In this paper, we aim to build a novel bandits algorithm that is capable of fully harnessing the power of multi-dimensional data and the inherent non-linearity of reward functions to provide high-usable and accountable decision-making services. To this end, we introduce a generalized low-rank tensor contextual bandits model in which an action is formed from three feature vectors, and thus is represented by a tensor. In this formulation, the reward is determined through a generalized linear function applied to the inner product of the action’s feature tensor and a fixed but unknown parameter tensor with low-rank structure. To effectively achieve the trade-off between exploration and exploitation, we introduce an algorithm called “Generalized Low-Rank Tensor Exploration Subspace then Refine” (G-LowTESTR). This algorithm first collects data to explore the intrinsic low-rank tensor subspace information embedded in the scenario, and then converts the original problem into a lower-dimensional generalized linear contextual bandits problem. Rigorous theoretical analysis shows that the regret bound of G-LowTESTR is superior to those in vectorization and matricization cases. We conduct a series of synthetic and real data experiments to further highlight the effectiveness of G-LowTESTR, leveraging its ability to capitalize on the low-rank tensor structure for enhanced learning.

We propose a preference-learning algorithm for uncovering Decision Makers’ (DMs’) contingent evaluation strategies in the context of multiple criteria sorting. We assume the preference information in the form of holistic assignment examples derived from the analysis of alternatives’ performance vectors and textual descriptions. We characterize the decision policies using a mixture of threshold-based, value-driven preference models and associated latent topics. The latter serve as the stimuli underlying the contingency in decision behavior. Such a probabilistic model is constructed by using a flexible and nonparametric Bayesian framework. The proposed method adopts a hierarchical Dirichlet process as the prior so that a group of DMs can share a countably infinite number of contingent models and topics. For all DMs, it automatically identifies the components representing their evaluation strategies adequately. The posterior is summarized by using the Hamiltonian Monte Carlo sampling method. We demonstrate the method’s practical usefulness in a real-world recruitment problem considered by a Chinese IT company. We also compare the approach with counterparts that use a single preference model, implement the parametric framework, or consider each DM’s preferences individually. The results indicate that our approach performs favorably in both interpreting DMs’ contingent decision behavior and recommending decisions on new alternatives. Furthermore, the approach’s performance and robustness are investigated through a computational experiment involving real-world data sets. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: J. Liu received financial support from the National Natural Science Foundation of China [Grants 72071155 and 71701160]. M. Kadziński received financial support from the Polish National Science Center under the SONATA BIS project [Grant DEC-2019/34/E/HS4/00045]. X. Liao received financial support from the National Natural Science Foundation of China [Grant 71872144]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1292 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0328 ) at ( http://dx.doi.org/10.5281/zenodo.7608750 ).

Ordinal regression predicts the objects’ labels that exhibit a natural ordering, which is vital to decision-making problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the individual features and their interactions affect the decisions is as critical as model performance. Unfortunately, the existing ordinal regression models in the machine learning community aim at improving prediction accuracy rather than explore explainability. To achieve high accuracy while explaining the relationships between the features and the predictions, we propose a new method for ordinal regression problems, namely the Explainable Ordinal Factorization Model (XOFM). XOFM uses piecewise linear functions to approximate the shape functions of individual features, and renders the pairwise features interaction effects as heat-maps. The proposed XOFM captures the nonlinearity in the main effects and ensures the interaction effects’ same flexibility. Therefore, the underlying model yields comparable performance while remaining explainable by explicitly describing the main and interaction effects. To address the potential sparsity problem caused by discretizing the whole feature scale into several sub-intervals, XOFM integrates the Factorization Machines (FMs) to factorize the model parameters. Comprehensive experiments with benchmark real-world and synthetic datasets demonstrate that the proposed XOFM leads to state-of-the-art prediction performance while preserving an easy-to-understand explainability.

The learning of predictive models for data-driven decision support has been a prevalent topic in many fields. However, construction of models that would capture interactions among input variables is a challenging task. In this paper, we present a new preference learning approach for multiple criteria sorting with potentially interacting criteria. It employs an additive piecewise-linear value function as the basic preference model, which is augmented with components for handling the interactions. To construct such a model from a given set of assignment examples concerning reference alternatives, we develop a convex quadratic programming model. Because its complexity does not depend on the number of training samples, the proposed approach is capable for dealing with data-intensive tasks. To improve the generalization of the constructed model on new instances and to overcome the problem of overfitting, we employ the regularization techniques. We also propose a few novel methods for classifying nonreference alternatives in order to enhance the applicability of our approach to different data sets. The practical usefulness of the proposed approach is demonstrated on a problem of parametric evaluation of research units, whereas its predictive performance is studied on several monotone classification problems. The experimental results indicate that our approach compares favourably with the classical UTilités Additives DIScriminantes (UTADIS) method and the Choquet integral-based sorting model. Summary of Contribution. The paper tackles vital challenges at the intersections of multiple criteria decision analysis and machine learning, showing how computationally advanced techniques can be used for faithfully representing human preferences and dealing with complex decision problems. Specifically, we propose a novel preference learning method for multiple criteria sorting problems. The introduced approach incorporates convex quadratic programming to construct a value-based preference model based on large sets of preference statements. In this way, we extend the applicability of decision analysis methods to preferences derived from historical data or observation of users' behavior in addition to the preference judgments explicitly revealed by the decision-makers. The method's practical usefulness is illustrated on a variety of real-world datasets from fields such as higher education, medicine, human resources, and housing market. Its potential for supporting better decision-making is enhanced by both an interpretable form of the assumed model handling interactions between criteria as well as a high predictive performance demonstrated in the extensive computational experiments.