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Conformal Symplectic and Relativistic Optimization

Authors: Guilherme Franca, Jeremias Sulam, Daniel Robinson, Rene Vidal

Published: 2019 (Conference Paper)

Source: Advances in Neural Information Processing Systems

Algorithm: Conformal Symplectic Optimization

arXiv: 1903.04100

Summary

Analyzes momentum-based optimization algorithms (Nesterov, heavy ball) through the lens of structure-preserving discretizations of dissipative Hamiltonian systems. Proposes a novel relativistic optimizer that normalizes momentum, unifying both Nesterov and heavy ball as special limiting cases, with improved stability and no additional computational overhead. Published at NeurIPS 2020.

Abstract

Primary

Paper arxiv.org

Standard

arXiv Abstract 1903.04100 arXiv PDF 1903.04100 arXiv HTML 1903.04100

Alternate

proceedings.neurips.cc proceedings.neurips.cc

Tags

  • Optimization

  • Symplectic geometry

  • Momentum methods

  • Nesterov acceleration

  • Hamiltonian systems

  • Relativistic mechanics