Mechanical ventilation is one of the most widely used therapies in the ICU. However, despite broad application from anaesthesia to COVID-related life support, many injurious challenges remain. We frame these as a control problem: ventilators must let air in and out of the patient's lungs according to a prescribed trajectory of airway pressure. Industry-standard controllers, based on the PID method, are neither optimal nor robust. Our data-driven approach learns to control an invasive ventilator by training on a simulator itself trained on data collected from the ventilator. This method outperforms popular reinforcement learning algorithms and even controls the physical ventilator more accurately and robustly than PID. These results underscore how effective data-driven methodologies can be for invasive ventilation and suggest that more general forms of ventilation (e.g., non-invasive, adaptive) may also be amenable.
Intrinsic rewards play a central role in handling the exploration-exploitation trade-off when designing sequential decision-making algorithms, in both foundational theory and state-of-the-art deep reinforcement learning. The LinUCB algorithm, a centerpiece of the stochastic linear bandits literature, prescribes an elliptical bonus which addresses the challenge of leveraging shared information in large action spaces. This bonus scheme cannot be directly transferred to high-dimensional exploration problems, however, due to the computational cost of maintaining the inverse covariance matrix of action features. We introduce \emph{anti-concentrated confidence bounds} for efficiently approximating the elliptical bonus, using an ensemble of regressors trained to predict random noise from policy network-derived features. Using this approximation, we obtain stochastic linear bandit algorithms which obtain $\tilde O(d \sqrt{T})$ regret bounds for $\mathrm{poly}(d)$ fixed actions. We develop a practical variant for deep reinforcement learning that is competitive with contemporary intrinsic reward heuristics on Atari benchmarks.
Self-attention, an architectural motif designed to model long-range interactions in sequential data, has driven numerous recent breakthroughs in natural language processing and beyond. This work provides a theoretical analysis of the inductive biases of self-attention modules, where our focus is to rigorously establish which functions and long-range dependencies self-attention blocks prefer to represent. Our main result shows that bounded-norm Transformer layers create sparse variables: they can represent sparse functions of the input sequence, with sample complexity scaling only logarithmically with the context length. Furthermore, we propose new experimental protocols to support this analysis and to guide the practice of training Transformers, built around the large body of work on provably learning sparse Boolean functions.
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable linear dynamical systems. However, in practice, we often encounter systems in which a large set of state variables evolve exogenously and independently of the control inputs; such systems are only \emph{partially controllable}. The focus of this work is on a large class of partially controllable linear dynamical systems, specified by an underlying sparsity pattern. Our main results establish structural conditions and finite-sample guarantees for learning to control such systems. In particular, our structural results characterize those state variables which are irrelevant for optimal control, an analysis which departs from classical control techniques. Our algorithmic results adapt techniques from high-dimensional statistics -- specifically soft-thresholding and semiparametric least-squares -- to exploit the underlying sparsity pattern in order to obtain finite-sample guarantees that significantly improve over those based on certainty-equivalence. We also corroborate these theoretical improvements over certainty-equivalent control through a simulation study.
When balancing the practical tradeoffs of iterative methods for large-scale optimization, the learning rate schedule remains notoriously difficult to understand and expensive to tune. We demonstrate the presence of these subtleties even in the innocuous case when the objective is a convex quadratic. We reinterpret an iterative algorithm from the numerical analysis literature as what we call the Chebyshev learning rate schedule for accelerating vanilla gradient descent, and show that the problem of mitigating instability leads to a fractal ordering of step sizes. We provide some experiments and discussion to challenge current understandings of the "edge of stability" in deep learning: even in simple settings, provable acceleration can be obtained by making negative local progress on the objective.
We consider the problem of controlling an invasive mechanical ventilator for pressure-controlled ventilation: a controller must let air in and out of a sedated patient's lungs according to a trajectory of airway pressures specified by a clinician. Hand-tuned PID controllers and similar variants have comprised the industry standard for decades, yet can behave poorly by over- or under-shooting their target or oscillating rapidly. We consider a data-driven machine learning approach: First, we train a simulator based on data we collect from an artificial lung. Then, we train deep neural network controllers on these simulators.We show that our controllers are able to track target pressure waveforms significantly better than PID controllers. We further show that a learned controller generalizes across lungs with varying characteristics much more readily than PID controllers do.
We present an open-source library of natively differentiable physics and robotics environments, accompanied by gradient-based control methods and a benchmark-ing suite. The introduced environments allow auto-differentiation through the simulation dynamics, and thereby permit fast training of controllers. The library features several popular environments, including classical control settings from OpenAI Gym. We also provide a novel differentiable environment, based on deep neural networks, that simulates medical ventilation. We give several use-cases of new scientific results obtained using the library. This includes a medical ventilator simulator and controller, an adaptive control method for time-varying linear dynamical systems, and new gradient-based methods for control of linear dynamical systems with adversarial perturbations.
State-of-the-art optimization is steadily shifting towards massively parallel pipelines with extremely large batch sizes. As a consequence, CPU-bound preprocessing and disk/memory/network operations have emerged as new performance bottlenecks, as opposed to hardware-accelerated gradient computations. In this regime, a recently proposed approach is data echoing (Choi et al., 2019), which takes repeated gradient steps on the same batch while waiting for fresh data to arrive from upstream. We provide the first convergence analyses of "data-echoed" extensions of common optimization methods, showing that they exhibit provable improvements over their synchronous counterparts. Specifically, we show that in convex optimization with stochastic minibatches, data echoing affords speedups on the curvature-dominated part of the convergence rate, while maintaining the optimal statistical rate.