refactor momentum op to combine weight

paddle/fluid/operators/optimizers/momentum_op.cc

@@ -61,6 +61,11 @@ void MomentumOpMaker::Make() {
                 "(bool, default false) "
                 "Use Nesterov Momentum")
       .SetDefault(false);
+  AddAttr<std::string>("regularization_method",
+                       "(string) regularization_method")
+      .SetDefault("");
+  AddAttr<float>("regularization_coeff", "(float) regularization_coeff")
+      .SetDefault(1.0);
   AddComment(R"DOC(
 Momentum Optimizer.
 

paddle/fluid/operators/optimizers/momentum_op.h

@@ -29,6 +29,12 @@ using framework::SelectedRows;
 struct NoNesterov;
 struct UseNesterov;
 
+enum class RegularizationFlag {
+  kNONE = 0,
+  kL1DECAY = 1,  // do not need support right now
+  kL2DECAY = 2,
+};
+
 class MomentumOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   void Make() override;
@@ -100,6 +106,8 @@ class CPUDenseMomentumFunctor {
   const Tensor* learning_rate;
   const T mu;
   const T use_nesterov;
+  const RegularizationFlag regularization_flag;
+  const T regularization_coeff;
   Tensor* param_out;
   Tensor* velocity_out;
 
@@ -107,13 +115,17 @@ class CPUDenseMomentumFunctor {
   CPUDenseMomentumFunctor(const Tensor* param, const Tensor* grad,
                           const Tensor* velocity, const Tensor* learning_rate,
                           const T mu, const bool use_nesterov,
-                          Tensor* param_out, Tensor* velocity_out)
+                          const RegularizationFlag regularization_flag,
+                          const T regularization_coeff, Tensor* param_out,
+                          Tensor* velocity_out)
       : param(param),
         grad(grad),
         velocity(velocity),
         learning_rate(learning_rate),
         mu(mu),
         use_nesterov(use_nesterov),
+        regularization_flag(regularization_flag),
+        regularization_coeff(regularization_coeff),
         param_out(param_out),
         velocity_out(velocity_out) {}
 
@@ -126,6 +138,14 @@ class CPUDenseMomentumFunctor {
     auto g = framework::EigenVector<T>::Flatten(*grad);
     auto* lr = learning_rate->data<T>();
 
+    if (regularization_flag == RegularizationFlag::kL2DECAY) {
+      v_out = v * mu + p * regularization_coeff + g;
+      if (use_nesterov) {
+        p_out = p - (p * regularization_coeff + g + v_out * mu) * lr[0];
+      } else {
+        p_out = p - lr[0] * v_out;
+      }
+    } else {
       v_out = v * mu + g;
       if (use_nesterov) {
         p_out = p - (g + v_out * mu) * lr[0];
@@ -133,6 +153,7 @@ class CPUDenseMomentumFunctor {
         p_out = p - lr[0] * v_out;
       }
     }
+  }
 };
 
 template <typename T, typename UpdateMethod>
@@ -152,11 +173,14 @@ class DenseMomentumFunctor<T, UseNesterov> {
   const int64_t num_;
   T* p_out_;
   T* v_out_;
+  const RegularizationFlag regularization_flag;
+  const T regularization_coeff;
 
  public:
   DenseMomentumFunctor(const T* p, const T* g, const T* v,
                        const T* learning_rate, const T mu, const int64_t num,
-                       T* p_out, T* v_out)
+                       const RegularizationFlag regularization_flag,
+                       const T regularization_coeff, T* p_out, T* v_out)
       : p_(p),
         g_(g),
         v_(v),
@@ -164,13 +188,20 @@ class DenseMomentumFunctor<T, UseNesterov> {
         mu_(mu),
         num_(num),
         p_out_(p_out),
-        v_out_(v_out) {}
+        v_out_(v_out),
+        regularization_flag(regularization_flag),
+        regularization_coeff(regularization_coeff) {}
   inline HOSTDEVICE void operator()(size_t i) const {
     // put memory access in register
     const T p = p_[i];
-    const T g = g_[i];
+    T g = g_[i];
     const T lr = lr_[0];
     const T v = v_[i];
+
+    g = regularization_flag == RegularizationFlag::kL2DECAY
+            ? g + regularization_coeff * p
+            : g;
+
     T v_out = v * mu_ + g;
     T p_out = p - (g + v_out * mu_) * lr;
     // write reigster to memory
@@ -190,11 +221,14 @@ class DenseMomentumFunctor<T, NoNesterov> {
   const int64_t num_;
   T* p_out_;
   T* v_out_;
+  const RegularizationFlag regularization_flag;
+  const T regularization_coeff;
 
