DeepAI AI Chat
Log In Sign Up

Wasserstein Distributionally Robust Inverse Multiobjective Optimization

by   Chaosheng Dong, et al.

Inverse multiobjective optimization provides a general framework for the unsupervised learning task of inferring parameters of a multiobjective decision making problem (DMP), based on a set of observed decisions from the human expert. However, the performance of this framework relies critically on the availability of an accurate DMP, sufficient decisions of high quality, and a parameter space that contains enough information about the DMP. To hedge against the uncertainties in the hypothetical DMP, the data, and the parameter space, we investigate in this paper the distributionally robust approach for inverse multiobjective optimization. Specifically, we leverage the Wasserstein metric to construct a ball centered at the empirical distribution of these decisions. We then formulate a Wasserstein distributionally robust inverse multiobjective optimization problem (WRO-IMOP) that minimizes a worst-case expected loss function, where the worst case is taken over all distributions in the Wasserstein ball. We show that the excess risk of the WRO-IMOP estimator has a sub-linear convergence rate. Furthermore, we propose the semi-infinite reformulations of the WRO-IMOP and develop a cutting-plane algorithm that converges to an approximate solution in finite iterations. Finally, we demonstrate the effectiveness of our method on both a synthetic multiobjective quadratic program and a real world portfolio optimization problem.


page 1

page 2

page 3

page 4


Distributionally Robust Logistic Regression

This paper proposes a distributionally robust approach to logistic regre...

Principled Learning Method for Wasserstein Distributionally Robust Optimization with Local Perturbations

Wasserstein distributionally robust optimization (WDRO) attempts to lear...

The Performance of Wasserstein Distributionally Robust M-Estimators in High Dimensions

Wasserstein distributionally robust optimization has recently emerged as...

Robust Metric Learning by Smooth Optimization

Most existing distance metric learning methods assume perfect side infor...

Distributionally robust halfspace depth

Tukey's halfspace depth can be seen as a stochastic program and as such ...

The quadratic Wasserstein metric for inverse data matching

This work characterizes, analytically and numerically, two major effects...

Markov Decision Processes under Model Uncertainty

We introduce a general framework for Markov decision problems under mode...