Inferring Parameters Through Inverse Multiobjective Optimization
This work addresses the challenge of accurately inferring decision-making parameters in multiobjective scenarios, which is important for applications where understanding population-level preferences is needed, representing an incremental improvement over single-objective methods.
The paper tackles the problem of inferring parameters of multiobjective decision-making problems from noisy observations, developing a sophisticated inverse optimization framework that demonstrates strong capacity in estimating critical parameters and deriving denoised optimal decisions, with numerical results confirming its effectiveness and computational efficacy.
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.