Preference Learning and Optimization for Partial Lexicographic Preference Forests over Combinatorial Domains

Learning Partial Lexicographic Preference Trees and Forests over Multi-Valued Attributes

“…PLP-trees were originally defined to represent preference orders over combinatorial domains with binary attributes [12]. In this work, we expand the definition to the general case where attributes are multi-valued (not necessarily binary), which is relevant to practical applications.…”

“…Depending on whether preferences in CI trees are unconditional or not, we refer to them as conditional importance and unconditional preference trees (or CIUP trees), and conditional importance and conditional preference trees (or CICP trees). We refer to the paper by Liu and Truszczynski [12] for formal definitions and examples of CI PLP-trees.…”

“…They include conditional preference networks (CP-nets) [2], and models ordering outcomes lexicographically such as lexicographic strategies [16], conditional preference trees (CP-trees) [17], lexicographic preference trees (LP-trees) [1], conditional lexicographic preference trees [3], partial lexicographic preference trees (PLP-trees) [12], and preference trees [6,13]. As with quantitative models, learning qualitative models is important because eliciting them directly from users is often impractical.…”

“…In this work, we study the problem of learning PLP-trees over multi-valued attributes, which generalize the original binary version of PLP-trees [12]. As in the binary case, multi-valued PLP-trees can be grouped into four classes that capture different types of orders: unconditional importance and unconditional preference (UIUP) trees, unconditional importance and conditional preference (UICP) trees, conditional importance and unconditional preference (CIUP) trees, and conditional importance and conditional preference (CICP) trees.…”

“…Schmitt and Martignon [16] showed that for lexicographic strategies, a special case of UIUP PLP-trees, computing a lexicographic strategy maximizing the number of correctly handled examples is NP-hard, and Liu and Truszczynski [12] extended this result to other classes of PLP-trees. Therefore, in this paper, we focus on the problem of practicality of learning PLP-trees and using them to represent preferences.…”