Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent

• URL: http://arxiv.org/abs/2604.13022v1
• Date: Tue, 14 Apr 2026 17:56:33 GMT
• Title: Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent
• Abstract summary: Energy Con Descent (ECD) was recently proposed (De Luca & Silverstein, 2022) as a global non- gradient algorithm.<n>We formalize ECD dynamics with energy-serving as well as quantum noise, providing the foundation for a quantum algorithm through Hamiltonian simulation.
• Score: 2.516459841225004
• License: http://creativecommons.org/licenses/by/4.0/
• 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 papers

• The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization [50.59470683896735]
  min-max optimization has attracted increasing attention due to its applications in modern machine learning.<n>We provide a comprehensive theoretical of gradient descent (SGDA)<n>We develop new clipping-free algorithms, i.e., Stoc-GDAM and Stoc-TRmax, and they both can achieve the optimal dependence on the target accuracy without using gradient clipping.
  arXiv  Detail & Related papers  (2026-09-05T12:49:28Z)
• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization [3.967275814479281]
  We study multi-objective optimization over probability distributions in Wasserstein space.<n>We propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration.<n>We show that A-MWGraD consistently outperforms MWGraD in convergence speed and sampling efficiency on multi-target sampling tasks.
  arXiv  Detail & Related papers  (2026-01-27T05:41:36Z)
• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer [0.0]
  We study the projective quantum eigensolver (PQE) approach to optimizing unitary coupled cluster wave functions on quantum hardware.<n>We derive a bound relating off-diagonal coefficients (residues) of the Hamiltonian to the energy error of the algorithm and the overlap achieved by the obtained wavefunction.
  arXiv  Detail & Related papers  (2024-10-19T15:03:59Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Quantum Langevin Dynamics for Optimization [14.447963674485132]
  We utilize Quantum Langevin Dynamics (QLD) to solve optimization problems.<n>Specifically, we examine the dynamics of a system coupled with an infinite heat bath.<n>We demonstrate that the average energy of the system can approach zero in the low temperature limit.
  arXiv  Detail & Related papers  (2023-11-27T07:25:47Z)
• Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization [108.35402316802765]
  We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Ascent. We show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings. We extend our algorithm to extend the setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings.
  arXiv  Detail & Related papers  (2022-10-31T17:59:29Z)
• NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer [45.47667026025716]
  We propose a novel, robust and accelerated iteration that relies on two key elements. The convergence and stability of the obtained method, referred to as NAG-GS, are first studied extensively. We show that NAG-arity is competitive with state-the-art methods such as momentum SGD with weight decay and AdamW for the training of machine learning models.
  arXiv  Detail & Related papers  (2022-09-29T16:54:53Z)
• Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization [0.0]
  We introduce a framework based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and its key properties analytically and numerically. The prototype is establish a discretization of Born-Infeld dynamics, depending on the objective function.
  arXiv  Detail & Related papers  (2022-01-26T19:00:05Z)
• AEGD: Adaptive Gradient Descent with Energy [0.0]
  We propose AEGD, a new algorithm for first-order gradient non-energy objective functions variable. We show energy-dependent AEGD for both non-energy convergence and desired small step size.
  arXiv  Detail & Related papers  (2020-10-10T22:17:27Z)
• A Dynamical Systems Approach for Convergence of the Bayesian EM Algorithm [59.99439951055238]
  We show how (discrete-time) Lyapunov stability theory can serve as a powerful tool to aid, or even lead, in the analysis (and potential design) of optimization algorithms that are not necessarily gradient-based. The particular ML problem that this paper focuses on is that of parameter estimation in an incomplete-data Bayesian framework via the popular optimization algorithm known as maximum a posteriori expectation-maximization (MAP-EM) We show that fast convergence (linear or quadratic) is achieved, which could have been difficult to unveil without our adopted S&C approach.
  arXiv  Detail & Related papers  (2020-06-23T01:34:18Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.