Add centered mode rmsprop (#13161)

* rmsprop optimizer support v1 mode

* typo

* optimize code

* refine code

* optimize unit test

* update test_rmsprop_op.py

* update formula of rmsprop

* optimize document

* update API.spec for RMSPropOptimizer

* add default value to check_output_with_place equal_nan

paddle/fluid/API.spec

@@ -376,7 +376,7 @@ paddle.fluid.optimizer.DecayedAdagradOptimizer.__init__ ArgSpec(args=['self', 'l
 paddle.fluid.optimizer.DecayedAdagradOptimizer.minimize ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None))
 paddle.fluid.optimizer.FtrlOptimizer.__init__ ArgSpec(args=['self', 'learning_rate', 'l1', 'l2', 'lr_power'], varargs=None, keywords='kwargs', defaults=(0.0, 0.0, -0.5))
 paddle.fluid.optimizer.FtrlOptimizer.minimize ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None))
-paddle.fluid.optimizer.RMSPropOptimizer.__init__ ArgSpec(args=['self', 'learning_rate', 'rho', 'epsilon', 'momentum'], varargs=None, keywords='kwargs', defaults=(0.95, 1e-06, 0.0))
+paddle.fluid.optimizer.RMSPropOptimizer.__init__ ArgSpec(args=['self', 'learning_rate', 'rho', 'epsilon', 'momentum', 'centered'], varargs=None, keywords='kwargs', defaults=(0.95, 1e-06, 0.0, False))
 paddle.fluid.optimizer.RMSPropOptimizer.minimize ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None))
 paddle.fluid.optimizer.AdadeltaOptimizer.__init__ ArgSpec(args=['self', 'learning_rate', 'epsilon', 'rho'], varargs=None, keywords='kwargs', defaults=(1e-06, 0.95))
 paddle.fluid.optimizer.AdadeltaOptimizer.minimize ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None))

paddle/fluid/operators/rmsprop_op.cc

@@ -36,9 +36,13 @@ class RmspropOp : public framework::OperatorWithKernel {
     PADDLE_ENFORCE(ctx->HasOutput("ParamOut"),
                    "Output(param_out) of RmspropOp should not be null.");
     PADDLE_ENFORCE(ctx->HasOutput("MomentOut"),
-                   "Output(Momentum_out) of RmspropOp should not be null.");
+                   "Output(MomentOut) of RmspropOp should not be null.");
     PADDLE_ENFORCE(ctx->HasOutput("MeanSquareOut"),
                    "Output(MeanSquareOut) of RmspropOp should not be null.");
+    if (ctx->Attrs().Get<bool>("centered")) {
+      PADDLE_ENFORCE(ctx->HasOutput("MeanGradOut"),
+                     "Output(MeanGradOut) of RmspropOp should not be null.");
+    }
 
     auto param_dim = ctx->GetInputDim("Param");
     PADDLE_ENFORCE_EQ(
@@ -58,6 +62,9 @@ class RmspropOp : public framework::OperatorWithKernel {
     ctx->SetOutputDim("ParamOut", param_dim);
     ctx->SetOutputDim("MomentOut", param_dim);
     ctx->SetOutputDim("MeanSquareOut", param_dim);
+    if (ctx->Attrs().Get<bool>("centered")) {
+      ctx->SetOutputDim("MeanGradOut", param_dim);
+    }
   }
 };
 
@@ -70,6 +77,10 @@ class RmspropOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("MeanSquare",
              "(Tensor, default Tensor<float>)"
              " The mean square value that gets updated.");
+    AddInput("MeanGrad",
+             "(Tensor, default Tensor<float>)"
+             " The moving average of gradient")
+        .AsDispensable();
     AddInput("LearningRate",
              "(Tensor, default Tensor<float>) "
              "The learning rate should be a tensor of size 1.");
@@ -82,6 +93,8 @@ class RmspropOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("ParamOut", "(Tensor) Output updated parameter value.");
     AddOutput("MomentOut", "(Tensor) Output updated moment.");
     AddOutput("MeanSquareOut", "(Tensor) Output Mean squared updated value.");
+    AddOutput("MeanGradOut",
+              "(Tensor) Output moving average of gradient updated value.");
 
