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Not Variance-AdaptedSGDSSD "Stochastic Sign Descent"
Variance-Adapted
SVAG “Stochastic Variance-Adapted Gradient"ADAM
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Require: initial value 0o,step size α, momentum parameter μ ∈ [0,1], number of steps T
1:Initialize m= O,v = 0
2: for t =1,...,T do
3: 4:Compute stochastic gradient g = g(0)
5:Update moving average m ← μm + g
6: end forUpdateθ ←θ-α sign(m)
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Require: initial value Oo,step size α, momentum/averaging constant μ ∈[0,1],number of steps T 1:Initialize m= O,s= 0
2: for t=1,...,Tdo 3:Compute stochastic gradient g(θ) and variance estimate s(0)
4:Update aggregators m ← μm+ g(0)， s ← μ²s+ $(0)
5: Compute relative variance estimate n² = s/m²
6:
Compute variance adaptation factors γ = (1 + n2)-1/2 Update0 ←0-α(γ ⊙ sign(m))
7: 8: end for
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