Reinforcement learning (RL) methods have demonstrated their efficiency in simulation environments. However, many applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified closed-loop behavior in order to meet safety specifications in the presence of physical constraints. This paper introduces a concept, called probabilistic model predictive safety certification (PMPSC), which can be combined with any RL algorithm and provides provable safety certificates in terms of state and input chance constraints for potentially large-scale systems. The certificate is realized through a stochastic tube that safely connects the current system state with a terminal set of states, that is known to be safe. A novel formulation in terms of a convex receding horizon problem allows a recursively feasible real-time computation of such probabilistic tubes, despite the presence of possibly unbounded disturbances. A design procedure for PMPSC relying on bayesian inference and recent advances in probabilistic set invariance is presented. Using a numerical car simulation, the method and its design procedure are illustrated by enhancing a simple RL algorithm with safety certificates.
In model-free safe reinforcement learning methods, policy search algorithms have been proposed, e.g. @cite_44 , which provide safety guarantees in expectation by solving a constrained policy optimization using a modified trust-region policy gradient method @cite_50 . Efficient policy tuning with respect to best worst-case performance (also worst-case stability under physical constraints) can be achieved using Bayesian min-max optimization, see e.g. @cite_40 , or by safety constrained Bayesian optimization as e.g. in @cite_52 @cite_38 . These techniques share the limitation that they need to be tailored to a task-specific class of policies. Furthermore, most techniques require to repeatedly execute experiments, which prohibits fully autonomous safe learning in closed-loop'.
@cite_38 @cite_52 @cite_44 @cite_40 @cite_50
2100484286 2143346970 2962803570 2209113413 2949608212
In this paper, the problem of safe exploration in the active learning context is considered. Safe exploration is especially important for data sampling from technical and industrial systems, e.g. combustion engines and gas turbines, where critical and unsafe measurements need to be avoided. The objective is to learn data-based regression models from such technical systems using a limited budget of measured, i.e. labelled, points while ensuring that critical regions of the considered systems are avoided during measurements. We propose an approach for learning such models and exploring new data regions based on Gaussian processes GP's. In particular, we employ a problem specific GP classifier to identify safe and unsafe regions, while using a differential entropy criterion for exploring relevant data regions. A theoretical analysis is shown for the proposed algorithm, where we provide an upper bound for the probability of failure. To demonstrate the efficiency and robustness of our safe exploration scheme in the active learning setting, we test the approach on a policy exploration task for the inverse pendulum hold up problem. This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle. For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact with or around humans should satisfy safety constraints. Recent advances in policy search algorithms (, 2016; , 2015; , 2016; , 2016) have enabled new capabilities in high-dimensional control, but do not consider the constrained setting. We propose Constrained Policy Optimization (CPO), the first general-purpose policy search algorithm for constrained reinforcement learning with guarantees for near-constraint satisfaction at each iteration. Our method allows us to train neural network policies for high-dimensional control while making guarantees about policy behavior all throughout training. Our guarantees are based on a new theoretical result, which is of independent interest: we prove a bound relating the expected returns of two policies to an average divergence between them. We demonstrate the effectiveness of our approach on simulated robot locomotion tasks where the agent must satisfy constraints motivated by safety. Robotic systems typically have numerous parameters, e.g. the choice of planning algorithm, real-valued parameters of motion and vision modules, and control parameters. We consider the problem of optimizing these parameters for best worst-case performance over a range of environments. To this end we first propose to evaluate system parameters by adversarially optimizing over environment parameters to find particularly hard environments. This is then nested in a game-theoretic minimax optimization setting, where an outerloop aims to find best worst-case system parameters. For both optimization levels we use Bayesian global optimization (GP-UCB) which provides the necessary confidence bounds to handle the stochasticity of the performance. We compare our method (Nested Minimax) with an existing relaxation method we adapted to become applicable in our setting. By construction our approach provides more robustness to performance stochasticity. We demonstrate the method for planning algorithm selection on a pick'n'place application and for control parameter optimization on a triple inverted pendulum for robustness to adversarial perturbations. We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.