NADAM optimizer

src/Flux.jl

@@ -9,7 +9,7 @@ using MacroTools: @forward
 
 export Chain, Dense, RNN, LSTM, GRU, Conv, Conv2D,
   Dropout, LayerNorm, BatchNorm,
-  SGD, ADAM, Momentum, Nesterov, AMSGrad,
+  SGD, ADAM, Momentum, Nesterov, AMSGrad, NADAM,
   param, params, mapleaves, cpu, gpu
 
 @reexport using NNlib

src/optimise/Optimise.jl

@@ -1,7 +1,7 @@
 module Optimise
 
 export update!, params, train!,
-  SGD, ADAM, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad
+  SGD, ADAM, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad, NADAM
 
 struct Param{T}
   x::T

src/optimise/interface.jl

@@ -82,3 +82,12 @@ tuning.
 """
 AMSGrad(ps, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0) =
   optimiser(ps, p -> amsgrad(p; η = η, β1 = β1, β2 = β2, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+
+"""
+    NADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+
+[NADAM](https://openreview.net/pdf?id=OM0jvwB8jIp57ZJjtNEZ) optimiser. Parameters other
+than learning rate don't need tuning.
+"""
+NADAM(ps, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0) =
+  optimiser(ps, p->nadam(p; η=η, β1=β1, β2=β2, ϵ=ϵ), p->invdecay(p,decay), p->descent(p,1))

src/optimise/optimisers.jl

@@ -74,6 +74,19 @@ function amsgrad(p::Param; η::Real = 0.001, β1::Real = 0.9, β2::Real = 0.999,
   end
 end
 
+function nadam(p::Param; η::Real = 0.001, β1::Real = 0.9, β2::Real = 0.999, ϵ::Real = 1e-8)
+  mt = zeros(p.x)
+  vt = zeros(p.x)
+  β1p, β2p = β1, β2
+  function ()
+    @. mt = β1 * mt + (1 - β1) * p.Δ
+    @. vt = β2 * vt + (1 - β2) * p.Δ^2
+    @. p.Δ =  (β1 * mt + (1 - β1) * p.Δ) / (1 - β1p) / (√(vt / (1 - β2p)) + ϵ) * η
+    β1p *= β1
+    β2p *= β2
+  end
+end
+
 clip(p::Param, thresh::Real) = () -> clamp!(p.Δ, -thresh, thresh)
 
 function expdecay(p::Param, γ::Real)

test/optimise.jl

@@ -3,7 +3,7 @@ using Flux.Tracker
 
 @testset "Optimise" begin
   w = randn(10, 10)
-  @testset for Opt in [SGD, Nesterov, Momentum, ADAM, RMSProp, ps -> ADAGrad(ps, 0.1), ADADelta, AMSGrad]
+  @testset for Opt in [SGD, Nesterov, Momentum, ADAM, RMSProp, ps -> ADAGrad(ps, 0.1), ADADelta, AMSGrad, NADAM]
     w′ = param(randn(10, 10))
     loss(x) = Flux.mse(w*x, w′*x)
     opt = Opt([w′])