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pgd.lua
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pgd.lua
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local torch = require 'torch'
local argcheck = require 'argcheck'
local M = {}
local solveCheck = argcheck{
pack=true,
-- TODO: Comments
{name='x0', type='torch.*Tensor'},
{name='f', type='function'},
{name='g', type='function'},
{name='proj', type='function'},
{name='acc', type='boolean', default=true, opt=true},
{name='lambda', type='number', opt=true,
help='Fixed step size. If not provided this is found with a line search.'},
{name='eps', type='number', default=1e-6, opt=true},
{name='maxit', type='number', default=1000, opt=true},
{name='callback', type='function', opt=true},
}
function M.solve(...)
local args = solveCheck(...)
local results = {}
local x0 = args.x0
local f = args.f
local g = args.g
local proj = args.proj
local acc = args.acc
local lambda = args.lambda == nil and 1.0 or args.lambda
local eps = args.eps
local maxit = args.maxit
local callback = args.callback
results.feval = 0
results.geval = 0
local x = proj(x0)
local prev_x = x
results.bestF = nil
results.bestX = x:clone()
for k = 1, maxit do
local omega = (k-1.0)/(k+2.0)
local d = torch.csub(x, prev_x)
local y = acc and torch.add(x, omega, d) or x
if k > 1 and d:norm(2) < eps then
break
end
local f_y = f(y)
local g_y = g(y)
prev_x = x
local f_x
if args.lambda == nil then
-- Line search.
local beta = 0.5
while true do
x = proj(torch.add(y, -lambda, g_y))
local dxy = torch.csub(x, y)
f_x = f(x)
results.feval = results.feval + 1
if f_x <= f_y + g_y:dot(dxy) + dxy:norm(2)^2/(2*lambda) then
break
end
lambda = beta * lambda
end
else
x = proj(torch.add(y, -lambda, g_y))
f_x = f(x)
results.feval = results.feval + 1
end
if results.bestF == nil or f_x < results.bestF then
results.bestF = f_x
results.bestX:copy(x)
end
if callback then callback(k, results.bestF, y, g_y, lambda) end
end
return results
end
local solveBatchCheck = argcheck{
pack=true,
-- TODO: Comments
{name='x0s', type='torch.*Tensor'},
{name='f', type='function'},
{name='g', type='function'},
{name='proj', type='function'},
{name='acc', type='boolean', default=true, opt=true},
{name='lambda', type='number', opt=true,
help='Fixed step size. If not provided this is found with a line search.'},
{name='eps', type='number', default=1e-6, opt=true},
{name='maxit', type='number', default=1000, opt=true},
{name='callback', type='function', opt=true},
}
function M.solveBatch(...)
local args = solveBatchCheck(...)
local results = {}
local x0s = args.x0s
local f = args.f
local g = args.g
local proj = args.proj
local acc = args.acc
local lambda = args.lambda == nil and 1.0 or args.lambda
local eps = args.eps
local maxit = args.maxit
local callback = args.callback
results.feval = 0
results.geval = 0
local xs = proj(x0s)
local prev_xs = xs
local nSamples = xs:size(1)
results.bestFs = nil
results.bestXs = xs:clone()
for k = 1, maxit do
local omega = (k-1.0)/(k+2.0)
local ds = torch.csub(xs, prev_xs)
local ys = acc and torch.add(xs, omega, ds) or xs
if k > 1 and ds:norm(2) < eps then
break
end
-- local f_ys = f(ys)
local g_ys = g(ys)
prev_xs = xs
local f_xs
if args.lambda == nil then
-- Line search.
assert(false, 'unimplemented')
-- local beta = 0.5
-- while true do
-- x = proj(torch.add(y, -lambda, g_y))
-- local dxy = torch.csub(x, y)
-- f_x = f(x)
-- results.feval = results.feval + 1
-- if f_x <= f_y + g_y:dot(dxy) + dxy:norm(2)^2/(2*lambda) then
-- break
-- end
-- lambda = beta * lambda
-- end
else
xs = proj(torch.add(ys, -lambda, g_ys))
f_xs = f(xs)
results.feval = results.feval + 1
end
if results.bestF == nil then
results.bestFs = f_xs
results.bestXs:copy(xs)
else
local betterIdxs = f_xs:lt(results.bestFs)
results.bestFs[betterIdxs] = f_xs[betterIdxs]
local xs_flat = xs:view(nSamples, -1)
local betterIdxsX = betterIdxs:view(-1,1):repeatTensor(1, xs_flat:size(2)):viewAs(xs)
results.bestXs[betterIdxsX] = xs[betterIdxsX]
end
if callback then callback(k, results.bestFs, ys, g_ys, lambda) end
end
return results
end
return M