     AddAttr<float>("epsilon",
                    "(float, default 1e-10) Constant "
@@ -93,6 +106,8 @@ class RmspropOpMaker : public framework::OpProtoAndCheckerMaker {
         .SetDefault(0.9f);
     AddAttr<float>("momentum", "(float, default 0.0) Constant value.")
         .SetDefault(0.0f);
+    AddAttr<bool>("centered", "(bool, default false) use centered rmsprop.")
+        .SetDefault(false);
     AddComment(R"DOC(
 Rmsprop Optimizer. 
 
@@ -103,6 +118,14 @@ MomentOut = momentum * Moment +
 ParamOut = Param -  MomentOut
 $$
 
+if centered is true:
+
+mean_grad = decay * mean_square{t-1} + (1-decay) * gradient
+mean_square = decay * mean_square{t-1} + (1-decay) * gradient ** 2
+mom = momentum * mom{t-1} + learning_rate * g_t /
+    sqrt(mean_square - mean_grad**2 + epsilon)
+param -= mom
+
 The original slides that proposed Rmsprop: Slide 29 of
 http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
 

paddle/fluid/operators/rmsprop_op.h

@@ -41,6 +41,7 @@ class RmspropOpKernel : public framework::OpKernel<T> {
     float epsilon = ctx.Attr<float>("epsilon");
     float rho = ctx.Attr<float>("decay");
     float momentum = ctx.Attr<float>("momentum");
+    bool centered = ctx.Attr<bool>("centered");
 
     auto p = EigenVector<T>::Flatten(*ctx.Input<Tensor>("Param"));
     auto ms = EigenVector<T>::Flatten(*ctx.Input<Tensor>("MeanSquare"));
@@ -53,12 +54,24 @@ class RmspropOpKernel : public framework::OpKernel<T> {
     auto ms_out = EigenVector<T>::Flatten(*mean_square_out);
     auto& place = *ctx.template device_context<DeviceContext>().eigen_device();
 
-    Eigen::DSizes<int, 1> grad_dsize(grad->numel());
+    Eigen::DSizes<int, 1> grad_dsize(static_cast<int>(grad->numel()));
 
     ms_out.device(place) = rho * ms + (1 - rho) * g * g;
+    if (centered) {
+      auto mg = EigenVector<T>::Flatten(*ctx.Input<Tensor>("MeanGrad"));
+      auto* mean_grad_out = ctx.Output<Tensor>("MeanGradOut");
+      mean_grad_out->mutable_data<T>(ctx.GetPlace());
+      auto mg_out = EigenVector<T>::Flatten(*mean_grad_out);
+
+      mg_out.device(place) = rho * mg + (1 - rho) * g;
+      mom_out.device(place) = momentum * mom +
+                              lr.broadcast(grad_dsize) * g /
+                                  (ms_out - mg_out.square() + epsilon).sqrt();
+    } else {
       mom_out.device(place) =
           momentum * mom +
           lr.broadcast(grad_dsize) * g / (ms_out + epsilon).sqrt();
+    }
     p_out.device(place) = p - mom_out;
   }
 };

python/paddle/fluid/optimizer.py

@@ -897,7 +897,20 @@ class RMSPropOptimizer(Optimizer):
 
         r(w, t) & = \\rho r(w, t-1) + (1 - \\rho)(\\nabla Q_{i}(w))^2
 
-        v(w, t) & = \\beta v(w, t-1) + \\frac{\\eta} {\\sqrt{v(w,t) +
+        v(w, t) & = \\beta v(w, t-1) + \\frac{\\eta} {\\sqrt{r(w,t) +
+            \\epsilon}} \\nabla Q_{i}(w)
+
+        w & = w - v(w, t)
+
+    if centered is True:
+
+    ..  math::
+
+        r(w, t) & = \\rho r(w, t-1) + (1 - \\rho)(\\nabla Q_{i}(w))^2
+
+        g(w, t) & = \\rho g(w, t-1) + (1 - \\rho)\\nabla Q_{i}(w)
+
+        v(w, t) & = \\beta v(w, t-1) + \\frac{\\eta} {\\sqrt{r(w,t) - (g(w, t))^2 +
             \\epsilon}} \\nabla Q_{i}(w)
 