  public:
   DenseMomentumFunctor(const T* p, const T* g, const T* v,
                        const T* learning_rate, const T mu, const int64_t num,
-                       T* p_out, T* v_out)
+                       const RegularizationFlag regularization_flag,
+                       const T regularization_coeff, T* p_out, T* v_out)
       : p_(p),
         g_(g),
         v_(v),
@@ -202,13 +236,20 @@ class DenseMomentumFunctor<T, NoNesterov> {
         mu_(mu),
         num_(num),
         p_out_(p_out),
-        v_out_(v_out) {}
+        v_out_(v_out),
+        regularization_flag(regularization_flag),
+        regularization_coeff(regularization_coeff) {}
   inline HOSTDEVICE void operator()(size_t i) const {
     // put memory access in register
     const T p = p_[i];
-    const T g = g_[i];
+    T g = g_[i];
     const T lr = lr_[0];
     const T v = v_[i];
+
+    g = regularization_flag == RegularizationFlag::kL2DECAY
+            ? g + regularization_coeff * p
+            : g;
+
     T v_out = v * mu_ + g;
     T p_out = p - lr * v_out;
     // write reigster to memory
@@ -233,11 +274,15 @@ class SparseMomentumFunctor<T, UseNesterov> {
   const int64_t row_height_;
   T* p_out_;
   T* v_out_;
+  const RegularizationFlag regularization_flag;
+  const T regularization_coeff;
 
  public:
   SparseMomentumFunctor(const T* p, const T* g, const T* v, const T* lr,
                         const T mu, const int64_t* rows, int64_t row_numel,
-                        int64_t row_height, T* p_out, T* v_out)
+                        int64_t row_height,
+                        const RegularizationFlag regularization_flag,
+                        const T regularization_coeff, T* p_out, T* v_out)
       : p_(p),
         g_(g),
         v_(v),
@@ -247,7 +292,9 @@ class SparseMomentumFunctor<T, UseNesterov> {
         row_numel_(row_numel),
         row_height_(row_height),
         p_out_(p_out),
-        v_out_(v_out) {}
+        v_out_(v_out),
+        regularization_flag(regularization_flag),
+        regularization_coeff(regularization_coeff) {}
 
   inline HOSTDEVICE void operator()(size_t i) {
     auto row_idx =
@@ -258,6 +305,11 @@ class SparseMomentumFunctor<T, UseNesterov> {
     const T p = p_[i];
     const T lr = lr_[0];
     const T v = v_[i];
+
+    g = regularization_flag == RegularizationFlag::kL2DECAY
+            ? g + regularization_coeff * p
+            : g;
+
     T v_out = v * mu_ + g;
     T p_out = p - (g + v_out * mu_) * lr;
     // write reigster to memory
@@ -279,11 +331,15 @@ class SparseMomentumFunctor<T, NoNesterov> {
   const int64_t row_height_;
   T* p_out_;
   T* v_out_;
+  const RegularizationFlag regularization_flag;
+  const T regularization_coeff;
 
  public:
   SparseMomentumFunctor(const T* p, const T* g, const T* v, const T* lr,
                         const T mu, const int64_t* rows, int64_t row_numel,
-                        int64_t row_height, T* p_out, T* v_out)
+                        int64_t row_height,
+                        const RegularizationFlag regularization_flag,
+                        const T regularization_coeff, T* p_out, T* v_out)
       : p_(p),
         g_(g),
         v_(v),
@@ -293,7 +349,9 @@ class SparseMomentumFunctor<T, NoNesterov> {
         row_numel_(row_numel),
         row_height_(row_height),
         p_out_(p_out),
-        v_out_(v_out) {}
+        v_out_(v_out),
+        regularization_flag(regularization_flag),
+        regularization_coeff(regularization_coeff) {}
 
