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----------------------------------------------------------------------
-- An implementation of SGD adapted with features of Nesterov's
-- Accelerated Gradient method, based on the paper
-- On the Importance of Initialization and Momentum in Deep Learning
-- Sutsveker et. al., ICML 2013
--
-- ARGS:
-- opfunc : a function that takes a single input (X), the point of
-- evaluation, and returns f(X) and df/dX
-- x : the initial point
-- state : a table describing the state of the optimizer; after each
-- call the state is modified
-- state.learningRate : learning rate
-- state.learningRateDecay : learning rate decay
-- state.weightDecay : weight decay
-- state.momentum : momentum
-- state.learningRates : vector of individual learning rates
--
-- RETURN:
-- x : the new x vector
-- f(x) : the function, evaluated before the update
--
-- (Dilip Krishnan, 2013)
--
function optim.nag(opfunc, x, config, state)
-- (0) get/update state
local config = config or {}
local state = state or config
local lr = config.learningRate or 1e-3
local lrd = config.learningRateDecay or 0
local wd = config.weightDecay or 0
local mom = config.momentum or 0.9
local damp = config.dampening or mom
local lrs = config.learningRates
state.evalCounter = state.evalCounter or 0
local nevals = state.evalCounter
if mom <= 0 then
error('Momentum must be positive for Nesterov Accelerated Gradient')
end
-- (1) evaluate f(x) and df/dx
-- first step in the direction of the momentum vector
if state.dfdx then
x:add(mom, state.dfdx)
end
-- then compute gradient at that point
-- comment out the above line to get the original SGD
local fx,dfdx = opfunc(x)
-- (2) weight decay
if wd ~= 0 then
dfdx:add(wd, x)
end
-- (3) learning rate decay (annealing)
local clr = lr / (1 + nevals*lrd)
-- (4) apply momentum
if not state.dfdx then
state.dfdx = torch.Tensor():typeAs(dfdx):resizeAs(dfdx):fill(0)
else
state.dfdx:mul(mom)
end
-- (5) parameter update with single or individual learning rates
if lrs then
if not state.deltaParameters then
state.deltaParameters = torch.Tensor():typeAs(x):resizeAs(dfdx)
end
state.deltaParameters:copy(lrs):cmul(dfdx)
x:add(-clr, state.deltaParameters)
state.dfdx:add(-clr, state.deltaParameters)
else
x:add(-clr, dfdx)
state.dfdx:add(-clr, dfdx)
end
-- (6) update evaluation counter
state.evalCounter = state.evalCounter + 1
-- return x, f(x) before optimization
return x,{fx}
end
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