Bias correction for exponential moving average (#17677)

* Bias correction for exponential moving average

test=develop, test=document_preview

* Fix docs

test=develop, test=document_preview

paddle/fluid/API.spec

@@ -523,7 +523,7 @@ paddle.fluid.optimizer.LambOptimizer.apply_optimize (ArgSpec(args=['self', 'loss
 paddle.fluid.optimizer.LambOptimizer.backward (ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set', 'callbacks'], varargs=None, keywords=None, defaults=(None, None, None, None)), ('document', 'ba3a113d0229ff7bc9d39bda0a6d947f'))
 paddle.fluid.optimizer.LambOptimizer.get_opti_var_name_list (ArgSpec(args=['self'], varargs=None, keywords=None, defaults=None), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.optimizer.LambOptimizer.minimize (ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None)), ('document', '35fd5d3330c97903528c7e0dacc7f6ea'))
-paddle.fluid.optimizer.ExponentialMovingAverage.__init__ (ArgSpec(args=['self', 'decay', 'zero_init', 'name'], varargs=None, keywords=None, defaults=(0.999, False, None)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
+paddle.fluid.optimizer.ExponentialMovingAverage.__init__ (ArgSpec(args=['self', 'decay', 'thres_steps', 'name'], varargs=None, keywords=None, defaults=(0.999, None, None)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.optimizer.ExponentialMovingAverage.apply (ArgSpec(args=['self', 'executor', 'need_restore'], varargs=None, keywords=None, defaults=(True,)), ('document', '30f494752ac8921dc5835a63637f453a'))
 paddle.fluid.optimizer.ExponentialMovingAverage.restore (ArgSpec(args=['self', 'executor'], varargs=None, keywords=None, defaults=None), ('document', '8c8a1791608b02a1ede53d6dd3a4fcec'))
 paddle.fluid.backward.append_backward (ArgSpec(args=['loss', 'parameter_list', 'no_grad_set', 'callbacks'], varargs=None, keywords=None, defaults=(None, None, None)), ('document', '08a5dd9f6f376ff3d55e0b1d92115cbd'))

python/paddle/fluid/optimizer.py

@@ -14,6 +14,7 @@
 
 from __future__ import print_function
 
+import numpy as np
 from collections import defaultdict
 from functools import reduce
 
@@ -2175,19 +2176,41 @@ class ExponentialMovingAverage(object):
 
     ..  math::
 
-	\\text{EMA}_t = \\text{decay} * \\text{EMA}_{t-1} + (1 - \\text{decay}) * \\theta_t
+        \\text{EMA}_0 & = 0
 
+	\\text{EMA}_t & = \\text{decay} * \\text{EMA}_{t-1} + (1 - \\text{decay}) * \\theta_t
 
-    The average results will be saved in temporary variables which can be 
-    applied to parameters of current model by calling `apply()` method. And 
-    the `restore()` method is used to restore the parameters.
+    The average results will be saved in temporary variables which are created 
+    and maintained by the object, and can be applied to parameters of current 
+    model by calling **apply()** method. And the **restore()** method is used to 
+    restore the parameters.
+
+    **Bias correction**. All EMAs are initialized to :math:`0` and hence they will be 
+    zero biased, which can be corrected by divided by a factor 
+    :math:`(1 - \\text{decay}^t)` , i.e., the actual EMAs applied to parameters 
+    when calling **apply()** method would be 
+
+    ..  math::
+    
+        \\widehat{\\text{EMA}}_t = \\frac{\\text{EMA}_t}{1 - \\text{decay}^t}
+
+    **Decay rate scheduling**. A large decay rate very close to 1 would result 
+    in that the averages move very slowly. And a better strategy is to set a 
+    relative smaller decay rate in the very beginning. The argument **thres_steps**
+    allows users to pass a Variable to schedule the decay rate, in this case, 
+    the actual decay rate becomes
+     
+    ..  math::
+    
+        \\min(\\text{decay}, \\frac{1 + \\text{thres_steps}}{10 + \\text{thres_steps}})
+
+    Usually **thres_steps** can be the global training steps.
 
 
     Args:
-	decay (float|Variable): The exponential decay rate. Can be scheduled like 
-                                learning rate.
-	zero_init (bool): Whether using zero to initialize EMA Variable. If set to 
-            `True`, :math:`\\text{EMA}_0 = 0.0` else :math:`\\text{EMA}_0 = \\theta_0`.
+	decay (float): The exponential decay rate, usually close to 1, such as 
+                       0.999, 0.9999, ... .
+        thres_steps (Variable|None): If not `None`, schedule the decay rate.
 	name (str|None): An optional name prefix.
 
