好地处理可能出现的最糟糕的情况，而这些情况是不确定的。传统上，不确定性集只是由用户选择，或者它可能是以过于简单的方式进行估计，具有很强的假设;而在这项工作中，我们从过去收集的数据中学习不确定性集。过去的数据是从（未知的）可能复杂的高维分布中随机抽取的。我们提出了一个新的不确定性集的设计，并展示了如何从统计学习理论的工具可以用来提供概率保证的政策的鲁棒性。
Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about the future. In particular, we want our policy to best handle the the worst possible situation that could arise, out of an uncertainty set of possible situations. Classically, the uncertainty set is simply chosen by the user, or it might be estimated in overly simplistic ways with strong assumptions; whereas in this work, we learn the uncertainty set from data collected in the past. The past data are drawn randomly from an (unknown) possibly complicated high-dimensional distribution. We propose a new uncertainty set design and show how tools from statistical learning theory can be employed to provide probabilistic guarantees on the robustness of the policy.