It's All in the Mix: Wasserstein Machine Learning with Mixed Features
Reza Belbasi Aras Selvi Wolfram Wiesemann
Problem definition: The recent advent of data-driven and end-to-end
decision-making across different areas of operations management has led to an
ever closer integration of prediction models from machine learning and
optimization models from operations research. A key challenge in this context
is the presence of estimation errors in the prediction models, which tend to be
amplified by the subsequent optimization model -- a phenomenon that is often
referred to as the Optimizer's Curse or the Error-Maximization Effect of
Optimization.
  Methodology/results: A contemporary approach to combat such estimation errors
is offered by distributionally robust problem formulations that consider all
data-generating distributions close to the empirical distribution derived from
historical samples, where `closeness' is determined by the Wasserstein
distance. While those techniques show significant promise in problems where all
input features are continuous, they scale exponentially when binary and/or
categorical features are present. This paper demonstrates that such
mixed-feature problems can indeed be solved in polynomial time. We present a
practically efficient algorithm to solve mixed-feature problems, and we compare
our method against alternative techniques both theoretically and empirically on
standard benchmark instances.
  Managerial implications: Data-driven operations management problems often
involve prediction models with discrete features. We develop and analyze a
methodology that faithfully accounts for the presence of discrete features, and
we demonstrate that our approach can significantly outperform existing methods
that are agnostic to the presence of discrete features, both theoretically and
across standard benchmark instances.