Inferring Parameters Through Inverse Multiobjective Optimization

TL;DR

This paper introduces a new inverse multiobjective optimization framework that accurately infers decision-making parameters from noisy data, effectively separating true preferences from errors and providing insights into population-level decision diversity.

Contribution

The paper develops a novel inverse optimization model for multiobjective problems, with advanced algorithms and theoretical analysis, to improve parameter inference from noisy observations.

Findings

Effective estimation of decision maker preferences.

Ability to denoise and recover optimal decisions.

Insights into population preference distribution.

Abstract

Given a set of human's decisions that are observed, inverse optimization has been developed and utilized to infer the underlying decision making problem. The majority of existing studies assumes that the decision making problem is with a single objective function, and attributes data divergence to noises, errors or bounded rationality, which, however, could lead to a corrupted inference when decisions are tradeoffs among multiple criteria. In this paper, we take a data-driven approach and design a more sophisticated inverse optimization formulation to explicitly infer parameters of a multiobjective decision making problem from noisy observations. This framework, together with our mathematical analyses and advanced algorithm developments, demonstrates a strong capacity in estimating critical parameters, decoupling "interpretable" components from noises or errors, deriving the denoised \emph{optimal} decisions, and ensuring statistical significance. In particular, for the whole decision maker population, if suitable conditions hold, we will be able to understand the overall diversity and the distribution of their preferences over multiple criteria, which is important when a precise inference on every single decision maker is practically unnecessary or infeasible. Numerical results on a large number of experiments are reported to confirm the effectiveness of our unique inverse optimization model and the computational efficacy of the developed algorithms.