Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. However, the majority of autonomous RL algorithms require a large number of interactions with the environment. A large number of interactions may be impractical in many real-world applications, such as robotics, and many practical systems have to obey limitations in the form of state space or control constraints. To reduce the number of system interactions while simultaneously handling constraints, we propose a model-based RL framework based on probabilistic Model Predictive Control (MPC). In particular, we propose to learn a probabilistic transition model using Gaussian Processes (GPs) to incorporate model uncertainty into long-term predictions, thereby, reducing the impact of model errors. We then use MPC to find a control sequence that minimises the expected long-term cost. We provide theoretical guarantees for first-order optimality in the GP-based transition models with deterministic approximate inference for long-term planning. We demonstrate that our approach does not only achieve state-of-the-art data efficiency, but also is a principled way for RL in constrained environments.
This paper proposes a discontinuity-sensitive approach to learn the solutions of parametric optimal control problems with high accuracy. Many tasks, ranging from model predictive control to reinforcement learning, may be solved by learning optimal solutions as a function of problem parameters. However, nonconvexity, discrete homotopy classes, and control switching cause discontinuity in the parameter-solution mapping, thus making learning difficult for traditional continuous function approximators. A mixture of experts (MoE) model composed of a classifier and several regressors is proposed to address such an issue. The optimal trajectories of different parameters are clustered such that in each cluster the trajectories are continuous function of problem parameters. Numerical examples on benchmark problems show that training the classifier and regressors individually outperforms joint training of MoE. With suitably chosen clusters, this approach not only achieves lower prediction error with less training data and fewer model parameters, but also leads to dramatic improvements in the reliability of trajectory tracking compared to traditional universal function approximation models (e.g., neural networks).
Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.
We propose the use of Bayesian networks, which provide both a mean value and an uncertainty estimate as output, to enhance the safety of learned control policies under circumstances in which a test-time input differs significantly from the training set. Our algorithm combines reinforcement learning and end-to-end imitation learning to simultaneously learn a control policy as well as a threshold over the predictive uncertainty of the learned model, with no hand-tuning required. Corrective action, such as a return of control to the model predictive controller or human expert, is taken when the uncertainty threshold is exceeded. We validate our method on fully-observable and vision-based partially-observable systems using cart-pole and autonomous driving simulations using deep convolutional Bayesian neural networks. We demonstrate that our method is robust to uncertainty resulting from varying system dynamics as well as from partial state observability.
The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.
Multiple-step lookahead policies have demonstrated high empirical competence in Reinforcement Learning, via the use of Monte Carlo Tree Search or Model Predictive Control. In a recent work \cite{efroni2018beyond}, multiple-step greedy policies and their use in vanilla Policy Iteration algorithms were proposed and analyzed. In this work, we study multiple-step greedy algorithms in more practical setups. We begin by highlighting a counter-intuitive difficulty, arising with soft-policy updates: even in the absence of approximations, and contrary to the 1-step-greedy case, monotonic policy improvement is not guaranteed unless the update stepsize is sufficiently large. Taking particular care about this difficulty, we formulate and analyze online and approximate algorithms that use such a multi-step greedy operator.