         w & = w - v(w, t)
@@ -915,6 +928,10 @@ class RMSPropOptimizer(Optimizer):
             avoid division by zero, set 1e-6 by default.
         momentum(float): :math:`\\beta` in equation is the momentum term,
             set 0.0 by default.
+        centered(bool): If True, gradients are normalized by the estimated variance of
+            the gradient; if False, by the uncentered second moment. Setting this to
+            True may help with training, but is slightly more expensive in terms of
+            computation and memory. Defaults to False.
 
     Raises:
         ValueError: If learning_rate, rho, epsilon, momentum are None.
@@ -928,12 +945,14 @@ class RMSPropOptimizer(Optimizer):
 
     _momentum_acc_str = "momentum"
     _mean_square_acc_str = "mean_square"
+    _mean_grad_acc_str = "mean_grad"
 
     def __init__(self,
                  learning_rate,
                  rho=0.95,
                  epsilon=1.0e-6,
                  momentum=0.0,
+                 centered=False,
                  **kwargs):
         super(RMSPropOptimizer, self).__init__(
             learning_rate=learning_rate, **kwargs)
@@ -950,6 +969,7 @@ class RMSPropOptimizer(Optimizer):
         self._rho = rho
         self._epsilon = epsilon
         self._momentum = momentum
+        self._centered = centered
 
     def _create_accumulators(self, block, parameters):
         if not isinstance(block, framework.Block):
@@ -958,6 +978,7 @@ class RMSPropOptimizer(Optimizer):
         for p in parameters:
             self._add_accumulator(self._momentum_acc_str, p)
             self._add_accumulator(self._mean_square_acc_str, p)
+            self._add_accumulator(self._mean_grad_acc_str, p)
 
     def _append_optimize_op(self, block, param_and_grad):
         if not isinstance(block, framework.Block):
@@ -967,6 +988,8 @@ class RMSPropOptimizer(Optimizer):
                                              param_and_grad[0])
         mean_square_acc = self._get_accumulator(self._mean_square_acc_str,
                                                 param_and_grad[0])
+        mean_grad_acc = self._get_accumulator(self._mean_grad_acc_str,
+                                              param_and_grad[0])
         rmsprop_op = block.append_op(
             type=self.type,
             inputs={
@@ -974,17 +997,20 @@ class RMSPropOptimizer(Optimizer):
                 "Grad": param_and_grad[1],
                 "Moment": momentum_acc,
                 "MeanSquare": mean_square_acc,
+                "MeanGrad": mean_grad_acc,
                 "LearningRate": self._create_param_lr(param_and_grad),
             },
             outputs={
                 "ParamOut": param_and_grad[0],
                 "MomentOut": momentum_acc,
-                "MeanSquareOut": mean_square_acc
+                "MeanSquareOut": mean_square_acc,
+                "MeanGradOut": mean_grad_acc
             },
             attrs={
                 "epsilon": self._epsilon,
                 "decay": self._rho,
-                "momentum": self._momentum
+                "momentum": self._momentum,
+                "centered": self._centered
             })
 
         return rmsprop_op

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

@@ -291,7 +291,7 @@ class OpTest(unittest.TestCase):
                             return_numpy=False)
         return outs, fetch_list
 
