Jul 12, 2020

We study a new unsupervised learning task of inferring objective functions or constraints of a multiobjective decision making model, based on a set of observed decisions. Specifically, we formulate such a learning problem as an inverse multiobjective optimization problem (IMOP) and propose its first sophisticated model with statistical guarantees. Then, we some fundamental connections between IMOP, K-means clustering and manifold learning. More precisely, we prove that every K-means clustering problem can be transformed equivalently into an IMOP, and every IMOP can be conversely interpreted as a constrained K-means clustering problem. In addition, we show that the Pareto optimal set is a piecewise continuous manifold with an intrinsic dimension of p-1 (where p is the number of objectives) under suitable conditions. Hence, IMOP can also be interpreted as a manifold learning problem. Leveraging these critical insights and connections, we propose two algorithms to solve IMOP through manifold learning and clustering. Numerical results confirm the effectiveness of our model and the computational efficacy of algorithms.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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