Implement AMSGrad optimiser

src/optimise/Optimise.jl

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

src/optimise/interface.jl

@@ -71,3 +71,12 @@ tuning.
 """
 ADADelta(ps; η = 0.01, ρ = 0.95, ϵ = 1e-8, decay = 0) =
   optimiser(ps, p -> adadelta(p; ρ = ρ, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+
+  """
+      AMSGrad(params; η = 0.001, β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+
+  [AMSGrad](https://openreview.net/forum?id=ryQu7f-RZ) optimiser. Parameters don't need
+  tuning.
+  """
+  AMSGrad(params; 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))

src/optimise/optimisers.jl

@@ -67,8 +67,20 @@ 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 = √(1 - β2p) / √(1 - β1p) * mt / √vt * η
+    @. p.Δ = √(1 - β2p) / (1 - β1p) * mt / √vt * η
     β1p *= β1
     β2p *= β2
   end
 end
+
+function amsgrad(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) .+ ϵ
+  v̂t = zeros(p.x) .+ ϵ
+  function ()
+    @. mt = β1 * mt + (1 - β1) * p.Δ
+    @. vt = β2 * vt + (1 - β2) * p.Δ ^ 2
+    @. v̂t = max.(v̂t, vt)
+    @. p.Δ = η * mt / √v̂t
+  end
+end