-    def check_output_with_place(self, place, atol):
+    def check_output_with_place(self, place, atol, equal_nan=False):
         outs, fetch_list = self._calc_output(place)
         for out_name, out_dup in Operator.get_op_outputs(self.op_type):
             if out_name not in self.outputs:
@@ -321,7 +321,7 @@ class OpTest(unittest.TestCase):
                         if isinstance(expect, tuple) else expect
                     self.assertTrue(
                         np.allclose(
-                            actual_t, expect_t, atol=atol),
+                            actual_t, expect_t, atol=atol, equal_nan=equal_nan),
                         "Output (" + sub_out_name + ") has diff at " +
                         str(place))
                     if isinstance(expect, tuple):
@@ -337,7 +337,7 @@ class OpTest(unittest.TestCase):
                 expect_t = expect[0] if isinstance(expect, tuple) else expect
                 self.assertTrue(
                     np.allclose(
-                        actual_t, expect_t, atol=atol),
+                        actual_t, expect_t, atol=atol, equal_nan=equal_nan),
                     "Output (" + out_name + ") has diff at " + str(place) +
                     "\nExpect " + str(expect_t) + "\n" + "But Got" +
                     str(actual_t))
@@ -360,10 +360,10 @@ class OpTest(unittest.TestCase):
             places.append(core.CUDAPlace(0))
         return places
 
-    def check_output(self, atol=1e-5):
+    def check_output(self, atol=1e-5, equal_nan=False):
         places = self._get_places()
         for place in places:
-            self.check_output_with_place(place, atol)
+            self.check_output_with_place(place, atol, equal_nan)
 
     def check_output_customized(self, checker):
         places = self._get_places()

