An Efficient Algorithm To Compute Distance Between Lexicographic Preference Trees

Group decision-making, in which a collective decision needs to be derived from individual agents’ preferences has been an active area of research. In group decisionmaking, autonomous agents need some procedures or mechanisms that can collect preference information from them and make a decision; or some protocols that enable them to be involved in the decision process, to interact with each other and to jointly make a collective decision. Examples include preference aggregation mechanisms, negotiation protocols, voting procedures, and auctions. This thesis studies the problem of agent-based group decision-making in various problem settings, proposing several efficient approaches to support multiple agents in reaching efficient and fair collective decisions overmultiple issues. The research work in this thesis can be divided into two parts, addressing the agent-based group decision-making problem in circumstances in which there is, respectively, complete and incomplete information available. The first part of this thesis focuses on preference aggregation in combinatorial domains, provided all agents’ preferences. Structured preferences Conditional Preference Network (CP-nets) and its variant Trade-off enhanced CP-nets (TCP-nets) are used as formal models for representing the agents’ preferences in group decision-making. Before going into the problem of making a group decision from a collection of CP-nets or TCP-nets, the problem of individual preference reasoning is studied and a computationally efficient heuristic algorithm for dominance testing in CP-nets, which forms the basis for many group decision-making mechanisms, is introduced. Subsequently, we consider the group decision-making problem with multiple agents’ CP-nets and TCP-nets. As the space of possible outcomes in combinatorial domains has a size exponential in the number of variables, computational complexity in group decision-making will be one of the issues that need to be addressed. Two computationally efficient approaches are proposed in order to support agent-based group decisionmaking in combinatorial domains with different decision criteria: (i) an approach that converts the qualitative preferences derived from CP-nets or TCP-nets into numerical penalty scoring functions, and then searches for an optimal collective decision based on the individual penalty scores; and (ii) an approach that focuses on combinatorial vote and computes the winners (i.e., winning alternatives) from a collection of CP-nets according to Majority voting rule. The second part of this thesis is concerned with the disadvantage of disclosing preference information in group decision-making and considers the incomplete information setting. Two negotiation approaches are presented in order to support agent-based group decision-making in, respectively, combinatorial domains and in domains with multiple continuous issues. Firstly, a negotiation protocol in combinatorial domains is proposed, which enables agents to distributively make decisions and leads them to Pareto-optimal agreements under incomplete information setting. Then for the domains with multiple continuous issues, a cooperative mediated negotiation approach is proposed to support the agents searching for joint utility gains and reaching an efficient and fair agreement. For every approach introduced in this thesis, experiments are carried out and the results are presented and analysed in order to provide insights into the performance of these approaches.

We study the problem of learning lexicographic preferences on multiattribute domains, and propose Rankdom Forests as a compact way to express preferences in learning to rank scenarios. We start generalizing Conditional Lexicographic Preference Trees by introducing multiple kernels in order to handle non-categorical attributes. Then, we define a learning strategy for inferring lexicographic rankers from partial pairwise comparisons between options. Finally, a Lexicographic Ensemble is introduced to handle multiple weak partial rankers, being Rankdom Forests one of these ensembles. We tested the performance of the proposed method using several datasets and obtained competitive results when compared with other lexicographic rankers.

We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be taken as a model of the agent’s preference relation. We show that when learned from examples, PLP-forests have better accuracy than single PLP-trees. We also show that the choice of a voting rule does not have a major effect on the aggregated order, thus rendering the problem of selecting the “right” rule less critical. Next, for the proposed PLP-forest preference models, we develop methods to compute optimal and near-optimal outcomes, the tasks that appear difficult for some other common preference models. Lastly, we compare our models with those based on decision trees, which brings up questions for future research.

ABSTRACTIntroductionMany patients with Acute Coronary Syndrome (ACS) are newly diagnosed with Type 2 Diabetes Mellitus (T2DM) with very high hbA1c levels (> 10%). Early achievement of glycaemic control is of prime importance in such cases, and many guidelines recommend starting insulin together with oral anti‐diabetic drugs (OAD) as part of discharge medications. However, large numbers of treatment‐naïve patients are hesitant to use insulin due to various factors.MethodsIn this retrospective, single‐centre, observational study, we compared the hbA1c at 1‐year follow‐up between newly diagnosed DM patients with initial hbA1c > 10% who were discharged on insulin plus OAD versus those only on OAD after admission with ACS. Pairwise comparisons between continuous and categorical study variables were performed using t‐test, Mann–Whitney test, and chi‐square. We used STATA 18 for analysis. Baseline characteristics have been described for all the patients included in the study. In the analysis of outcomes at follow‐up, only patients who had follow‐up at 1‐year were included.ResultsOf 149 patients eligible for inclusion, the majority were males (97.3%). The mean age was 47 ± 8.3 years. The baseline hbA1c at diagnosis was 11.2 (10.5–12.3) %. 38 (25.5%) Were Discharged on insulin + OADs, whereas 111 (75.5%) Were Discharged Only on OADs. There was no statistically significant difference in change in hbA1c from baseline between the two groups (Mean (SD) 4.4% ± 1.8% vs. 4% ± 1.5%, p = 0.07). None of the patients had any hyperglycaemic emergency, and there were no differences in recurrent admissions due to cardiac indications (p = 0.5).ConclusionAn anti‐DM regimen consisting of multiple oral agents is a safe and effective alternative to insulin plus OAD and can lead to a comparable reduction in hbA1c at 1‐year in patients who are not willing to use insulin early after diagnosis of T2DM.

We introduce probabilistic lexicographic preference trees (or PrLPTs for short). We show that they offer intuitive and often compact representations of non-deterministic qualitative preferences over alternatives in multi-attribute (or, combinatorial) binary domains. We specify how a PrLPT defines the probability that a given outcome has a given rank, and the probability that a given outcome is preferred to another one, and show how to compute these probabilities in polynomial time. We also show that computing outcomes that are optimal with the probability equal to or exceeding a given threshold for some classes of PrLP-trees is in P, but for some other classes the problem is NP-hard.