Keras implementation of AMSGrad optimizer from “On the Convergence of Adam and Beyond” paper.

```
class AMSgrad(Optimizer):
"""AMSGrad optimizer.
Default parameters follow those provided in the Adam paper.
# Arguments
lr: float >= 0. Learning rate.
beta_1: float, 0 < beta < 1. Generally close to 1.
beta_2: float, 0 < beta < 1. Generally close to 1.
epsilon: float >= 0. Fuzz factor.
decay: float >= 0. Learning rate decay over each update.
# References
- [On the Convergence of Adam and Beyond](https://openreview.net/forum?id=ryQu7f-RZ)
- [Adam - A Method for Stochastic Optimization](http://arxiv.org/abs/1412.6980v8)
"""
def __init__(self, lr=0.001, beta_1=0.9, beta_2=0.999,
epsilon=1e-8, decay=0., **kwargs):
super(AMSgrad, self).__init__(**kwargs)
with K.name_scope(self.__class__.__name__):
self.iterations = K.variable(0, dtype='int64', name='iterations')
self.lr = K.variable(lr, name='lr')
self.beta_1 = K.variable(beta_1, name='beta_1')
self.beta_2 = K.variable(beta_2, name='beta_2')
self.decay = K.variable(decay, name='decay')
self.epsilon = epsilon
self.initial_decay = decay
@interfaces.legacy_get_updates_support
def get_updates(self, loss, params):
grads = self.get_gradients(loss, params)
self.updates = [K.update_add(self.iterations, 1)]
lr = self.lr
if self.initial_decay > 0:
lr *= (1. / (1. + self.decay * K.cast(self.iterations,
K.dtype(self.decay))))
t = K.cast(self.iterations, K.floatx()) + 1
lr_t = lr * (K.sqrt(1. - K.pow(self.beta_2, t)) /
(1. - K.pow(self.beta_1, t)))
ms = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
vs = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
vhats = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params]
self.weights = [self.iterations] + ms + vs + vhats
for p, g, m, v, vhat in zip(params, grads, ms, vs, vhats):
m_t = (self.beta_1 * m) + (1. - self.beta_1) * g
v_t = (self.beta_2 * v) + (1. - self.beta_2) * K.square(g)
vhat_t = K.maximum(vhat, v_t)
p_t = p - lr_t * m_t / (K.sqrt(vhat_t) + self.epsilon)
self.updates.append(K.update(m, m_t))
self.updates.append(K.update(v, v_t))
self.updates.append(K.update(vhat, vhat_t))
new_p = p_t
# Apply constraints.
if getattr(p, 'constraint', None) is not None:
new_p = p.constraint(new_p)
self.updates.append(K.update(p, new_p))
return self.updates
def get_config(self):
config = {'lr': float(K.get_value(self.lr)),
'beta_1': float(K.get_value(self.beta_1)),
'beta_2': float(K.get_value(self.beta_2)),
'decay': float(K.get_value(self.decay)),
'epsilon': self.epsilon}
base_config = super(AMSgrad, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
```