   inline HOSTDEVICE void operator()(size_t i) {
     auto row_idx =
@@ -304,6 +362,11 @@ class SparseMomentumFunctor<T, NoNesterov> {
     const T p = p_[i];
     const T lr = lr_[0];
     const T v = v_[i];
+
+    g = regularization_flag == RegularizationFlag::kL2DECAY
+            ? g + regularization_coeff * p
+            : g;
+
     T v_out = v * mu_ + g;
     T p_out = p - v_out * lr;
     // write reigster to memory
@@ -316,6 +379,16 @@ template <typename DeviceContext, typename T>
 class MomentumOpKernel : public framework::OpKernel<T> {
  public:
   void Compute(const framework::ExecutionContext& ctx) const override {
+    std::string regularization_method =
+        ctx.Attr<std::string>("regularization_method");
+    T regularization_coeff =
+        static_cast<T>(ctx.Attr<float>("regularization_coeff"));
+    RegularizationFlag regularization_flag{
+        RegularizationFlag::kNONE};  // disable regularization
+    if (regularization_method == "l2_decay") {
+      regularization_flag = RegularizationFlag::kL2DECAY;
+    }
+
     T mu = static_cast<T>(ctx.Attr<float>("mu"));
     bool use_nesterov = ctx.Attr<bool>("use_nesterov");
 
@@ -324,6 +397,7 @@ class MomentumOpKernel : public framework::OpKernel<T> {
     auto param_out = ctx.Output<framework::Tensor>("ParamOut");
     auto* velocity = ctx.Input<framework::Tensor>("Velocity");
     auto velocity_out = ctx.Output<framework::Tensor>("VelocityOut");
+
     param_out->mutable_data<T>(ctx.GetPlace());
     velocity_out->mutable_data<T>(ctx.GetPlace());
 
@@ -331,9 +405,9 @@ class MomentumOpKernel : public framework::OpKernel<T> {
     if (grad_var->IsType<framework::LoDTensor>()) {
       auto grad = ctx.Input<framework::Tensor>("Grad");
       if (platform::is_cpu_place(ctx.GetPlace())) {
-        CPUDenseMomentumFunctor<T> functor(param, grad, velocity, learning_rate,
-                                           mu, use_nesterov, param_out,
-                                           velocity_out);
+        CPUDenseMomentumFunctor<T> functor(
+            param, grad, velocity, learning_rate, mu, use_nesterov,
+            regularization_flag, regularization_coeff, param_out, velocity_out);
         functor();
       } else if (platform::is_gpu_place(ctx.GetPlace())) {
         platform::ForRange<DeviceContext> for_range(
@@ -342,16 +416,16 @@ class MomentumOpKernel : public framework::OpKernel<T> {
         if (use_nesterov) {
           DenseMomentumFunctor<T, UseNesterov> functor(
               param->data<T>(), grad->data<T>(), velocity->data<T>(),
-              learning_rate->data<T>(), mu, param->numel(),
-              param_out->mutable_data<T>(ctx.GetPlace()),
+              learning_rate->data<T>(), mu, param->numel(), regularization_flag,
+              regularization_coeff, param_out->mutable_data<T>(ctx.GetPlace()),
               velocity_out->mutable_data<T>(ctx.GetPlace()));
           for_range(functor);
 
