Effect of barren plateaus on gradient-free optimization

• URL: http://arxiv.org/abs/2011.12245v2
• Date: Thu, 30 Sep 2021 23:37:23 GMT
• Title: Effect of barren plateaus on gradient-free optimization
• Authors: Andrew Arrasmith, M. Cerezo, Piotr Czarnik, Lukasz Cincio, Patrick J. Coles
• Abstract summary: Barren plateau landscapes correspond to 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.
• Score: 0.755972004983746
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Gradient-free neural topology optimization [0.0]
  gradient-free algorithms require many more iterations to converge when compared to gradient-based algorithms. This has made them unviable for topology optimization due to the high computational cost per iteration and high dimensionality of these problems. We propose a pre-trained neural reparameterization strategy that leads to at least one order of magnitude decrease in iteration count when optimizing the designs in latent space.
  arXiv  Detail & Related papers  (2024-03-07T23:00:49Z)
• How to guess a gradient [68.98681202222664]
  We show that gradients are more structured than previously thought. Exploiting this structure can significantly improve gradient-free optimization schemes. We highlight new challenges in overcoming the large gap between optimizing with exact gradients and guessing the gradients.
  arXiv  Detail & Related papers  (2023-12-07T21:40:44Z)
• ELRA: Exponential learning rate adaption gradient descent optimization method [83.88591755871734]
  We present a novel, fast (exponential rate), ab initio (hyper-free) gradient based adaption. The main idea of the method is to adapt the $alpha by situational awareness. It can be applied to problems of any dimensions n and scales only linearly.
  arXiv  Detail & Related papers  (2023-09-12T14:36:13Z)
• Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels [78.6096486885658]
  We introduce lower bounds to the linearized Laplace approximation of the marginal likelihood. These bounds are amenable togradient-based optimization and allow to trade off estimation accuracy against computational complexity.
  arXiv  Detail & Related papers  (2023-06-06T19:02:57Z)
• Optimization using Parallel Gradient Evaluations on Multiple Parameters [51.64614793990665]
  We propose a first-order method for convex optimization, where gradients from multiple parameters can be used during each step of gradient descent. Our method uses gradients from multiple parameters in synergy to update these parameters together towards the optima.
  arXiv  Detail & Related papers  (2023-02-06T23:39:13Z)
• Plateau-reduced Differentiable Path Tracing [18.174063717952187]
  We show that inverse rendering might not converge due to inherent plateaus, i.e. regions of zero gradient, in the objective function. We propose to alleviate this by convolving the high-dimensional rendering function that maps parameters to images with an additional kernel that blurs the parameter space.
  arXiv  Detail & Related papers  (2022-11-30T18:58:53Z)
• BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms [0.7462336024223667]
  Barren plateaus are a notorious problem in the optimization of variational quantum algorithms. We propose an alternative strategy which initializes the parameters of a unitary gate by drawing from a beta distribution. We empirically show that our proposed framework significantly reduces the possibility of a complex quantum neural network getting stuck in a barren plateau.
  arXiv  Detail & Related papers  (2022-04-28T19:46:10Z)
• Avoiding barren plateaus using classical shadows [1.5749416770494702]
  Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The optimization landscape of expressive variational ans"atze is dominated by large regions in parameter space, known as barren plateaus.
  arXiv  Detail & Related papers  (2022-01-20T14:19:36Z)
• Self-Tuning Stochastic Optimization with Curvature-Aware Gradient Filtering [53.523517926927894]
  We explore the use of exact per-sample Hessian-vector products and gradients to construct self-tuning quadratics. We prove that our model-based procedure converges in noisy gradient setting. This is an interesting step for constructing self-tuning quadratics.
  arXiv  Detail & Related papers  (2020-11-09T22:07:30Z)
• Channel-Directed Gradients for Optimization of Convolutional Neural Networks [50.34913837546743]
  We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental.
  arXiv  Detail & Related papers  (2020-08-25T00:44:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.