Research map / Optimization / Nonconvex and smooth optimization
A Variational Perspective on High-Resolution ODEs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the paper's variational HR-ODE analysis and discrete Lyapunov function for NAG | NAG · Smooth convex minimization | minimum squared gradient norm: \frac{8568}{(k+1)^3s^2}\|x_0-x^*\|^2 -> \frac{12}{k^3s^2}\|x_0-x^*\|^2 | Helped |
| Add noisy-gradient handling with a decreasing step size | NAG · Smooth convex minimization with noisy gradients | expected objective residual: \tilde{\mathcal{O}}(1/k^{1/2}) | Helped |
| Add noisy-gradient handling with a decreasing step size | NAG · Smooth convex minimization with noisy gradients | expected squared gradient norm: \tilde{\mathcal{O}}(1/k^{3/4}) | Helped |
| Use modified NNAG update rather than the NNAG update (ablation) | NNAG · Smooth convex minimization with noisy gradients | expected minimum squared gradient norm: O(\log(k)/k^{(3/4)}) | Helped |
| Mix NNAG with SGD-like gradients | SGD · Binary classification with logistic regression | performance | Helped |
| Mix NNAG with SVRG snapshots | SVRG · Binary classification with logistic regression | performance | Helped |
| Mix NNAG with SVRG | CNN training · CIFAR10 | training error | Helped |
| Use NNAG instead of the other compared methods | CNN training · CIFAR10 | validation accuracy | Helped |
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