Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysis

• URL: http://arxiv.org/abs/2012.15477v1
• Date: Thu, 31 Dec 2020 07:07:32 GMT
• Title: Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysis
• Authors: Atsushi Nitanda, Denny Wu, Taiji Suzuki
• Abstract summary: We propose the particle dual averaging (PDA) method, which generalizes the dual averaging method in convex optimization. An important application of the proposed method is the optimization of two-layer neural network in the mean field regime. We show that neural networks in the mean field limit can be globally optimized by PDA.
• Score: 40.762447301225926
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose the particle dual averaging (PDA) method, which generalizes the dual averaging method in convex optimization to the optimization over probability distributions with quantitative runtime guarantee. The algorithm consists of an inner loop and outer loop: the inner loop utilizes the Langevin algorithm to approximately solve for a stationary distribution, which is then optimized in the outer loop. The method can thus be interpreted as an extension of the Langevin algorithm to naturally handle nonlinear functional on the probability space. An important application of the proposed method is the optimization of two-layer neural network in the mean field regime, which is theoretically attractive due to the presence of nonlinear feature learning, but quantitative convergence rate can be challenging to establish. We show that neural networks in the mean field limit can be globally optimized by PDA. Furthermore, we characterize the convergence rate by leveraging convex optimization theory in finite-dimensional spaces. Our theoretical results are supported by numerical simulations on neural networks with reasonable size.

Related papers

• The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models [75.33431791218302]
  Deep Neural Network Network (DNN) models are used for programming purposes. In this paper we examine the use of convex neural recovery models. We show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program. We also show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program.
  arXiv  Detail & Related papers  (2023-12-19T23:04:56Z)
• Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation [28.413085548038932]
  We propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective.
  arXiv  Detail & Related papers  (2023-12-16T11:32:28Z)
• Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization [73.80101701431103]
  The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. We study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility.
  arXiv  Detail & Related papers  (2023-04-17T14:23:43Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Near-Optimal High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [63.304196997102494]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity with bounds dependence on the confidence level that is either negative-power or logarithmic. We propose novel stepsize rules for two gradient methods with clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• A Dynamical View on Optimization Algorithms of Overparameterized Neural Networks [23.038631072178735]
  We consider a broad class of optimization algorithms that are commonly used in practice. As a consequence, we can leverage the convergence behavior of neural networks. We believe our approach can also be extended to other optimization algorithms and network theory.
  arXiv  Detail & Related papers  (2020-10-25T17:10:22Z)
• Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition [63.011641517977644]
  Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.
  arXiv  Detail & Related papers  (2020-09-08T06:54:11Z)
• An Outer-approximation Guided Optimization Approach for Constrained Neural Network Inverse Problems [0.0]
  constrained neural network inverse problems refer to an optimization problem to find the best set of input values of a given trained neural network. This paper analyzes the characteristics of optimal solutions of neural network inverse problems with rectified activation units. Experiments demonstrate the superiority of the proposed algorithm compared to a projected gradient method.
  arXiv  Detail & Related papers  (2020-02-24T17:49:24Z)

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.