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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2402.13988 |
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- We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic functions and show that the method has a non-trivial accelerated rate as that of Heavy Ball flow. We also propose Frictionless Coordinate Hamiltonian Descent and its parallelizable variant, which turns out to encapsulate the classical Gauss-Seidel method, Successive Over-relaxation, Jacobi method, and more, for solving a linear system of equations. The result not only offers a new perspective on these existing algorithms but also leads to a broader class of update schemes that guarantee the convergence.