         } else {
           DenseMomentumFunctor<T, NoNesterov> functor(
               param->data<T>(), grad->data<T>(), velocity->data<T>(),
-              learning_rate->data<T>(), mu, param->numel(),
-              param_out->mutable_data<T>(ctx.GetPlace()),
+              learning_rate->data<T>(), mu, param->numel(), regularization_flag,
+              regularization_coeff, param_out->mutable_data<T>(ctx.GetPlace()),
               velocity_out->mutable_data<T>(ctx.GetPlace()));
           for_range(functor);
         }
@@ -384,6 +458,7 @@ class MomentumOpKernel : public framework::OpKernel<T> {
             param->data<T>(), merged_grad->value().data<T>(),
             velocity->data<T>(), learning_rate->data<T>(), mu, rows, row_numel,
             static_cast<int64_t>(merged_grad->rows().size()),
+            regularization_flag, regularization_coeff,
             param_out->mutable_data<T>(ctx.GetPlace()),
             velocity_out->mutable_data<T>(ctx.GetPlace()));
         for_range(functor);
@@ -393,6 +468,7 @@ class MomentumOpKernel : public framework::OpKernel<T> {
             param->data<T>(), merged_grad->value().data<T>(),
             velocity->data<T>(), learning_rate->data<T>(), mu, rows, row_numel,
             static_cast<int64_t>(merged_grad->rows().size()),
+            regularization_flag, regularization_coeff,
             param_out->mutable_data<T>(ctx.GetPlace()),
             velocity_out->mutable_data<T>(ctx.GetPlace()));
         for_range(functor);

python/paddle/fluid/contrib/__init__.py

@@ -35,6 +35,8 @@ from . import mixed_precision
 from .mixed_precision import *
 from . import layers
 from .layers import *
+from . import optimizer
+from .optimizer import *
 
 __all__ = []
 __all__ += decoder.__all__
@@ -46,3 +48,4 @@ __all__ += utils.__all__
 __all__ += extend_optimizer.__all__
 __all__ += ['mixed_precision']
 __all__ += layers.__all__
+__all__ += optimizer.__all__

