Bayesian Optimization with Informative Covariance

Bayesian Optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression models are Gaussian processes with stationary covariance functions, which, however, are unable to express prior input-dependent information, in particular information about possible locations of the optimum. The ubiquity of stationary models has led to the common practice of exploiting prior information via informative mean functions. In this paper, we highlight that these models can lead to poor performance, especially in high dimensions. We propose novel informative covariance functions that leverage nonstationarity to encode preferences for certain regions of the search space and adaptively promote local exploration during the optimization. We demonstrate that they can increase the sample efficiency of the optimization in high dimensions, even under weak prior information

Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.Comment: NIPS 2018 Workshop on Machine Learning for Molecules and Materials. arXiv admin note: substantial text overlap with arXiv:1811.0075

Bayesian Optimization with Unknown Constraints

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tuning a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.Comment: 14 pages, 3 figure

Unscented Bayesian Optimization for Safe Robot Grasping

We address the robot grasp optimization problem of unknown objects considering uncertainty in the input space. Grasping unknown objects can be achieved by using a trial and error exploration strategy. Bayesian optimization is a sample efficient optimization algorithm that is especially suitable for this setups as it actively reduces the number of trials for learning about the function to optimize. In fact, this active object exploration is the same strategy that infants do to learn optimal grasps. One problem that arises while learning grasping policies is that some configurations of grasp parameters may be very sensitive to error in the relative pose between the object and robot end-effector. We call these configurations unsafe because small errors during grasp execution may turn good grasps into bad grasps. Therefore, to reduce the risk of grasp failure, grasps should be planned in safe areas. We propose a new algorithm, Unscented Bayesian optimization that is able to perform sample efficient optimization while taking into consideration input noise to find safe optima. The contribution of Unscented Bayesian optimization is twofold as if provides a new decision process that drives exploration to safe regions and a new selection procedure that chooses the optimal in terms of its safety without extra analysis or computational cost. Both contributions are rooted on the strong theory behind the unscented transformation, a popular nonlinear approximation method. We show its advantages with respect to the classical Bayesian optimization both in synthetic problems and in realistic robot grasp simulations. The results highlights that our method achieves optimal and robust grasping policies after few trials while the selected grasps remain in safe regions.Comment: conference pape