Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time

Xiuyuan Wang, Vishwak Srinivasan, Qiang Fu, Siddharth Mitra, Andre Wibisono, Ashia Wilson
Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:6692-6742, 2026.

Abstract

We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated optimization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v336-wang26c, title = {Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time}, author = {Wang, Xiuyuan and Srinivasan, Vishwak and Fu, Qiang and Mitra, Siddharth and Wibisono, Andre and Wilson, Ashia}, booktitle = {Proceedings of Thirty Ninth Conference on Learning Theory}, pages = {6692--6742}, year = {2026}, editor = {Hanneke, Steve and Lattimore, Tor}, volume = {336}, series = {Proceedings of Machine Learning Research}, month = {29 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v336/main/assets/wang26c/wang26c.pdf}, url = {https://proceedings.mlr.press/v336/wang26c.html}, abstract = {We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated optimization.} }
Endnote
%0 Conference Paper %T Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time %A Xiuyuan Wang %A Vishwak Srinivasan %A Qiang Fu %A Siddharth Mitra %A Andre Wibisono %A Ashia Wilson %B Proceedings of Thirty Ninth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Steve Hanneke %E Tor Lattimore %F pmlr-v336-wang26c %I PMLR %P 6692--6742 %U https://proceedings.mlr.press/v336/wang26c.html %V 336 %X We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated optimization.
APA
Wang, X., Srinivasan, V., Fu, Q., Mitra, S., Wibisono, A. & Wilson, A.. (2026). Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time. Proceedings of Thirty Ninth Conference on Learning Theory, in Proceedings of Machine Learning Research 336:6692-6742 Available from https://proceedings.mlr.press/v336/wang26c.html.

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