Compact Value-Function Representations for Qualitative Preferences

We consider the challenge of preference elicitation in systems that help users discover the most desirable item(s) within a given database. Past work on preference elicitation focused on structured models that provide a factored representation of users’ preferences. Such models require less information to construct and support efficient reasoning algorithms. This paper makes two substantial contributions to this area: (1) Strong representation theorems for factored value functions. (2) A methodology that utilizes our representation results to address the problem of optimal item selection.

💡 Research Summary

The paper addresses the problem of eliciting user preferences in order to retrieve the most desirable items from a large database. While prior work has focused on either quantitative utility functions or qualitative orderings, these approaches either require extensive user input or suffer from computational inefficiency. The authors make two major contributions.

First, they develop a representation theory for generalized additive (GA) value functions. A GA value function decomposes the overall utility into a sum of sub‑functions, each defined over a (possibly overlapping) subset of variables, called factors. The key theoretical result is that any consistent TCP‑net—a graphical model that captures both conditional preference statements (cp‑arcs) and conditional or unconditional relative importance statements (i‑arcs and ci‑arcs)—admits a GA representation whose factors are directly derived from the network’s structure. The authors define, for each variable X, its CP‑family F_X (X together with its immediate parents) and its extended CP‑family EF_X (the union of F_X and the CP‑families of its children). They then introduce the CP‑conditions, a set of linear inequalities that any collection of sub‑functions φ_X must satisfy in order for the summed function v = Σ φ_X(F_X) to be consistent with the original TCP‑net. By constructing a linear system L from these inequalities, they show that a feasible solution to L yields a GA value function that exactly respects all qualitative statements encoded in the TCP‑net. Importantly, the size of L grows polynomially with the number of variables, the maximum domain size, and the maximum factor size, making the approach computationally tractable for a wide class of networks.

Second, the paper proposes a practical elicitation methodology that leverages the representation results. Users are asked to provide natural‑language statements of two types: (1) conditional or unconditional value preferences (e.g., “I prefer British Airways to KLM on morning flights”) and (2) conditional or unconditional relative importance between attributes (e.g., “Departure time is more important than airline if I travel business class”). These statements are automatically organized into a TCP‑net. The system then builds the linear system L, solves it (using linear programming or sampling within the feasible polytope), and obtains an initial GA value function. This function is used to rank all items in the database; the top‑k items are presented to the user. The user either selects the best presented item or rejects it, which generates additional linear constraints that refine the value function. The process iterates until the optimal item is identified.

The authors validate their approach with a prototype for online flight reservation. In experiments, users supplied a modest number of qualitative statements (typically 5–7). The system identified the optimal flight configuration after an average of 3.2 interaction rounds, dramatically fewer than the 7–8 rounds required by a standard Multi‑Attribute Utility Theory (MAUT) based method. Moreover, the GA value functions produced involved small factors (most containing only 2–3 variables), leading to low memory consumption and fast evaluation.

Overall, the paper demonstrates that qualitative preference information, when structured as a TCP‑net, can be compiled into a compact, tractable GA value function. The representation theorems require weaker assumptions than classic additive utility models, and the linear‑programming based compilation is efficient. This yields a user‑friendly elicitation process that minimizes cognitive load while guaranteeing efficient optimal‑item retrieval in large databases.