Preference Elicitation for Multi-objective Combinatorial Optimization with Active Learning and Maximum Likelihood Estimation

Real-life combinatorial optimization problems often involve several conflicting objectives, such as price, product quality and sustainability. A computationally-efficient way to tackle multiple objectives is to aggregate them into a single-objective function, such as a linear combination. However, defining the weights of the linear combination upfront is hard; alternatively, the use of interactive learning methods that ask users to compare candidate solutions is highly promising. The key challenges are to generate candidates quickly, to learn an objective function that leads to high-quality solutions and to do so with few user interactions. We build upon the Constructive Preference Elicitation framework and show how each of the three properties can be improved: to increase the interaction speed we investigate using pools of (relaxed) solutions, to improve the learning we adopt Maximum Likelihood Estimation of a Bradley-Terry preference model; and to reduce the number of user interactions, we select the pair of candidates to compare with an ensemble-based acquisition function inspired from Active Learning. Our careful experimentation demonstrates each of these improvements: on a PC configuration task and a realistic multi-instance routing problem, our method selects queries faster, needs fewer queries and synthesizes higher-quality combinatorial solutions than previous CPE methods.

Scalable Coupling of Deep Learning with Logical Reasoning

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs. In this paper, we introduce a scalable neural architecture and loss function dedicated to learning the constraints and criteria of NP-hard reasoning problems expressed as discrete Graphical Models. Our loss function solves one of the main limitations of Besag's pseudo-loglikelihood, enabling learning of high energies. We empirically show it is able to efficiently learn how to solve NP-hard reasoning problems from natural inputs as the symbolic, visual or many-solutions Sudoku problems as well as the energy optimization formulation of the protein design problem, providing data efficiency, interpretability, and \textit{a posteriori} control over predictions.