Reliable Machine Learning in Feedback Systems

Machine learning is a promising tool for processing complex information, but it remains anunreliable tool for control and decision making. Applying techniques developed for static datasets to real world problems requires grappling with the effects of feedback and systems that change over time. In these settings, classic statistical and algorithmic guarantees do not always hold. How do we anticipate the dynamical behavior of machine learning systems before we deploy them? Towards the goal of ensuring reliable behavior, this thesis takes steps towards developing an understanding of the trade-offs and limitations that arise in feedback settings./nIn Part I, we focus on the application of machine learning to automatic feedback control.Inspired by physical autonomous systems, we attempt to build a theoretical foundation for the data-driven design of optimal controllers. We focus on systems governed by linear dynamics with unknown components that must be characterized from data. We study unknown dynamics in the setting of the Linear Quadratic Regulator (LQR), a classical optimal control problem, and show that a procedure of least-squares estimation followed by robust control design guarantees safety and bounded sub-optimality. Inspired by the use of cameras in robotics, we also study a setting in which the controller must act on the basis of complex observations, where a subset of the state is encoded by an unknown nonlinear and potentially high dimensional sensor. We propose using a perception map, which acts as an approximate inverse, and show that the resulting perception-control loop has favorable properties, so long as either a) the controller is robustly designed to account for perception errors or b) the perception map is learned from sufficiently dense data./nIn Part II, we shift our attention to algorithmic decision making systems, where machinelearning models are used in feedback with people. Due to the difficulties of measure- ment, limited predictability, and the indeterminacy of translating human values into mathematical objectives, we eschew the framework of optimal control. Instead, our goal is to articulate the impacts of simple decision rules under one-step feedback models. We first consider consequential decisions, inspired by the example of lending in the presence of credit score. Under a simple model of impact, we show that several group fairness constraints, proposed to mitigate inequality, may harm the groups they aim to protect. In fact, fairness criteria can be viewed as a special case of a broader framework for de- signing decision policies that trade off between private and public objectives, in which notions of impact and wellbeing can be encoded directly. Finally, we turn to the setting of recommendation systems, which make selections from a wide array of choices based on personalized relevance predictions. We develop a novel perspective based on reachability that quantifies agency and access. While empirical audits show that models optimized for accuracy may limit reachability, theoretical results show that this is not due to an in- herent trade-off, suggesting a path forward. Broadly, this work attempts to re-imagine the goals of predictive models ubiquitous in machine learning, moving towards new design principles that prioritize human values.

Advisor: Recht, Benjamin