Inference with Choice Functions Made Practical
This work addresses the challenge of practical decision-making under uncertainty for researchers and practitioners in fields like AI and operations research, though it appears incremental as it builds on existing coherence axioms.
The paper tackles the problem of making conservative inferences from previous choices using choice functions, presenting a practical algorithm to compute the natural extension of choice assessments to coherent choice functions and methods to improve scalability.
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose axioms directly on the represented decisions. We here adopt the coherence axioms of De Bock and De Cooman (2019). We show how to naturally extend any given choice assessment to such a coherent choice function, whenever possible, and use this natural extension to make new choices. We present a practical algorithm to compute this natural extension and provide several methods that can be used to improve its scalability.