Robust simplex algorithm for online optimization

Huang, Xiaobiao

doi:10.1103/physrevaccelbeams.21.104601

Cited by 26 publications

(16 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When used in an environment where the errors in those cost function values are large enough to cause mistakes in these comparisons, however, this algorithm is vulnerable to performing shrink operations prematurely, which slows the optimization down and may lead to a false appearance of convergence [46]. Due to this difficulty, one would expect the number of iterations required to converge with Nelder-Mead to be especially bad in limited precision environments, though we note that there are a number of modifications that attempt to improve the method's robustness to noise [46,47].…”

Section: Nelder-meadmentioning

confidence: 99%

Effect of barren plateaus on gradient-free optimization

Arrasmith

Cerezo

Czarnik

et al. 2021

Quantum

151

View full text Add to dashboard Cite

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

show abstract

Section: Nelder-meadmentioning

confidence: 99%

Effect of barren plateaus on gradient-free optimization

Arrasmith

Cerezo

Czarnik

et al. 2021

Quantum

151

View full text Add to dashboard Cite

show abstract

“…At LCLS, skilled human operators tune dozens of control parameters on-the-fly to achieve custom photon beam characteristics, and this process cuts into valuable time allocated for each user experiment. Model-independent optimizers can help automate tuning, with successful demonstrations using simplex [2,3], extremum seeking [4,5], and robust conjugate direction search [6,7]. However, these methods require a large number of expensive acquisitions and can become stuck in local optima.…”

mentioning

confidence: 99%

Bayesian Optimization of a Free-Electron Laser

et al. 2020

View full text Add to dashboard Cite

The Linac Coherent Light Source changes configurations multiple times per day, necessitating fast tuning strategies to reduce setup time for successive experiments. To this end, we employ a Bayesian approach to transport optics tuning to optimize groups of quadrupole magnets. We use a Gaussian process to provide a probabilistic model of the machine response with respect to control parameters from a modest number of samples. Subsequent samples are selected during optimization using a statistical test combining the model prediction and uncertainty. The model parameters are fit from archived scans, and correlations between devices are added from a simple beam transport model. The result is a sample-efficient optimization routine, which we show significantly outperforms existing optimizers.

show abstract

“…As our parameter space is a two-dimensional space (frequency and phase), the Simplex shape is a triangle. The main reason for choosing Simplex optimization is its ease of implementation in the real-time setting and its robustness (Huang, 2018;Price, Coope, & Byatt, 2002). The study protocol introduced in this paper is a real-time experiment (Figure 2A) with only 30 opportunities for functional connectivity calculation (2x15 stimulation blocks in training 1 and training 2).…”

Section: Parameter Optimizationmentioning

confidence: 99%

Online Closed-Loop Real-Time tES-fMRI for Brain Modulation: Feasibility, Noise/Safety and Pilot Study

Mulyana

Tsuchiyagaito

Smith

et al. 2021

Preprint

View full text Add to dashboard Cite

Recent studies suggest that transcranial electrical stimulation (tES) can be performed during functional magnetic resonance imaging (fMRI). The novel approach of using concurrent tES-fMRI to modulate and measure targeted brain activity/connectivity may provide unique insights into the causal interactions between the brain neural responses and psychiatric/neurologic signs and symptoms, and importantly, guide the development of new treatments. However, tES stimulation parameters to optimally influence the underlying brain activity in health and disorder may vary with respect to phase, frequency, intensity, and electrode's montage. Here, we delineate how a closed-loop tES-fMRI study of frontoparietal network modulation can be designed and performed. We also discuss the challenges of running a concurrent tES-fMRI, describing how we can distinguish clinically meaningful physiological changes caused by tES from tES-related artifacts. There is a large methodological parameter space including electrode types, electrolytes, electrode montages, concurrent tES-fMRI hardware, online fMRI processing pipelines and closed-loop optimization algorithms that should be carefully selected for closed-loop tES-fMRI brain modulation. We also provide technical details on how safety and quality of tES-fMRI settings can be tested, and how these settings can be monitored during the study to ensure they do not exceed safety standards. The initial results of feasibility and applicability of closed-loop tES-fMRI are reported and potential hypotheses for the outcomes are discussed.

show abstract

Robust simplex algorithm for online optimization

Cited by 26 publications

References 14 publications

Effect of barren plateaus on gradient-free optimization

Effect of barren plateaus on gradient-free optimization

Bayesian Optimization of a Free-Electron Laser

Online Closed-Loop Real-Time tES-fMRI for Brain Modulation: Feasibility, Noise/Safety and Pilot Study

Contact Info

Product

Resources

About