python/paddle/fluid/contrib/optimizer.py

+# Copyright (c) 2019 PaddlePaddle Authors. All Rights Reserved.
+#
+# 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.
+from ..optimizer import Optimizer
+from ..regularizer import L1DecayRegularizer
+from ..regularizer import L2DecayRegularizer
+from .. import framework
+from .. import core
+from ..framework import program_guard
+from ..clip import append_gradient_clip_ops
+
+__all__ = ['Momentum']
+
+
+class Momentum(Optimizer):
+    """
+
+    Simple Momentum optimizer with velocity state
+
+    This optimizer has a flag for Nestrov Momentum.
+
+    The update equations are as follows:
+
+    .. math::
+
+        & velocity = mu * velocity + gradient
+
+        & if (use\_nesterov):
+
+        &\quad   param = param - (gradient + mu * velocity) * learning\_rate
+
+        & else:
+
+        &\quad   param = param - learning\_rate * velocity
+
+    Parameters:
+        learning_rate (float|Variable): The learning rate used to update parameters. \
+            Can be a float value or a Variable with one float value as data element.
+        momentum (float): Momentum factor
+        parameter_list (Iterable, optional):  Iterable of ``Variable`` names to update to minimize ``loss``. \
+            This parameter is required in dygraph mode. \
+            The default value is None in static mode, at this time all parameters will be updated.
+        use_nesterov (bool, optional): Enables Nesterov momentum, default is false.
+        regularization (WeightDecayRegularizer, optional): The strategy of regularization. There are two method: \
+             :ref:`api_fluid_regularizer_L1Decay` , :ref:`api_fluid_regularizer_L2Decay` . If a parameter has set \
+            regularizer using :ref:`api_fluid_ParamAttr` already, the regularization setting here in optimizer will be \
+            ignored for this parameter. Otherwise, the regularization setting here in optimizer will take effect.  \
+            Default None, meaning there is no regularization.
+        grad_clip (GradientClipBase, optional): Gradient cliping strategy, it's an instance of 
+            some derived class of ``GradientClipBase`` . There are three cliping strategies 
+            ( :ref:`api_fluid_clip_GradientClipByGlobalNorm` , :ref:`api_fluid_clip_GradientClipByNorm` , 
+            :ref:`api_fluid_clip_GradientClipByValue` ). Default None, meaning there is no gradient clipping.
+        name (str, optional): This parameter is used by developers to print debugging information. \
+            For details, please refer to :ref:`api_guide_Name`. Default is None.
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import paddle.fluid as fluid
+            import numpy as np
+
+            place = fluid.CPUPlace()
+            main = fluid.Program()
+            with fluid.program_guard(main):
+                x = fluid.layers.data(name='x', shape=[13], dtype='float32')
+                y = fluid.layers.data(name='y', shape=[1], dtype='float32')
+                y_predict = fluid.layers.fc(input=x, size=1, act=None)
+                cost = fluid.layers.square_error_cost(input=y_predict, label=y)
+                avg_cost = fluid.layers.mean(cost)
+
+                moment_optimizer = fluid.optimizer.MomentumOptimizer(learning_rate=0.001, momentum=0.9)
+                moment_optimizer.minimize(avg_cost)
+
+                fetch_list = [avg_cost]
+                train_reader = paddle.batch(
+                    paddle.dataset.uci_housing.train(), batch_size=1)
+                feeder = fluid.DataFeeder(place=place, feed_list=[x, y])
+                exe = fluid.Executor(place)
+                exe.run(fluid.default_startup_program())
+                for data in train_reader():
+                    exe.run(main, feed=feeder.feed(data), fetch_list=fetch_list)
+
+    """
+    _velocity_acc_str = "velocity"
+
+    def __init__(self,
+                 learning_rate,
+                 momentum,
+                 parameter_list=None,
+                 use_nesterov=False,
+                 regularization=None,
+                 grad_clip=None,
+                 name=None):
+        assert learning_rate is not None
+        assert momentum is not None
+        super(Momentum, self).__init__(
+            learning_rate=learning_rate,
+            parameter_list=parameter_list,
+            regularization=regularization,
+            grad_clip=grad_clip,
+            name=name)
+        self.type = "momentum"
+        self._momentum = momentum
