rprop.lua

--[[ A plain implementation of RPROP

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.stepsize`    : initial step size, common to all components
- `state.etaplus`     : multiplicative increase factor, > 1 (default 1.2)
- `state.etaminus`    : multiplicative decrease factor, < 1 (default 0.5)
- `state.stepsizemax` : maximum stepsize allowed (default 50)
- `state.stepsizemin` : minimum stepsize allowed (default 1e-6)
- `state.niter`       : number of iterations (default 1)

RETURN:
- `x`     : the new x vector
- `f(x)`  : the function, evaluated before the update

(Martin Riedmiller, Koray Kavukcuoglu 2013)
--]]
function optim.rprop(opfunc, x, config, state)
    if config == nil and state == nil then
        print('no state table RPROP initializing')
    end
    -- (0) get/update state
    local config = config or {}
    local state = state or config
    local stepsize = config.stepsize or 0.1
    local etaplus = config.etaplus or 1.2
    local etaminus = config.etaminus or 0.5
    local stepsizemax = config.stepsizemax or 50.0
    local stepsizemin = config.stepsizemin or 1E-06
    local niter = config.niter or 1

    local hfx = {}

    for i=1,niter do

        -- (1) evaluate f(x) and df/dx
        local fx,dfdx = opfunc(x)

        -- init temp storage
        if not state.delta then
            state.delta    = dfdx.new(dfdx:size()):zero()
            state.stepsize = dfdx.new(dfdx:size()):fill(stepsize)
            state.sign     = dfdx.new(dfdx:size())
            state.psign    = torch.ByteTensor(dfdx:size())
            state.nsign    = torch.ByteTensor(dfdx:size())
            state.zsign    = torch.ByteTensor(dfdx:size())
            state.dminmax  = torch.ByteTensor(dfdx:size())
			if torch.type(x)=='torch.CudaTensor' then
				-- Push to GPU
				state.psign    = state.psign:cuda()
				state.nsign    = state.nsign:cuda()
				state.zsign    = state.zsign:cuda()
				state.dminmax  = state.dminmax:cuda()
			end
        end

        -- sign of derivative from last step to this one
        torch.cmul(state.sign, dfdx, state.delta)
        torch.sign(state.sign, state.sign)

        -- get indices of >0, <0 and ==0 entries
        state.sign.gt(state.psign, state.sign, 0)
        state.sign.lt(state.nsign, state.sign, 0)
        state.sign.eq(state.zsign, state.sign, 0)

        -- get step size updates
        state.sign[state.psign] = etaplus
        state.sign[state.nsign] = etaminus
        state.sign[state.zsign] = 1

        -- update stepsizes with step size updates
        state.stepsize:cmul(state.sign)

        -- threshold step sizes
        -- >50 => 50
        state.stepsize.gt(state.dminmax, state.stepsize, stepsizemax)
        state.stepsize[state.dminmax] = stepsizemax
        -- <1e-6 ==> 1e-6
        state.stepsize.lt(state.dminmax, state.stepsize, stepsizemin)
        state.stepsize[state.dminmax] = stepsizemin

        -- for dir<0, dfdx=0
        -- for dir>=0 dfdx=dfdx
        dfdx[state.nsign] = 0
        -- state.sign = sign(dfdx) 
        torch.sign(state.sign,dfdx)

        -- update weights
        x:addcmul(-1,state.sign,state.stepsize)

        -- update state.dfdx with current dfdx
        state.delta:copy(dfdx)

        table.insert(hfx,fx)
    end

   -- return x*, f(x) before optimization
   return x,hfx
end