--- a
+++ b/pytorch_pretrained_bert/optimization.py
@@ -0,0 +1,180 @@
+# coding=utf-8
+# Copyright 2018 The Google AI Language Team Authors and The HuggingFace Inc. team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""PyTorch optimization for BERT model."""
+
+import math
+import torch
+from torch.optim import Optimizer
+from torch.optim.optimizer import required
+from torch.nn.utils import clip_grad_norm_
+import logging
+
+logger = logging.getLogger(__name__)
+
+def warmup_cosine(x, warmup=0.002):
+    if x < warmup:
+        return x/warmup
+    x_ = (x - warmup) / (1 - warmup)  # progress after warmup -
+    return 0.5 * (1. + math.cos(math.pi * x_))
+
+def warmup_constant(x, warmup=0.002):
+    """ Linearly increases learning rate over `warmup`*`t_total` (as provided to BertAdam) training steps.
+        Learning rate is 1. afterwards. """
+    if x < warmup:
+        return x/warmup
+    return 1.0
+
+def warmup_linear(x, warmup=0.002):
+    """ Specifies a triangular learning rate schedule where peak is reached at `warmup`*`t_total`-th (as provided to BertAdam) training step.
+        After `t_total`-th training step, learning rate is zero. """
+    if x < warmup:
+        return x/warmup
+    return max((x-1.)/(warmup-1.), 0)
+
+SCHEDULES = {
+    'warmup_cosine':   warmup_cosine,
+    'warmup_constant': warmup_constant,
+    'warmup_linear':   warmup_linear,
+}
+
+
+class BertAdam(Optimizer):
+    """Implements BERT version of Adam algorithm with weight decay fix.
+    Params:
+        lr: learning rate
+        warmup: portion of t_total for the warmup, -1  means no warmup. Default: -1
+        t_total: total number of training steps for the learning
+            rate schedule, -1  means constant learning rate. Default: -1
+        schedule: schedule to use for the warmup (see above). Default: 'warmup_linear'
+        b1: Adams b1. Default: 0.9
+        b2: Adams b2. Default: 0.999
+        e: Adams epsilon. Default: 1e-6
+        weight_decay: Weight decay. Default: 0.01
+        max_grad_norm: Maximum norm for the gradients (-1 means no clipping). Default: 1.0
+    """
+    def __init__(self, params, lr=required, warmup=-1, t_total=-1, schedule='warmup_linear',
+                 b1=0.9, b2=0.999, e=1e-6, weight_decay=0.01,
+                 max_grad_norm=1.0):
+        if lr is not required and lr < 0.0:
+            raise ValueError("Invalid learning rate: {} - should be >= 0.0".format(lr))
+        if schedule not in SCHEDULES:
+            raise ValueError("Invalid schedule parameter: {}".format(schedule))
+        if not 0.0 <= warmup < 1.0 and not warmup == -1:
+            raise ValueError("Invalid warmup: {} - should be in [0.0, 1.0[ or -1".format(warmup))
+        if not 0.0 <= b1 < 1.0:
+            raise ValueError("Invalid b1 parameter: {} - should be in [0.0, 1.0[".format(b1))
+        if not 0.0 <= b2 < 1.0:
+            raise ValueError("Invalid b2 parameter: {} - should be in [0.0, 1.0[".format(b2))
+        if not e >= 0.0:
+            raise ValueError("Invalid epsilon value: {} - should be >= 0.0".format(e))
+        defaults = dict(lr=lr, schedule=schedule, warmup=warmup, t_total=t_total,
+                        b1=b1, b2=b2, e=e, weight_decay=weight_decay,
+                        max_grad_norm=max_grad_norm)
+        super(BertAdam, self).__init__(params, defaults)
+
+    def get_lr(self):
+        lr = []
+        for group in self.param_groups:
+            for p in group['params']:
+                state = self.state[p]
+                if len(state) == 0:
+                    return [0]
+                if group['t_total'] != -1:
+                    schedule_fct = SCHEDULES[group['schedule']]
+                    lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
+                else:
+                    lr_scheduled = group['lr']
+                lr.append(lr_scheduled)
+        return lr
+
+    def step(self, closure=None):
+        """Performs a single optimization step.
+
+        Arguments:
+            closure (callable, optional): A closure that reevaluates the model
+                and returns the loss.
+        """
+        loss = None
+        if closure is not None:
+            loss = closure()
+
+        warned_for_t_total = False
+
+        for group in self.param_groups:
+            for p in group['params']:
+                if p.grad is None:
+                    continue
+                grad = p.grad.data
+                if grad.is_sparse:
+                    raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
+
+                state = self.state[p]
+
+                # State initialization
+                if len(state) == 0:
+                    state['step'] = 0
+                    # Exponential moving average of gradient values
+                    state['next_m'] = torch.zeros_like(p.data)
+                    # Exponential moving average of squared gradient values
+                    state['next_v'] = torch.zeros_like(p.data)
+
+                next_m, next_v = state['next_m'], state['next_v']
+                beta1, beta2 = group['b1'], group['b2']
+
+                # Add grad clipping
+                if group['max_grad_norm'] > 0:
+                    clip_grad_norm_(p, group['max_grad_norm'])
+
+                # Decay the first and second moment running average coefficient
+                # In-place operations to update the averages at the same time
+                next_m.mul_(beta1).add_(1 - beta1, grad)
+                next_v.mul_(beta2).addcmul_(1 - beta2, grad, grad)
+                update = next_m / (next_v.sqrt() + group['e'])
+
+                # Just adding the square of the weights to the loss function is *not*
+                # the correct way of using L2 regularization/weight decay with Adam,
+                # since that will interact with the m and v parameters in strange ways.
+                #
+                # Instead we want to decay the weights in a manner that doesn't interact
+                # with the m/v parameters. This is equivalent to adding the square
+                # of the weights to the loss with plain (non-momentum) SGD.
+                if group['weight_decay'] > 0.0:
+                    update += group['weight_decay'] * p.data
+
+                if group['t_total'] != -1:
+                    schedule_fct = SCHEDULES[group['schedule']]
+                    progress = state['step']/group['t_total']
+                    lr_scheduled = group['lr'] * schedule_fct(progress, group['warmup'])
+                    # warning for exceeding t_total (only active with warmup_linear
+                    if group['schedule'] == "warmup_linear" and progress > 1. and not warned_for_t_total:
+                        logger.warning(
+                            "Training beyond specified 't_total' steps with schedule '{}'. Learning rate set to {}. "
+                            "Please set 't_total' of {} correctly.".format(group['schedule'], lr_scheduled, self.__class__.__name__))
+                        warned_for_t_total = True
+                    # end warning
+                else:
+                    lr_scheduled = group['lr']
+
+                update_with_lr = lr_scheduled * update
+                p.data.add_(-update_with_lr)
+
+                state['step'] += 1
+
+                # step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1
+                # No bias correction
+                # bias_correction1 = 1 - beta1 ** state['step']
+                # bias_correction2 = 1 - beta2 ** state['step']
+
+        return loss