UC Santa Barbara

This dissertation investigates the challenges of improving the robustness and fairness of deep neural networks through the lens of optimal control theory. Deep neural networks, despite their extensive application across various engineering fields, are vulnerable to imperceptible perturbations and often exhibit biased performance towards underrepresented demographic populations. The first part of this dissertation presents a novel self-healing framework designed to improve the robustness of deep neural networks against unforeseen perturbations. This framework is realized by a novel closed-loop control approach grounded in optimal control theory, which adaptively generates control signals to identify and correct potential errors in the state trajectory of perturbed input data during inference. The second part of this dissertation introduces a PID control framework that generalizes the closed-loop method with additional integral and derivative controllers. We derive an analytical solution for fast online inference, making our control framework applicable to large-scale models. The third part of this dissertation addresses the fairness issue in machine learning within dynamic environments, where undesired model biases against minority users could lead to significant user churn, thereby diminishing the training data for model tuning in subsequent time steps. This negative feedback loop can further exacerbate demographic disparity. To address this, we introduce the concept of asymptotic fairness to maintain consistent model performance across all demographic groups and propose an optimal control solution to achieve this goal.