Adam Optimizer

adam.py

"""
The MIT License (MIT)

Copyright (c) 2015 Alec Radford

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""    

    def Adam(cost, params, lr=0.0002, b1=0.1, b2=0.001, e=1e-8):
        updates = []
        grads = T.grad(cost, params)
        i = theano.shared(floatX(0.))
        i_t = i + 1.
        fix1 = 1. - (1. - b1)**i_t
        fix2 = 1. - (1. - b2)**i_t
        lr_t = lr * (T.sqrt(fix2) / fix1)
        for p, g in zip(params, grads):
            m = theano.shared(p.get_value() * 0.)
            v = theano.shared(p.get_value() * 0.)
            m_t = (b1 * g) + ((1. - b1) * m)
            v_t = (b2 * T.sqr(g)) + ((1. - b2) * v)
            g_t = m_t / (T.sqrt(v_t) + e)
            p_t = p - (lr_t * g_t)
            updates.append((m, m_t))
            updates.append((v, v_t))
            updates.append((p, p_t))
        updates.append((i, i_t))
        return updates

Hey Alec, could you attach an explicit license to this?

Yep, no problem.

Initialization bias counteracting is not done correctly, still looking into it.

Looks correct now.

Maybe I'm missing something obvious but where did the lambda from the paper go?
β1,t ← 1 − (1 − β1)λ^(t−1)

Mgermain - The paper has been updated on Arxiv. V1 does not include lambda, but V2 adds it. The code here looks based on V1.

That said, I think the update rule you quote is wrong. Not that you quoted it wrong, but that it is wrong in v2 of the paper. As it is written it will just set β1,t close to 1 making their momentum calculation degenerate.

So what is the correct momentum calculation? Just for clarities sake?

Hi @Newmu,
Thank you for sharing this code,
Please can you show a basic usage of this code?
Sorry I'm new in this domain.
Thanks in advance,

Hi,
I guess that the 'm' and 'v' quantities have to be re-used in subsequent iterations, but then why are 'm' and 'v' initialized to 0, since the 'Adam' function has to be called many times for the same parameters?

To your question @stablum: this is how Theano constructs the computation graph. The adam() function should only be called once to define the updates in the computational graph, therefore m and v get initialized to 0 once.

For people who struggle with the provided code and the message "Incompatible broadcastable dimensions.", they may need to modify the theano.shared(p.get_value() ... ) calls by adding the broadcastable=p.broadcastable option. Then the updates will be broadcastable in the same way as the original variables.

One more proposed change:

m = theano.shared(np.zeros(p.get_value().shape).astype(dtype=theano.config.floatX))
v = theano.shared(np.zeros(p.get_value().shape).astype(dtype=theano.config.floatX))

The code above doesn't handle scalar parameters correctly - the p.get_value() * 0. will create a float64, even if p.get_value() returns a float32.

That's right @bspeice. However, I 'm confused of the value of the b1 and b2, their values are set to 0.9 and 0.999 respectively in original paper.

Yes that is a mistake I think

No it is correct, see the update here again.
It is 1 - beta1 as beta1 and beta1 as 1 - beta1...
Which is 1 - 0.1 hence beta1 = 0.9 exactly what paper says, and 1 - 0.001 = 0.999 which is again exactly what paper says. Here they r using original beta1 as 1-beta1 and similarly with beta2.... Hece the confusion.

please i have a question
is this function is the built in function in tensor flow or this function is another function ????