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AdaCN: An Adaptive Cubic Newton Method for Nonconvex Stochastic Optimization.

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We introduce AdaCN, an adaptive cubic Newton method for nonconvex stochastic optimization. This method improves convergence speed and generalization by dynamically capturing loss landscape curvature using only first-order gradients.

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Area of Science:

  • Machine Learning
  • Optimization Algorithms

Background:

  • Nonconvex stochastic optimization presents challenges in capturing complex loss landscapes.
  • Existing methods often struggle with convergence speed and generalization performance.

Purpose of the Study:

  • Introduce AdaCN, a novel adaptive cubic Newton method.
  • Improve convergence and generalization in nonconvex stochastic optimization.

Main Methods:

  • AdaCN dynamically captures loss landscape curvature using diagonal Hessian approximation and estimate differences.
  • Employs first-order gradients with linear time and memory complexity.
  • Utilizes exponential moving averages of gradients and Hessians to reduce stochastic variance.

Main Results:

  • AdaCN outperforms SGD, Adam, AdaBound, and Apollo in convergence speed.
  • Demonstrates superior generalization performance compared to existing methods.
  • Achieves linear time and memory complexity.

Conclusions:

  • AdaCN offers an effective approach for nonconvex stochastic optimization.
  • The method shows significant improvements in both speed and accuracy.
  • AdaCN provides a computationally efficient and robust optimization solution.