Machine learning provides a promising avenue for incorporating rich sensing modalities into autonomous systems. However, our coarse understanding of how ML systems fail limits the adoption of data-driven techniques in real-world applications. In particular, applications involving feedback require that errors do not accumulate and lead to instability. In this work, we propose and analyze a baseline method for incorporating a learning-enabled component into closed-loop control, providing bounds on the sample complexity of a reference tracking problem. Much recent work on developing guarantees for learning and control has focused on the case that dynamics are unknown [Dean et al., 2017, Simchowitz and Foster, 2020, Mania et al., 2020].

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints. Papers published at the Neural Information Processing Systems Conference.

Motivated by vision based control of autonomous vehicles, we consider the problem of controlling a known linear dynamical system for which partial state information, such as vehicle position, can only be extracted from high-dimensional data, such as an image. Our approach is to learn a perception map from high-dimensional data to partial-state observation and its corresponding error profile, and then design a robust controller. We show that under suitable smoothness assumptions on the perception map and generative model relating state to high-dimensional data, an affine error model is sufficiently rich to capture all possible error profiles, and can further be learned via a robust regression problem. We then show how to integrate the learned perception map and error model into a novel robust control synthesis procedure, and prove that the resulting perception and control loop has favorable generalization properties. Finally, we illustrate the usefulness of our approach on a synthetic example and on the self-driving car simulation platform CARLA.

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

While data-driven design has considerable potential in contemporary control systems where precise modeling of the dynamics is intractable (e.g., systems with complex contact forces), one of the biggest hurdles to overcome for practical deployment is maintaining safe execution during the learning process. Motivated by this issue, we study the data-driven design of a controller for the constrained Linear Quadratic Regulator (LQR) problem. In constrained LQR, we design a controller for a (potentially unknown) linear dynamical system that minimizes a given quadratic cost, subject to the additional requirement that both the state and input stay within a specified safe region. This is a problem that has received much attention within the model predictive control (MPC) community. For the LQR problem with no constraints, a natural method of exploration for learning the dynamics is to excite the system by injecting white noise. When safety is not an issue, this method is effective and recently Dean et al. [1] provide an end-to-end sample complexity S. Dean, S. Tu, N. Matni, and B. Recht are with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94709 USA (email: dean sarah@berkeley.edu,

Machine learning (ML) is increasingly deployed in real world contexts, supplying actionable insights and forming the basis of automated decision-making systems. While issues resulting from biases pre-existing in training data have been at the center of the fairness debate, these systems are also affected by technical and emergent biases, which often arise as context-specific artifacts of implementation. This position paper interprets technical bias as an epistemological problem and emergent bias as a dynamical feedback phenomenon. In order to stimulate debate on how to change machine learning practice to effectively address these issues, we explore this broader view on bias, stress the need to reflect on epistemology, and point to value-sensitive design methodologies to revisit the design and implementation process of automated decision-making systems.

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Fairness in machine learning has predominantly been studied in static classification settings without concern for how decisions change the underlying population over time. Conventional wisdom suggests that fairness criteria promote the long-term well-being of those groups they aim to protect. We study how static fairness criteria interact with temporal indicators of well-being, such as long-term improvement, stagnation, and decline in a variable of interest. We demonstrate that even in a one-step feedback model, common fairness criteria in general do not promote improvement over time, and may in fact cause harm in cases where an unconstrained objective would not. We completely characterize the delayed impact of three standard criteria, contrasting the regimes in which these exhibit qualitatively different behavior. In addition, we find that a natural form of measurement error broadens the regime in which fairness criteria perform favorably. Our results highlight the importance of measurement and temporal modeling in the evaluation of fairness criteria, suggesting a range of new challenges and trade-offs.

This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are nearly optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.