Adam Optimizer

adam.py

"""
The MIT License (MIT)

Copyright (c) 2015 Alec Radford

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"""    

    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

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 ????