adam.py

def adam(loss, all_params, learning_rate=0.001, b1=0.9, b2=0.999, e=1e-8,
         gamma=1-1e-8):
    """
    ADAM update rules
    Default values are taken from [Kingma2014]

    References:
    [Kingma2014] Kingma, Diederik, and Jimmy Ba.
    "Adam: A Method for Stochastic Optimization."
    arXiv preprint arXiv:1412.6980 (2014).
    http://arxiv.org/pdf/1412.6980v4.pdf

    """
    updates = []
    all_grads = theano.grad(loss, all_params)
    alpha = learning_rate
    t = theano.shared(np.float32(1))
    b1_t = b1*gamma**(t-1)   #(Decay the first moment running average coefficient)

    for theta_previous, g in zip(all_params, all_grads):
        m_previous = theano.shared(np.zeros(theta_previous.get_value().shape,
                                            dtype=theano.config.floatX))
        v_previous = theano.shared(np.zeros(theta_previous.get_value().shape,
                                            dtype=theano.config.floatX))

        m = b1_t*m_previous + (1 - b1_t)*g                             # (Update biased first moment estimate)
        v = b2*v_previous + (1 - b2)*g**2                              # (Update biased second raw moment estimate)
        m_hat = m / (1-b1**t)                                          # (Compute bias-corrected first moment estimate)
        v_hat = v / (1-b2**t)                                          # (Compute bias-corrected second raw moment estimate)
        theta = theta_previous - (alpha * m_hat) / (T.sqrt(v_hat) + e) #(Update parameters)

        updates.append((m_previous, m))
        updates.append((v_previous, v))
        updates.append((theta_previous, theta) )
    updates.append((t, t + 1.))
    return updates