 
@@ -2204,25 +2227,35 @@ class ExponentialMovingAverage(object):
 	     optimizer = fluid.optimizer.Adam(learning_rate=0.001)
 	     optimizer.minimize(cost)
 
-	     ema = fluid.optimizer.ExponentialMovingAverage(0.99)
+             global_steps = fluid.layers.learning_rate_scheduler._decay_step_counter()
+             ema = fluid.optimizer.ExponentialMovingAverage(0.999, thres_steps=global_steps)
 
 	     # pseudo code
 	     for pass_id in range(args.pass_num):
 		 for data in train_reader():
 		     exe.run(fluid.default_main_program()...)
                  
+                 # usage 1
 		 with ema.apply(exe):
 		     for data in test_reader():
 			 exe.run(inference_program...)
+
+                 # usage 2
+		 with ema.apply(exe, need_restore=False):
+		     for data in test_reader():
+			 exe.run(inference_program...)
+                 ...
+                 ema.restore(exe)
     """
 
-    def __init__(self, decay=0.999, zero_init=False, name=None):
+    def __init__(self, decay=0.999, thres_steps=None, name=None):
         self._decay = decay
-        self._zero_init = zero_init
+        self._thres_steps = thres_steps
         self._name = name if name is not None else ''
+        self._decay_var = self._get_ema_decay()
+
         self.params_tmps = []
-        for param in framework.default_main_program().global_block(
-        ).all_parameters():
+        for param in default_main_program().global_block().all_parameters():
             if param.do_model_average != False:
                 tmp = param.block.create_var(
                     name=unique_name.generate(".".join(
@@ -2232,22 +2265,23 @@ class ExponentialMovingAverage(object):
                     stop_gradient=True)
                 self.params_tmps.append((param, tmp))
 
-        startup_block = default_startup_program().global_block()
         ema_vars = {}
         for param, tmp in self.params_tmps:
             with param.block.program._optimized_guard(
                 [param, tmp]), name_scope('moving_average'):
-                ema_vars[param.name] = self._append_ema_ops(startup_block,
-                                                            param)
+                ema_vars[param.name] = self._append_ema_ops(param)
 
         self.apply_program = Program()
         block = self.apply_program.global_block()
         with program_guard(main_program=self.apply_program):
+            decay_pow = self._get_decay_pow(block)
             for param, tmp in self.params_tmps:
                 param = block._clone_variable(param)
                 tmp = block._clone_variable(tmp)
                 ema = block._clone_variable(ema_vars[param.name])
                 layers.assign(input=param, output=tmp)
+                # bias correction
+                ema = ema / (1.0 - decay_pow)
                 layers.assign(input=ema, output=param)
 
         self.restore_program = Program()
@@ -2258,25 +2292,43 @@ class ExponentialMovingAverage(object):
                 param = block._clone_variable(param)
                 layers.assign(input=tmp, output=param)
 
-    def _append_ema_ops(self, startup_block, param):
+    def _get_ema_decay(self):
+        with default_main_program()._lr_schedule_guard():
+            decay_var = layers.tensor.create_global_var(
+                shape=[1],
+                value=self._decay,
+                dtype='float32',
+                persistable=True,
+                name="scheduled_ema_decay_rate")
+
+            if self._thres_steps is not None:
+                decay_t = (self._thres_steps + 1.0) / (self._thres_steps + 10.0)
+                with layers.control_flow.Switch() as switch:
+                    with switch.case(decay_t < self._decay):
+                        layers.tensor.assign(decay_t, decay_var)
+                    with switch.default():
+                        layers.tensor.assign(
+                            np.array(
+                                [self._decay], dtype=np.float32),
+                            decay_var)
+        return decay_var
+
+    def _get_decay_pow(self, block):
+        global_steps = layers.learning_rate_scheduler._decay_step_counter()
+        decay_var = block._clone_variable(self._decay_var)
+        decay_pow_acc = layers.elementwise_pow(decay_var, global_steps + 1)
+        return decay_pow_acc
+
+    def _append_ema_ops(self, param):
         param_ema = layers.create_global_var(
             name=unique_name.generate(self._name + param.name + '_ema'),
             shape=param.shape,
             value=0.0,
             dtype=param.dtype,
             persistable=True)
-        # t = 0      
-        if self._zero_init is not True:
-            startup_p_ema = startup_block._clone_variable(param_ema)
-            startup_p = startup_block.var(param.name)
-            startup_block.append_op(
-                type="assign",
-                inputs={"X": startup_p},
-                outputs={"Out": startup_p_ema})
-        # t > 0
-        ema_t = param_ema * self._decay - param * (self._decay - 1)
-        layers.assign(input=ema_t, output=param_ema)
 
+        ema_t = param_ema * self._decay_var + param * (1 - self._decay_var)
+        layers.assign(input=ema_t, output=param_ema)
         return param_ema
 
     @signature_safe_contextmanager