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--[[ An implementation of Adam https://arxiv.org/abs/1412.6980
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.learningRateDecay` : learning rate decay
- 'config.beta1' : first moment coefficient
- 'config.beta2' : second moment coefficient
- 'config.epsilon' : for numerical stability
- 'config.weightDecay' : weight decay
- '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.adam(opfunc, x, config, state)
-- (0) get/update state
local config = config or {}
local state = state or config
local lr = config.learningRate or 0.001
local lrd = config.learningRateDecay or 0
local beta1 = config.beta1 or 0.9
local beta2 = config.beta2 or 0.999
local epsilon = config.epsilon or 1e-8
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 squared gradient values
state.v = state.v or x.new(dfdx:size()):zero()
-- A tmp tensor to hold the sqrt(v) + epsilon
state.denom = state.denom or x.new(dfdx:size()):zero()
-- (3) learning rate decay (annealing)
local clr = lr / (1 + state.t*lrd)
state.t = state.t + 1
-- Decay the first and second moment running average coefficient
state.m:mul(beta1):add(1-beta1, dfdx)
state.v:mul(beta2):addcmul(1-beta2, dfdx, dfdx)
state.denom:copy(state.v):sqrt():add(epsilon)
local biasCorrection1 = 1 - beta1^state.t
local biasCorrection2 = 1 - beta2^state.t
local stepSize = clr * math.sqrt(biasCorrection2)/biasCorrection1
-- (4) update x
x:addcdiv(-stepSize, state.m, state.denom)
-- return x*, f(x) before optimization
return x, {fx}
end
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