FTML optimizer (#110)

* add ftml.py and fix __init__.py

* fix PEP8

keras_contrib/optimizers/__init__.py

@@ -0,0 +1 @@
+from .ftml import FTML

keras_contrib/optimizers/ftml.py

@@ -0,0 +1,81 @@
+from __future__ import absolute_import
+from keras.optimizers import Optimizer
+from .. import backend as K
+
+
+class FTML(Optimizer):
+    """FTML optimizer.
+
+    # Arguments
+        lr: float >= 0. Learning rate.
+        beta_1: float, 0 < beta < 1. Generally close to 0.5.
+        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
+        - [FTML - Follow the Moving Leader in Deep Learning](http://www.cse.ust.hk/~szhengac/papers/icml17.pdf)
+    """
+
+    def __init__(self, lr=0.0025, beta_1=0.6, beta_2=0.999,
+                 epsilon=1e-8, decay=0., **kwargs):
+        super(FTML, self).__init__(**kwargs)
+        self.__dict__.update(locals())
+        self.iterations = K.variable(0)
+        self.lr = K.variable(lr)
+        self.beta_1 = K.variable(beta_1)
+        self.beta_2 = K.variable(beta_2)
+        self.decay = K.variable(decay)
+        self.inital_decay = decay
+
+    def get_updates(self, params, constraints, loss):
+        grads = self.get_gradients(loss, params)
+        self.updates = [K.update_add(self.iterations, 1)]
+
+        lr = self.lr
+        if self.inital_decay > 0:
+            lr *= (1. / (1. + self.decay * self.iterations))
+
+        t = self.iterations + 1
+
+        lr_t = lr / (1. - K.pow(self.beta_1, t))
+
+        shapes = [K.get_variable_shape(p) for p in params]
+        zs = [K.zeros(shape) for shape in shapes]
+        vs = [K.zeros(shape) for shape in shapes]
+        ds = [K.zeros(shape) for shape in shapes]
+        self.weights = [self.iterations] + zs + vs + ds
+
+        for p, g, z, v, d in zip(params, grads, zs, vs, ds):
+            v_t = self.beta_2 * v + (1. - self.beta_2) * K.square(g)
+            d_t = (K.sqrt(v_t / (1. - K.pow(self.beta_2, t))) + self.epsilon) / lr_t
+            sigma_t = d_t - self.beta_1 * d
+            z_t = self.beta_1 * z + (1. - self.beta_1) * g - sigma_t * p
+
+            p_t = - z_t / d_t
+
+            self.updates.append(K.update(z, z_t))
+            self.updates.append(K.update(v, v_t))
+            self.updates.append(K.update(d, d_t))
+
+            new_p = p_t
+            # apply constraints
+            if p in constraints:
+                c = constraints[p]
+                new_p = c(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(FTML, self).get_config()
+        return dict(list(base_config.items()) + list(config.items()))
+
+
+# Aliases.
+
+ftml = FTML