from keras import backend as K from keras.optimizers import Optimizer class AdaBound(Optimizer): """AdaBound optimizer. Default parameters follow those provided in the original paper. # Arguments lr: float >= 0. Learning rate. final_lr: float >= 0. Final learning rate. beta_1: float, 0 < beta < 1. Generally close to 1. beta_2: float, 0 < beta < 1. Generally close to 1. gamma: float >= 0. Convergence speed of the bound function. epsilon: float >= 0. Fuzz factor. If `None`, defaults to `K.epsilon()`. decay: float >= 0. Learning rate decay over each update. weight_decay: Weight decay weight. amsbound: boolean. Whether to apply the AMSBound variant of this algorithm. # References - [Adaptive Gradient Methods with Dynamic Bound of Learning Rate] (https://openreview.net/forum?id=Bkg3g2R9FX) - [Adam - A Method for Stochastic Optimization] (https://arxiv.org/abs/1412.6980v8) - [On the Convergence of Adam and Beyond] (https://openreview.net/forum?id=ryQu7f-RZ) """ def __init__(self, lr=0.001, final_lr=0.1, beta_1=0.9, beta_2=0.999, gamma=1e-3, epsilon=None, decay=0., amsbound=False, weight_decay=0.0, **kwargs): super(AdaBound, self).__init__(**kwargs) if not 0. <= gamma <= 1.: raise ValueError("Invalid `gamma` parameter. Must lie in [0, 1] range.") 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.final_lr = final_lr self.gamma = gamma if epsilon is None: epsilon = K.epsilon() self.epsilon = epsilon self.initial_decay = decay self.amsbound = amsbound self.weight_decay = float(weight_decay) self.base_lr = float(lr) 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 = lr * (1. / (1. + self.decay * K.cast(self.iterations, K.dtype(self.decay)))) t = K.cast(self.iterations, K.floatx()) + 1 # Applies bounds on actual learning rate step_size = lr * (K.sqrt(1. - K.pow(self.beta_2, t)) / (1. - K.pow(self.beta_1, t))) final_lr = self.final_lr * lr / self.base_lr lower_bound = final_lr * (1. - 1. / (self.gamma * t + 1.)) upper_bound = final_lr * (1. + 1. / (self.gamma * 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] if self.amsbound: vhats = [K.zeros(K.int_shape(p), dtype=K.dtype(p)) for p in params] else: vhats = [K.zeros(1) for _ in params] self.weights = [self.iterations] + ms + vs + vhats for p, g, m, v, vhat in zip(params, grads, ms, vs, vhats): # apply weight decay if self.weight_decay != 0.: g += self.weight_decay * K.stop_gradient(p) m_t = (self.beta_1 * m) + (1. - self.beta_1) * g v_t = (self.beta_2 * v) + (1. - self.beta_2) * K.square(g) if self.amsbound: vhat_t = K.maximum(vhat, v_t) denom = (K.sqrt(vhat_t) + self.epsilon) self.updates.append(K.update(vhat, vhat_t)) else: denom = (K.sqrt(v_t) + self.epsilon) # Compute the bounds step_size_p = step_size * K.ones_like(denom) step_size_p_bound = step_size_p / denom bounded_lr_t = m_t * K.minimum(K.maximum(step_size_p_bound, lower_bound), upper_bound) p_t = p - bounded_lr_t self.updates.append(K.update(m, m_t)) self.updates.append(K.update(v, v_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)), 'final_lr': float(self.final_lr), 'beta_1': float(K.get_value(self.beta_1)), 'beta_2': float(K.get_value(self.beta_2)), 'gamma': float(self.gamma), 'decay': float(K.get_value(self.decay)), 'epsilon': self.epsilon, 'weight_decay': self.weight_decay, 'amsbound': self.amsbound} base_config = super(AdaBound, self).get_config() return dict(list(base_config.items()) + list(config.items()))