Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time
arXiv:2606.17260v1 Announce Type: cross 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
This research builds on existing mathematical frameworks, arriving at a deterministic solution for accelerated convex optimization, indicating a maturation in theoretical AI and optimization research.
Improved optimization algorithms directly enhance the efficiency and speed of AI model training and other complex computational tasks, impacting the development timeline and energy requirements for advanced AI systems.
The ability to achieve accelerated convergence with deterministic guarantees for a broader class of optimization problems removes prior limitations to quadratic objectives or reliance on probabilistic outcomes.
- · AI researchers and developers
- · Cloud computing providers
- · Big data analytics companies
- · Companies relying on less efficient legacy optimization methods
Faster and more efficient training of large-scale AI models becomes possible.
Reduced computational costs and energy consumption for AI development could potentially accelerate the pace of AI innovation across various sectors.
The democratization of advanced AI development due to lower resource barriers, potentially leading to a wider array of specialized AI applications.
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Read at arXiv cs.LG