Merge pull request #224 from tejank10/nadam-opt

NADAM optimizer

src/Flux.jl

@@ -23,7 +23,7 @@ include("optimise/Optimise.jl")
 using .Optimise
 using .Optimise: @epochs
 export SGD, ADAM, AdaMax, Momentum, Nesterov,
-       RMSProp, ADAGrad, ADADelta, AMSGrad
+       RMSProp, ADAGrad, ADADelta, AMSGrad, NADAM
 
 include("utils.jl")
 include("onehot.jl")

src/optimise/Optimise.jl

@@ -1,7 +1,8 @@
 module Optimise
 
 export train!,
-  SGD, ADAM, AdaMax, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad
+  SGD, ADAM, AdaMax, Momentum, Nesterov,
+  RMSProp, ADAGrad, ADADelta, AMSGrad, NADAM
 
 struct Param{T}
   x::T

src/optimise/interface.jl

@@ -91,3 +91,12 @@ 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

@@ -27,7 +27,7 @@ function rmsprop(p::Param; η::Real = 0.001, ρ::Real = 0.9, ϵ::Real = 1e-8)
   acc  = zeros(p.x)
   function ()
     @. acc = ρ * acc + (1 - ρ) * p.Δ^2
-    @. p.Δ *= η / (√acc + ϵ)
+    @. p.Δ *= η / √(acc + ϵ)
   end
 end
 
@@ -35,7 +35,7 @@ function adagrad(p::Param; η::Real = 0.01, ϵ::Real = 1e-8)
   acc = zeros(p.x) .+ ϵ
   function ()
     @. acc += p.Δ^2
-    @. p.Δ *= η / √acc
+    @. p.Δ *= η / √(acc + ϵ)
   end
 end
 
@@ -56,7 +56,7 @@ function adam(p::Param; η::Real = 0.001, β1::Real = 0.9, β2::Real = 0.999, ϵ
   function ()
     @. mt = β1 * mt + (1 - β1) * p.Δ
     @. vt = β2 * vt + (1 - β2) * p.Δ^2
-    @. p.Δ =  mt / (1 - β1p) / (√(vt / (1 - β2p)) + ϵ) * η
+    @. p.Δ =  mt / (1 - β1p) / √(vt / (1 - β2p) + ϵ) * η
     β1p *= β1
     β2p *= β2
   end
@@ -86,6 +86,19 @@ 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 * β1p) + (1 - β1) * p.Δ / (1 - β1p)) / √(vt * β2 / (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, AdaMax, RMSProp, ps -> ADAGrad(ps, 0.1), ADADelta, AMSGrad]
+  @testset for Opt in [SGD, Nesterov, Momentum, ADAM, AdaMax, 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′])