Research map / Probabilistic and scientific modeling / Dynamical systems
A Dynamical Systems Perspective on Nesterov Acceleration
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add local curvature-dependent damping to constant damping | Dynamical system for accelerated gradient · Strongly convex smooth objectives | continuous-time convergence rate: 1/(2√κ)-1/(4κ) | Helped |
| Discretize the dynamical system with semi-implicit Euler at T_s=1 | Dynamical system for accelerated gradient · Strongly convex smooth objectives | discrete-time convergence rate: 1-T_s O(1/√κ) | Helped |
| Use time-varying damping and momentum parameters | Dynamical system for smooth non-strongly-convex optimization · Smooth non-strongly-convex objectives | objective decay rate: O(1/t^2) | Helped |
Closest papers by meaning
- Rethinking the Variational Interpretation of Accelerated Optimization Methods (NeurIPS 2021 · similarity 0.90)
- Dissipativity Theory for Nesterov’s Accelerated Method (ICML 2017 · similarity 0.89)
- Continuous-Time Analysis of Accelerated Gradient Methods via Conservation Laws in Dilated Coordinate Systems (ICML 2022 · similarity 0.88)
- Conformal Symplectic and Relativistic Optimization (NeurIPS 2020 · similarity 0.87)
- Accelerated Gradient Methods for Geodesically Convex Optimization: Tractable Algorithms and Convergence Analysis (ICML 2022 · similarity 0.87)
- Direct Runge-Kutta Discretization Achieves Acceleration (NeurIPS 2018 · similarity 0.87)
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