diff --git a/pytorch_pretrained_bert/optimization.py b/pytorch_pretrained_bert/optimization.py
index c72c552a23..c510109cb4 100644
--- a/pytorch_pretrained_bert/optimization.py
+++ b/pytorch_pretrained_bert/optimization.py
@@ -35,17 +35,6 @@ def warmup_constant(x, warmup=0.002):
         return x/warmup
     return 1.0
 
-class Warmup_Linear_with_Warning(object):
-    def __init__(self, **kw):
-        super(Warmup_Linear_with_Warning, self).__init__()
-        self.warned_at_x = -1
-
-    def __call__(self, x, warmup=0.002):
-        if x > 1 and x > self.warned_at_x:
-            logger.warning("Training beyond specified 't_total' steps. Learning rate set to zero. Please set 't_total' of BertAdam correctly.")
-            self.warned_at_x = x
-        return warmup_linear(x, warmup=warmup)
-
 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. """
@@ -54,9 +43,9 @@ def warmup_linear(x, warmup=0.002):
     return max((x-1.)/(warmup-1.), 0)
 
 SCHEDULES = {
-    'warmup_cosine':warmup_cosine,
-    'warmup_constant':warmup_constant,
-    'warmup_linear': Warmup_Linear_with_Warning(), #warmup_linear,
+    'warmup_cosine':   warmup_cosine,
+    'warmup_constant': warmup_constant,
+    'warmup_linear':   warmup_linear,
 }
 
 
@@ -93,6 +82,8 @@ class BertAdam(Optimizer):
                         b1=b1, b2=b2, e=e, weight_decay=weight_decay,
                         max_grad_norm=max_grad_norm)
         super(BertAdam, self).__init__(params, defaults)
+        # warning for t_total exceeded
+        self._warned_for_t_total_at_progress = -1 if schedule == "warmup_linear" else float("inf")
 
     def get_lr(self):
         lr = []
@@ -163,7 +154,15 @@ class BertAdam(Optimizer):
 
                 if group['t_total'] != -1:
                     schedule_fct = SCHEDULES[group['schedule']]
-                    lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
+                    # warning for exceeding t_total (only active with warmup_linear
+                    progress = state['step']/group['t_total']
+                    if progress > 1. and progress > self._warned_for_t_total_at_progress:
+                        logger.warning(
+                            "Training beyond specified 't_total' steps. Learning rate set to zero. "
+                            "Please set 't_total' of {} correctly.".format(self.__class__.__name__))
+                        self._warned_for_t_total_at_progress = progress
+                    # end warning
+                    lr_scheduled = group['lr'] * schedule_fct(progress, group['warmup'])
                 else:
                     lr_scheduled = group['lr']
 
diff --git a/pytorch_pretrained_bert/optimization_openai.py b/pytorch_pretrained_bert/optimization_openai.py
index 7df6369023..e76e84ac05 100644
--- a/pytorch_pretrained_bert/optimization_openai.py
+++ b/pytorch_pretrained_bert/optimization_openai.py
@@ -40,8 +40,6 @@ def warmup_linear(x, warmup=0.002):
         After `t_total`-th training step, learning rate is zero. """
     if x < warmup:
         return x/warmup
-    if x > 1:
-        logger.warning("Training beyond specified 't_total' steps. Learning rate set to zero. Please set 't_total' of BertAdam correctly.")
     return max((x-1.)/(warmup-1.), 0)
 
 SCHEDULES = {
@@ -73,6 +71,8 @@ class OpenAIAdam(Optimizer):
                         b1=b1, b2=b2, e=e, weight_decay=weight_decay, vector_l2=vector_l2,
                         max_grad_norm=max_grad_norm)
         super(OpenAIAdam, self).__init__(params, defaults)
+        # warning for t_total exceeded
+        self._warned_for_t_total_at_progress = -1 if schedule == "warmup_linear" else float("inf")
 
     def get_lr(self):
         lr = []
@@ -137,7 +137,15 @@ class OpenAIAdam(Optimizer):
 
                 if group['t_total'] != -1:
                     schedule_fct = SCHEDULES[group['schedule']]
-                    lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
+                    # warning for exceeding t_total (only active with warmup_linear
+                    progress = state['step']/group['t_total']
+                    if progress > 1. and progress > self._warned_for_t_total_at_progress:
+                        logger.warning(
+                            "Training beyond specified 't_total' steps. Learning rate set to zero. "
+                            "Please set 't_total' of {} correctly.".format(self.__class__.__name__))
+                        self._warned_for_t_total_at_progress = progress
+                    # end warning
+                    lr_scheduled = group['lr'] * schedule_fct(progress, group['warmup'])
                 else:
                     lr_scheduled = group['lr']