+        self._use_nesterov = bool(use_nesterov)
+        self._regularization_method = ""
+        self._regularization_coef = 0
+        if (isinstance(regularization, L2DecayRegularizer)):
+            self._regularization_method = "l2_decay"
+            self._regularization_coef = regularization._regularization_coeff
+        if (isinstance(regularization, L1DecayRegularizer)):
+            self._regularization_method = "l1_decay"
+            self._regularization_coef = regularization._regularization_coeff
+
+    def _create_accumulators(self, block, parameters):
+        assert isinstance(block, framework.Block)
+
+        for p in parameters:
+            self._add_accumulator(self._velocity_acc_str, p)
+
+    def _append_optimize_op(self, block, param_and_grad):
+        assert isinstance(block, framework.Block)
+
+        velocity_acc = self._get_accumulator(self._velocity_acc_str,
+                                             param_and_grad[0])
+        lr = self._create_param_lr(param_and_grad)
+
+        if framework.in_dygraph_mode():
+            _, _ = core.ops.momentum(param_and_grad[0], param_and_grad[1],
+                                     velocity_acc, lr, param_and_grad[0],
+                                     velocity_acc, 'mu', self._momentum,
+                                     'use_nesterov', self._use_nesterov)
+            return None
+
+        attrs = {
+            "mu": self._momentum,
+            "use_nesterov": self._use_nesterov,
+            "regularization_method": self._regularization_method,
+            "regularization_coeff": self._regularization_coef
+        }
+        inputs = {
+            "Param": [param_and_grad[0]],
+            "Grad": [param_and_grad[1]],
+            "Velocity": [velocity_acc],
+            "LearningRate": [lr]
+        }
+
+        outputs = {
+            "ParamOut": [param_and_grad[0]],
+            "VelocityOut": [velocity_acc]
+        }
+        # create the momentum optimize op
+        momentum_op = block.append_op(
+            type=self.type,
+            inputs=inputs,
+            outputs=outputs,
+            attrs=attrs,
+            stop_gradient=True)
+
+        return momentum_op
+
+    def apply_gradients(self, params_grads):
+        """
+        Second part of `minimize`, appending optimization operators for
+        given `params_grads` pairs.
+
+        Args:
+            params_grads (list): list of (param, grad) pair to do optimization.
+
+        Returns:
+            list: A list of operators appended to the current program.
+
+        Examples:
+            .. code-block:: python
+
+                import paddle.fluid as fluid
+                loss = network()
+                optimizer = fluid.optimizer.SGD(learning_rate=0.1)
+                params_grads = optimizer.backward(loss)
+                # you may append operations for params_grads here
+                # ...
+                optimizer.apply_gradients(params_grads)
+        """
+
+        params_grads = sorted(params_grads, key=lambda x: x[0].name)
+
+        # 'optimizer(grad_clip)' or 'set_gradient_clip'
+        if self._grad_clip is not None:
+            params_grads = self._grad_clip(params_grads)
+        else:
+            params_grads = append_gradient_clip_ops(params_grads)
+
+        optimize_ops = self._create_optimization_pass(params_grads)
+        return optimize_ops
+
+    def apply_optimize(self, loss, startup_program, params_grads):
+        """
+        Second part of `minimize`, appending optimization operators for
+        given `params_grads` pairs.
+        Args:
+            loss (Variable): loss variable to run optimizations.
+            startup_program (Program): startup_program for initializing parameters
+                in `parameter_list`.
+            params_grads (list): list of (param, grad) pair to do optimization.
+        Returns:
+            list: A list of operators appended to the current program.
+        """
+        if framework.in_dygraph_mode():
+            with program_guard(framework.default_main_program(),
+                               framework.default_startup_program()):
+                if self._grad_clip is not None:
+                    params_grads = self._grad_clip(params_grads)
+                optimize_ops = self._create_optimization_pass(params_grads)
+        else:
+            program = loss.block.program
+            with program_guard(program, startup_program):
+                optimize_ops = self.apply_gradients(params_grads)
+        return optimize_ops

