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Adaptive Smooth Optimizer
AdaSmooth
Introduced by Jun Lu in AdaSmooth: An Adaptive Learning Rate Method based on Effective Ratio
archive 2025-07-28 Description, source and code snippet are the archive's method entry.
AdaSmooth is a stochastic optimization technique that allows for per-dimension learning rate method for SGD. It is an extension of Adagrad and AdaDelta that seek to reduce its aggressive, monotonically decreasing learning rate. Instead of accumulating all past squared gradients, Adadelta restricts the window of accumulated past gradients to a fixed size w while AdaSmooth adaptively selects the size of the window.
Given the window size M, the effective ratio is calculated by
eₜ = sₜ/nₜ= (| xₜ - x_(t-M)|)/(∑ᵢ₌₀ᴹ⁻¹ | xₜ₋ᵢ - xₜ₋₁₋ᵢ|) = (| ∑ᵢ₌₀ᴹ⁻¹ Δxₜ₋₁₋ᵢ|)/(∑ᵢ₌₀ᴹ⁻¹ | Δxₜ₋₁₋ᵢ|).
Given the effective ratio, the scaled smoothing constant is obtained by:
cₜ = ( ρ₂- ρ₁) ×eₜ + (1-ρ₂),
The running average E[g²]ₜ at time step t then depends only on the previous average and current gradient:
E[g²]ₜ = cₜ² ⊙gₜ² + (1-cₜ² )⊙E[g²]ₜ₋₁
Usually ρ₁ is set to around $0.5$ and ρ₂ is set to around 0.99. The update step the follows:
Δxₜ = -η/(√(E[g²]ₜ + ϵ)) ⊙gₜ,
which is incorporated into the final update:
xₜ₊₁ = xₜ + Δxₜ.
The main advantage of AdaSmooth is its faster convergence rate and insensitivity to hyperparameters.
Papers archive 2025-07-28
2 shown of 2, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.
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Gradient Descent, Stochastic Optimization, and Other Tales 2 May 2022 · 0 repositories · arXiv:2205.00832
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AdaSmooth: An Adaptive Learning Rate Method based on Effective Ratio 2 Apr 2022 · 0 repositories · arXiv:2204.00825
Tasks archive 2025-07-28
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| Task | Papers |
|---|---|
| Stochastic Optimization | 2 |
Usage over time archive 2025-07-28
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Categories archive 2025-07-28
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