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Constructive Preference Elicitation over Hybrid Combinatorial Spaces

Preference elicitation is the task of suggesting a highly preferred configuration to a decision maker. The preferences are typically learned by querying the user for choice feedback over pairs or sets of objects. In its constructive variant, new objects are synthesized "from scratch" by maximizing an estimate of the user utility over a combinatorial (possibly infinite) space of candidates. In the constructive setting, most existing elicitation techniques fail because they rely on exhaustive enumeration of the candidates. A previous solution explicitly designed for constructive tasks comes with no formal performance guarantees, and can be very expensive in (or unapplicable to) problems with non-Boolean attributes. We propose the Choice Perceptron, a Perceptron-like algorithm for learning user preferences from set-wise choice feedback over constructive domains and hybrid Boolean-numeric feature spaces. We provide a theoretical analysis on the attained regret that holds for a large class of query selection strategies, and devise a heuristic strategy that aims at optimizing the regret in practice. Finally, we demonstrate its effectiveness by empirical evaluation against existing competitors on constructive scenarios of increasing complexity.

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