python/paddle/fluid/tests/unittests/test_momentum_op.py

@@ -279,5 +279,172 @@ class TestMomentumV2(unittest.TestCase):
         self.assertRaises(ValueError, paddle.optimizer.Momentum, momentum=None)
 
 
+class TestMomentumOpWithDecay(OpTest):
+    def setUp(self):
+        self.op_type = "momentum"
+        self.dtype = np.float32
+        self.use_nesterov = True
+        self.regularization_method = 'l2_decay'
+        self.regularization_coeff = 0.9
+        self.init_config()
+
+        param = np.random.random((123, 321)).astype(self.dtype)
+        grad = np.random.random((123, 321)).astype(self.dtype)
+        velocity = np.zeros((123, 321)).astype(self.dtype)
+        learning_rate = np.array([0.001]).astype(self.dtype)
+        mu = 0.0001
+        use_nesterov = self.use_nesterov
+        regularization_method = self.regularization_method
+        regularization_coeff = self.regularization_coeff
+
+        self.inputs = {
+            'Param': param,
+            'Grad': grad,
+            'Velocity': velocity,
+            'LearningRate': learning_rate
+        }
+
+        self.attrs = {
+            'mu': mu,
+            'use_nesterov': use_nesterov,
+            'regularization_method': regularization_method,
+            'regularization_coeff': regularization_coeff
+        }
+
+        param_decay = regularization_coeff * param
+        grad_new = grad + param_decay
+        grad = grad_new
+
+        velocity_out = mu * velocity + grad
+        if use_nesterov:
+            param_out = param - grad * learning_rate - \
+                        velocity_out * mu * learning_rate
+        else:
+            param_out = param - learning_rate * velocity_out
+
+        self.outputs = {'ParamOut': param_out, 'VelocityOut': velocity_out}
+
+    def init_config(self):
+        pass
+
+    def test_check_output(self):
+        self.check_output()
+
+
+class TestMomentumOpWithDecayFP16(TestMomentumOpWithDecay):
+    def init_config(self):
+        self.dtype = np.float16
+
+    def test_check_output(self):
+        self.check_output(atol=1e-3)
+
+
+class TestMomentumOpWithDecay2(OpTest):
+    def init_config(self):
+        self.use_nesterov = False
+
+
+class TestSparseMomentumOpWithDecay(unittest.TestCase):
+    def setUp(self):
+        self.use_nesterov = False
+
+    def check_with_place(self, place):
+        self.init_kernel()
+        scope = core.Scope()
+        # create and initialize Grad Variable
+        height = 10
+        rows = [0, 4, 7]
+        row_numel = 12
+        mu = 1.0
+        use_nesterov = self.use_nesterov
+        regularization_method = 'l2_decay'
+        regularization_coeff = 0.9
+
+        # create and initialize Param Variable
+        param = scope.var('Param').get_tensor()
+        param_array = np.full((height, row_numel), 5.0).astype("float32")
+        param.set(param_array, place)
+        param_out = scope.var("ParamOut").get_tensor()
+        param_out_array = np.full((height, row_numel), 0.0).astype("float32")
+        param_out.set(param_out_array, place)
+
+        grad_selected_rows = scope.var('Grad').get_selected_rows()
+        grad_selected_rows.set_height(height)
+        grad_selected_rows.set_rows(rows)
+        grad_np_array = np.ones((len(rows), row_numel)).astype("float32")
+        grad_np_array[0, 0] = 2.0
+        grad_np_array[2, 8] = 4.0
+        grad_tensor = grad_selected_rows.get_tensor()
+        grad_tensor.set(grad_np_array, place)
+
+        velocity = scope.var('Velocity').get_tensor()
+        velocity_np_array = np.ones((height, row_numel)).astype("float32")
+        velocity.set(velocity_np_array, place)
+        velocity_out = scope.var('VelocityOut').get_tensor()
+        velocity_out_np_array = np.full((height, row_numel),
+                                        0.0).astype("float32")
+        velocity_out.set(velocity_out_np_array, place)
+
+        # create and initialize LeraningRate Variable
+        lr = scope.var('LearningRate').get_tensor()
+        lr_array = np.full((1), 2.0).astype("float32")
+        lr.set(lr_array, place)
+
+        # create and run operator
+        op = Operator(
+            "momentum",
+            Param='Param',
+            Grad='Grad',
+            Velocity='Velocity',
+            ParamOut='ParamOut',
+            VelocityOut='VelocityOut',
+            LearningRate='LearningRate',
+            mu=mu,
+            use_nesterov=use_nesterov,
+            regularization_method=regularization_method,
+            regularization_coeff=regularization_coeff)
+        op.run(scope, place)
+
+        # get and compare result
+        param_out_np_array = np.array(param_out)
+        velocity_out_np_array = np.array(velocity_out)
+
+        # TODO(dzh): add a more suitable general numpy interface
+        # for sparse update.
+        _grad_np_array = np.full((height, row_numel), 0.0).astype("float32")
+        for i in range(len(rows)):
+            _grad_np_array[rows[i]] = grad_np_array[i]
+
+        _param = param_array
+
+        _param_decay = regularization_coeff * _param
+        _grad_np_array_new = _grad_np_array + _param_decay
+        _grad_np_array = _grad_np_array_new
+
+        _velocity_out = mu * velocity_np_array + _grad_np_array
+        if use_nesterov:
+            _param_out = _param - (_grad_np_array + _velocity_out * mu
+                                   ) * lr_array
+        else:
+            _param_out = _param - lr_array * _velocity_out
+        self.assertTrue((_velocity_out == velocity_out_np_array).all())
+        self.assertTrue((_param_out == param_out_np_array).all())
+
+    def init_kernel(self):
+        pass
+
+    def test_sparse_momentum(self):
+        places = [core.CPUPlace()]
+        if core.is_compiled_with_cuda():
+            places.append(core.CUDAPlace(0))
+        for place in places:
+            self.check_with_place(place)
+
+
+class TestSparseMomentumOpWithDecay2(TestSparseMomentumOpWithDecay):
+    def init_kernel(self):
+        self.use_nesterov = True
+
+
 if __name__ == "__main__":
     unittest.main()