Online Optimization With Costly and Noisy Measurements Using Random Fourier Expansions

Abstract

Abstract-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 an analytic 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.

Integrated microwave photonics for 5G

“…2 shows the measurement setup and the results of automatically tuning the OSBF using the DONE algorithm [4], and manual tuning, both averaged over ten measurements. Manual tuning was performed by a human expert by looking at the frequency response of an OSBF, averaged over ten measurements (to reduce the noise level).…”

Wavefront sensorless adaptive optics OCT with the DONE algorithm for in vivo human retinal imaging [Invited]

“…The maximum stroke of the MAL limits the maximum amplitudes of the modes, hence the exploration parameters and bounds for each mode should be carefully chosen. Previously, DONE has successfully been used in WFSL-AO OCT, light sheet microscopy, and simulations of an optical beam forming network [29,38,47]. It was shown that DONE outperforms other algorithms in residual wavefront error and convergence speed [29].…”

“…In order to perform the DONE model computations in near real-time, fast algorithms are necessary. We present an improved and faster implementation of the DONE algorithm [29,38] used to maximize the AO-OCT signal for human retinal imaging. The biggest difference between the DONE algorithm reported in [29] and the current work is a faster implementation that allows the exploration and the bounds for each aberration to be set independently.…”

“…With the implementation of the recursive routine, the time per iteration of the DONE algorithm was reduced to ∼1 ms, which is smaller than the settling time of the MAL. A pseudocode description of the DONE algorithm was presented in [38]. In iteration n of DONE, we define a n = cos(ω T x n + B), where the vector x n contains the coefficients of the Zernike aberrations of the MAL and y n is the corresponding OCT signal metric value.…”

Automatic Delay Tuning of a Novel Ring Resonator-Based Photonic Beamformer for a Transmit Phased Array Antenna

“…The automatic tuning algorithm used in this paper contains several hyper-parameters that are explained and investigated in [17]. Their values as used in this paper are shown in Table II for the OSBF and OBFN tuning results.…”