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adam_optimizer.jl
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adam_optimizer.jl
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@doc raw"""
AdamOptimizer(η, ρ₁, ρ₂, δ)
Make an instance of the Adam Optimizer.
Here the cache consists of first and second moments that are updated as
```math
B_1 \gets ((\rho_1 - \rho_1^t)/(1 - \rho_1^t))\cdot{}B_1 + (1 - \rho_1)/(1 - \rho_1^t)\cdot{}\nabla{}L,
```
and
```math
B_2 \gets ((\rho_2 - \rho_1^t)/(1 - \rho_2^t))\cdot{}B_2 + (1 - \rho_2)/(1 - \rho_2^t)\cdot\nabla{}L\odot\nabla{}L.
```
The final velocity is computed as:
```math
\mathrm{velocity} \gets -\eta{}B_1/\sqrt{B_2 + \delta}.
```
# Implementation
The *velocity* is stored in the input to save memory.
Algorithm and suggested defaults are taken from [goodfellow2016deep; page 301](@cite).
"""
struct AdamOptimizer{T<:Real} <: OptimizerMethod
η::T
ρ₁::T
ρ₂::T
δ::T
AdamOptimizer(η = 1f-3, ρ₁ = 9f-1, ρ₂ = 9.9f-1, δ = 3f-7; T=typeof(η)) = new{T}(T(η), T(ρ₁), T(ρ₂), T(δ))
end
function AdamOptimizer(T::Type)
AdamOptimizer(T(1f-3))
end
function update!(o::Optimizer{<:AdamOptimizer{T}}, C::AdamCache, B::AbstractArray) where T
add!(C.B₁, ((o.method.ρ₁ - o.method.ρ₁^o.step)/(T(1.) - o.method.ρ₁^o.step))*C.B₁, ((T(1.) - o.method.ρ₁)/(T(1.) - o.method.ρ₁^o.step))*B)
add!(C.B₂, ((o.method.ρ₂ - o.method.ρ₂^o.step)/(T(1.) - o.method.ρ₂^o.step))*C.B₂, ((T(1.) - o.method.ρ₂)/(T(1.) - o.method.ρ₂^o.step))*⊙²(B))
mul!(B, -o.method.η, /ᵉˡᵉ(C.B₁, scalar_add(racᵉˡᵉ(C.B₂), o.method.δ)))
end
# defaults:
⊙²(A::AbstractVecOrMat) = A.^2
racᵉˡᵉ(A::AbstractVecOrMat) = sqrt.(A)
/ᵉˡᵉ(A::AbstractVecOrMat, B::AbstractVecOrMat) = A./B
scalar_add(A::AbstractVecOrMat, δ::Real) = A .+ δ