Efficient Inference and Computation of Optimal Alternatives for Preference Languages Based On Lexicographic Models
Abstract: We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference statement, and that allows a greedy algorithm for determining consistency of a set of preference statements. We also consider different natural definitions of optimality, and their relations to each other, for general preference languages based on lexicographic models. Based on our framework, we show that testing consistency, and thus inference, is polynomial for a specific preference language LpqT, which allows strict and non-strict statements, comparisons between outcomes and between partial tuples, both ceteris paribus and strong statements, and their combination. Computing different kinds of optimal sets is also shown to be polynomial; this is backed up by our experimental results.
- R. Agrawal and E. L. Wimmers. A framework for expressing and combining preferences. In Proc. ACM SIGMOD 2000, pages 297–306, New York, NY, USA, 2000. ACM.
- K. Arrow and H. Raynaud. Social Choice and Multicriterion Decision-Making, volume 1. The MIT Press, 1 edition, 1986.
- Learning conditionally lexicographic preference relations. In Proc. ECAI 2010, pages 269–274, 2010.
- CP-nets: A tool for reasoning with conditional ceteris paribus preference statements. Journal of Artificial Intelligence Research, 21:135–191, 2004.
- M. Bräuning and E. Hüllermeier. Learning conditional lexicographic preference trees. In Preference Learning (PL-12), ECAI 2012 workshop, pages 11–15, 2012.
- L. Chen and P. Pu. Preference-based organization interfaces: aiding user critiques in recommender systems, pages 77–86. Springer, 2007.
- V. Conitzer. Eliciting single-peaked preferences using comparison queries. Journal of Artificial Intelligence Research, 35:161–191, 2009.
- Learning lexicographic orders. European Journal of Operational Research, 183(2):748–756, 2007.
- Interval-valued soft constraint problems. Ann. Math. Artif. Intell., 58(3-4):261–298, 2010.
- A. George and N. Wilson. Preference inference based on pareto models. In Proc. SUM 2016, pages 170–183, 2016.
- U. Junker and D. Mailharro. Preference programming: Advanced problem solving for configuration. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 17(1):13–29, 2003.
- W. Kießling. Foundations of preferences in database systems. In Proc. VLDB 2002, pages 311–322. VLDB Endowment, 2002.
- R. Kohli and K. Jedidi. Representation and inference of lexicographic preference models and their variants. Marketing Science, 26(3):380–399, 2007.
- J. Lang. From preference representation to combinatorial vote. In Proc. KR 2002, pages 277–288, 2002.
- M. Montazery and N. Wilson. Learning user preferences in matching for ridesharing. In Proc. ICAART 2016, pages 63–73, 2016.
- C. O’Mahony. Reasoning with sorted-pareto dominance and other qualitative and partially ordered preferences in soft constraints. In PhD Thesis, Cork, 2013. https://cora.ucc.ie/handle/10468/1498, 2013.
- T. Sandholm and C. Boutilier. Preference elicitation in combinatorial auctions. In Combinatorial Auctions, ed. P. Cramton, Y. Shoham, and R. Steinberg, Chapter 10, page 233–264. Cambridge, MA: MIT Press, 2006.
- Comparative preferences induction methods for conversational recommenders. In Proc. ADT 2013, pages 363–374, 2013.
- N. Wilson. Efficient inference for expressive comparative preference languages. In Proc. IJCAI-09, pages 961–966, 2009.
- N. Wilson. Preference inference based on lexicographic models. In Proc. ECAI 2014, pages 921–926, 2014.
- Computation and complexity of preference inference based on hierarchical models. In Proc. IJCAI 2015, pages 3271–3277, 2015.
- N. Wilson and C. O’Mahony. The relationships between qualitative notions of optimality for decision making under logical uncertainty. In Proc. AICS 2011, pages 66–75, 2011.
- Computing possibly optimal solutions for multi-objective constraint optimisation with tradeoffs. In Proc. IJCAI 2015, IJCAI’15, pages 815–821. AAAI Press, 2015.
- Learning lexicographic preference models. Preference learning, pages 251–272, 2011.
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