Robust Optimization using Machine Learning for Uncertainty Sets

By Theja Tulabandhula, Cynthia Rudin. 2014

52 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, background): “This common scenario has been called the “Rashomon” effect of statistics (Breiman et al., 2001; see also Lecué, 2011; Statnikov et al., 2013; Tulabandhula and Rudin, 2014; Nevo and Ritov, 2017; Letham et al., 2016).”
Distributionally Robust Optimization: A Review (2019, methodology): “Tulabandhula and Rudin [303] incorporate machine learning for the decision making.”
Data Science of the People , for the People , by the People : A Viewpoint on an Emerging Dichotomy (2015, background): “The main robustness considered in classification is against uncertainty in the class frequencies or relative costs of different types of errors [37, 17], but robustness against other uncertainties are also considered [49, 57].”
All Models are Wrong but many are Useful: Variable Importance for Black-Box, Proprietary, or Misspecified Prediction Models, using Model Class Reliance (2018, background): “This common scenario has been called the “Rashomon” effect of statistics (Breiman et al., 2001; see also Statnikov et al., 2013; Tulabandhula and Rudin, 2014; Nevo and Ritov, 2015; Letham et al., 2016).”
A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results (2018, background): “This is done by Tulabandhula and Rudin (2014b) for machine learning to determine uncertainty sets for decision making.”