Safe Controller Optimization for Quadrotors with Gaussian Processes

One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.Comment: IEEE International Conference on Robotics and Automation, 2016. 6 pages, 4 figures. A video of the experiments can be found at http://tiny.cc/icra16_video . A Python implementation of the algorithm is available at https://github.com/befelix/SafeOp

No-Regret Bayesian Optimization with Unknown Hyperparameters

Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance. This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima. In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters. During optimization we slowly adapt the hyperparameters of stationary kernels and thereby expand the associated function class over time, so that the BO algorithm considers more complex function candidates. Based on the theoretical insights, we propose several practical algorithms that achieve the empirical sample efficiency of BO with online hyperparameter estimation, but retain theoretical convergence guarantees. We evaluate our method on several benchmark problems

Projected Off-Policy Q-Learning (POP-QL) for Stabilizing Offline Reinforcement Learning

A key problem in off-policy Reinforcement Learning (RL) is the mismatch, or distribution shift, between the dataset and the distribution over states and actions visited by the learned policy. This problem is exacerbated in the fully offline setting. The main approach to correct this shift has been through importance sampling, which leads to high-variance gradients. Other approaches, such as conservatism or behavior-regularization, regularize the policy at the cost of performance. In this paper, we propose a new approach for stable off-policy Q-Learning. Our method, Projected Off-Policy Q-Learning (POP-QL), is a novel actor-critic algorithm that simultaneously reweights off-policy samples and constrains the policy to prevent divergence and reduce value-approximation error. In our experiments, POP-QL not only shows competitive performance on standard benchmarks, but also out-performs competing methods in tasks where the data-collection policy is significantly sub-optimal.Comment: 10 page

Safe and Robust Learning Control with Gaussian Processes

Abstract-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