Safe Exploration for Optimization with Gaussian Processes

We consider sequential decision problems under uncertainty, where we seek to optimize an unknown function from noisy samples. This requires balancing exploration (learning about the objective) and exploitation (localizing the maximum), a problem well-studied in the multi-armed bandit literature. In many applications, however, we require that the sampled function values exceed some prespecified "safety" threshold, a requirement that existing algorithms fail to meet. Examples include medical applications where patient comfort must be guaranteed, recommender systems aiming to avoid user dissatisfaction, and robotic control, where one seeks to avoid controls causing physical harm to the platform. We tackle this novel, yet rich, set of problems under the assumption that the unknown function satisfies regularity conditions expressed via a Gaussian process prior. We develop an efficient algorithm called SafeOpt, and theoretically guarantee its convergence to a natural notion of optimum reachable under safety constraints. We evaluate SafeOpt on synthetic data, as well as two real applications: movie recommendation, and therapeutic spinal cord stimulation

Automatic LQR Tuning Based on Gaussian Process Global Optimization

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four-dimensional tuning problems highlight the method's potential for automatic controller tuning on robotic platforms.Comment: 8 pages, 5 figures, to appear in IEEE 2016 International Conference on Robotics and Automation. Video demonstration of the experiments available at https://am.is.tuebingen.mpg.de/publications/marco_icra_201