Online Optimization with Costly and Noisy Measurements using Random Fourier Expansions
This work addresses optimization problems in fields like medical imaging and robotics where measurements are expensive and noisy, offering a faster alternative to Bayesian optimization, though it is incremental as it builds on existing surrogate modeling approaches.
The paper tackles online optimization of unknown functions using costly and noisy measurements by proposing the DONE algorithm, which uses random Fourier expansions to build a surrogate model and achieves similar or better performance than Bayesian optimization while being significantly faster, with computational complexity independent of measurement count.
This paper analyzes DONE, an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion (RFE). The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable to Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyper-parameters of the algorithm should be chosen. The algorithm is compared to a Bayesian optimization algorithm for a benchmark problem and three applications, namely, optical coherence tomography, optical beam-forming network tuning, and robot arm control. It is found that the DONE algorithm is significantly faster than Bayesian optimization in the discussed problems, while achieving a similar or better performance.