Persistent Preference Inference for Query-Efficient Interactive Multi-Objective Optimization

Interactive multi-objective optimization uses decision-maker feedback to steer search. However, repeated consultations become costly as candidate populations evolve during optimization. We ask whether earlier comparisons can reduce the decision-maker feedback required to select preferred candidates from subsequent populations. We introduce Persistent Preference Inference (PPL), a persistent preference inference framework that uses linear programming to certify pairwise relations over a feasible preference region maintained across consultations and compatible with historical comparisons. Only comparisons that cannot be resolved using previously elicited feedback require new queries. We prove an expected $\mathcal{O}(m\log N)$ upper bound on the number of explicit queries required by PPL to infer a preference-aligned ranking. We further evaluate its practical query efficiency by constructing preference-aligned model leaderboards from pairwise comparison data on Chatbot Arena. In this setting, PPL achieves ranking quality comparable to the baseline with $98.9\%$ fewer target-user queries. When integrated into multi-objective optimization to guide search, PPL improves preference-region alignment over competing interactive methods under matched cumulative query budgets across 36 benchmark configurations and an RfaH protein sequence design task. These improvements are achieved while resolving more than $99.3\%$ of processed pairwise comparisons through inference from previously elicited preference feedback. The results demonstrate that reusing preference information across evolving populations can substantially reduce interaction without compromising preference-guided search.