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+--[[ An implementation of AdaMax http://arxiv.org/pdf/1412.6980.pdf
+
+ARGS:
+
+- 'opfunc' : a function that takes a single input (X), the point
+ of a evaluation, and returns f(X) and df/dX
+- 'x' : the initial point
+- 'config` : a table with configuration parameters for the optimizer
+- 'config.learningRate' : learning rate
+- 'config.beta1' : first moment coefficient
+- 'config.beta2' : second moment coefficient
+- 'config.epsilon' : for numerical stability
+- 'state' : a table describing the state of the optimizer;
+ after each call the state is modified.
+
+RETURN:
+- `x` : the new x vector
+- `f(x)` : the function, evaluated before the update
+
+]]
+
+function optim.adamax(opfunc, x, config, state)
+ -- (0) get/update state
+ local config = config or {}
+ local state = state or config
+ local lr = config.learningRate or 0.002
+
+ local beta1 = config.beta1 or 0.9
+ local beta2 = config.beta2 or 0.999
+ local epsilon = config.epsilon or 1e-38
+ local wd = config.weightDecay or 0
+
+ -- (1) evaluate f(x) and df/dx
+ local fx, dfdx = opfunc(x)
+
+ -- (2) weight decay
+ if wd ~= 0 then
+ dfdx:add(wd, x)
+ end
+
+ -- Initialization
+ state.t = state.t or 0
+ -- Exponential moving average of gradient values
+ state.m = state.m or x.new(dfdx:size()):zero()
+ -- Exponential moving average of the infinity norm
+ state.u = state.u or x.new(dfdx:size()):zero()
+ -- A tmp tensor to hold the input to max()
+ state.max = state.max or x.new(2, unpack(dfdx:size():totable())):zero()
+
+ state.t = state.t + 1
+
+ -- Update biased first moment estimate.
+ state.m:mul(beta1):add(1-beta1, dfdx)
+ -- Update the exponentially weighted infinity norm.
+ state.max[1]:copy(state.u):mul(beta2)
+ state.max[2]:copy(dfdx):abs():add(epsilon)
+ state.u:max(state.max, 1)
+
+ local biasCorrection1 = 1 - beta1^state.t
+ local stepSize = lr/biasCorrection1
+ -- (2) update x
+ x:addcdiv(-stepSize, state.m, state.u)
+
+ -- return x*, f(x) before optimization
+ return x, {fx}
+end