Carlos Cardonha

Keliang Wang, Leonardo Lozano, Carlos Cardonha et al.

We study optimization problems where the objective function is modeled through feedforward neural networks with rectified linear unit (ReLU) activation. Recent literature has explored the use of a single neural network to model either uncertain or complex elements within an objective function. However, it is well known that ensembles of neural networks produce more stable predictions and have better generalizability than models with single neural networks, which motivates the investigation of ensembles of neural networks rather than single neural networks in decision-making pipelines. We study how to incorporate a neural network ensemble as the objective function of an optimization model and explore computational approaches for the ensuing problem. We present a mixed-integer linear program based on existing popular big-M formulations for optimizing over a single neural network. We develop a two-phase approach for our model that combines preprocessing procedures to tighten bounds for critical neurons in the neural networks with a Lagrangian relaxation-based branch-and-bound approach. Experimental evaluations of our solution methods suggest that using ensembles of neural networks yields more stable and higher quality solutions, compared to single neural networks, and that our optimization algorithm outperforms (the adaption of) a state-of-the-art approach in terms of computational time and optimality gaps.

Marisa Vasconcelos, Carlos Cardonha, Bernardo Gonçalves

Artificial Intelligence (AI) has been used extensively in automatic decision making in a broad variety of scenarios, ranging from credit ratings for loans to recommendations of movies. Traditional design guidelines for AI models focus essentially on accuracy maximization, but recent work has shown that economically irrational and socially unacceptable scenarios of discrimination and unfairness are likely to arise unless these issues are explicitly addressed. This undesirable behavior has several possible sources, such as biased datasets used for training that may not be detected in black-box models. After pointing out connections between such bias of AI and the problem of induction, we focus on Popper's contributions after Hume's, which offer a logical theory of preferences. An AI model can be preferred over others on purely rational grounds after one or more attempts at refutation based on accuracy and fairness. Inspired by such epistemological principles, this paper proposes a structured approach to mitigate discrimination and unfairness caused by bias in AI systems. In the proposed computational framework, models are selected and enhanced after attempts at refutation. To illustrate our discussion, we focus on hiring decision scenarios where an AI system filters in which job applicants should go to the interview phase.