Research
Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent
arXiv:2604.13022v1 Announce Type: cross Abstract: The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike g
arXiv:2604.13022v1 Announce Type: cross Abstract: The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and converge to a global minimum, making it appealing for machine learning optimization. We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation. For positive double-well objectives, we compute the expected hitting time from a local to the global minimum. We prove that both sECD and qECD yield exponential speedup over respective gradient descent baselines--stochastic gradient descent and its quantization. For objectives with tall barriers, qECD achieves a further speedup over sECD.
Related
- Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification
- AdaCubic: An Adaptive Cubic Regularization Optimizer for Deep Learning
- Fisher-Geometric Diffusion in Stochastic Gradient Descent: Optimal Rates, Oracle Complexity, and Information-Theoretic Limits
- Distributed Online Convex Optimization with Compressed Communication: Optimal Regret and Applications
- Generative Path-Finding Method for Wasserstein Gradient Flow
Source: arXiv cs.LG | 2026-04-15