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

@@ -15,90 +15,164 @@
 from __future__ import print_function
 
 import unittest
+
 import numpy as np
-from op_test import OpTest
-
-
-class TestRmspropOp1(OpTest):
-    ''' Test RMSProp with explicit inputs
-    '''
-
-    def setUp(self):
-        self.op_type = "rmsprop"
-
-        param = np.random.random((123, 321)).astype("float32")
-        mean_square = np.random.random((123, 321)).astype("float32")
-        learning_rate = np.array([0.01]).astype("float32")
-        grad = np.random.random((123, 321)).astype("float32")
-        moment = np.zeros((123, 321)).astype("float32")
-
-        epsilon = 1e-6
-        decay = 0.9
-        momentum = 0.0
-
-        self.inputs = {
-            'Param': param,
-            'MeanSquare': mean_square,
-            'LearningRate': learning_rate,
-            'Grad': grad,
-            'Moment': moment,
-        }
-
-        self.attrs = {'epsilon': epsilon, 'decay': decay, 'momentum': momentum}
-
-        ms_out = decay * mean_square + (1 - decay) * grad * grad
-        moment_out = momentum * moment + \
-            learning_rate * grad / np.sqrt(ms_out + epsilon)
-        param_out = param - moment_out
-
-        self.outputs = {
-            'ParamOut': param_out,
-            'MomentOut': moment_out,
-            'MeanSquareOut': ms_out
-        }
-
-    def test_check_output(self):
-        self.check_output()
-
-
-class TestRmspropOp2(OpTest):
-    '''Test RMSProp with default values for attributes
-    '''
-
-    def setUp(self):
-        self.op_type = "rmsprop"
-
-        param = np.random.random((123, 321)).astype("float32")
-        mean_square = np.random.random((123, 321)).astype("float32")
-        learning_rate = np.array([0.01]).astype("float32")
-        grad = np.random.random((123, 321)).astype("float32")
-        moment = np.zeros((123, 321)).astype("float32")
-
-        epsilon = 1.0e-10
-        decay = 0.9
-        momentum = 0.0
-
-        self.inputs = {
-            'Param': param,
-            'MeanSquare': mean_square,
-            'LearningRate': learning_rate,
-            'Grad': grad,
-            'Moment': moment,
-        }
-
-        ms_out = decay * mean_square + (1 - decay) * grad * grad
-        moment_out = momentum * moment + \
-            learning_rate * grad / np.sqrt(ms_out + epsilon)
-        param_out = param - moment_out
-
-        self.outputs = {
-            'ParamOut': param_out,
-            'MomentOut': moment_out,
-            'MeanSquareOut': ms_out
-        }
-
-    def test_check_output(self):
-        self.check_output()
+import paddle.fluid.core as core
+from paddle.fluid.op import Operator
+
+
+class TestBase(unittest.TestCase):
+    def setup(self, centered, epsilon=1e-6):
+        np.random.seed(5)  # fix seed
+
+        self.param_name = "param"
+        self.param = np.random.random((123, 321)).astype("float32")
+
+        self.mean_square_name = "mean_square"
+        self.mean_square = np.random.random((123, 321)).astype("float32")
+
+        self.mean_grad_name = "mean_grad"
+        self.mean_grad = np.random.random((123, 321)).astype("float32")
+
+        self.lr_name = "lr"
+        self.learning_rate = np.array([0.01]).astype("float32")
+
+        self.grad_name = "grad"
+        self.grad = np.random.random((123, 321)).astype("float32")
+
+        self.moment_name = "moment"
+        self.moment = np.zeros((123, 321)).astype("float32")
+
+        self.epsilon = epsilon
+        self.decay = 0.9
+        self.momentum = 0.0
+        self.centered = centered
+
+        self.ms_out = self.decay * self.mean_square + (1 - self.decay
+                                                       ) * self.grad * self.grad
+        if centered:
+            self.mg_out = self.decay * self.mean_grad + (1 - self.decay
+                                                         ) * self.grad
+            self.moment_out = self.momentum * self.moment + \
+                              self.learning_rate * self.grad / np.sqrt(self.ms_out - np.square(self.mg_out) + self.epsilon)
+        else:
+            self.moment_out = self.momentum * self.moment + \
+                              self.learning_rate * self.grad / np.sqrt(self.ms_out + self.epsilon)
+
+        self.param_out = self.param - self.moment_out
+
+    def check(self,
+              actual_t,
+              expect_t,
+              place,
+              out_name,
+              atol=1e-5,
+              equal_nan=False):
+        self.assertTrue(
+            np.allclose(
+                actual_t, expect_t, atol=atol, equal_nan=equal_nan),
+            "Output (" + out_name + ") has diff at " + str(place) + "\nExpect "
+            + str(expect_t) + "\n" + "But Got" + str(actual_t))
+
+
+class TestRmspropOp(TestBase):
+    def check_with_place(self, place, centered, epsilon):
+        self.setup(centered, epsilon)
+        scope = core.Scope()
+
+        # create and initialize Param Variable
+        param = scope.var(self.param_name).get_tensor()
+        param.set(self.param, place)
+
+        mean_square = scope.var(self.mean_square_name).get_tensor()
+        mean_square.set(self.mean_square, place)
+
+        lr = scope.var(self.lr_name).get_tensor()
+        lr.set(self.learning_rate, place)
+
+        grad = scope.var(self.grad_name).get_tensor()
+        grad.set(self.grad, place)
+
+        moment = scope.var(self.moment_name).get_tensor()
+        moment.set(self.moment, place)
+
+        # create and run sgd operator
+
+        if self.centered:
+            mean_grad = scope.var(self.mean_grad_name).get_tensor()
+            mean_grad.set(self.mean_grad, place)
+
+            rmsprop_op = Operator(
+                "rmsprop",
+                Param=self.param_name,
+                Grad=self.grad_name,
+                MeanSquare=self.mean_square_name,
+                MeanGrad=self.mean_grad_name,
+                Moment=self.moment_name,
+                LearningRate=self.lr_name,
+                ParamOut=self.param_name,
+                MeanSquareOut=self.mean_square_name,
+                MomentOut=self.moment_name,
+                MeanGradOut=self.mean_grad_name,
+                epsilon=self.epsilon,
+                decay=self.decay,
+                momentum=self.momentum,
+                centered=True)
+        else:
+            rmsprop_op = Operator(
+                "rmsprop",
+                Param=self.param_name,
+                Grad=self.grad_name,
+                MeanSquare=self.mean_square_name,
+                Moment=self.moment_name,
+                LearningRate=self.lr_name,
+                ParamOut=self.param_name,
+                MeanSquareOut=self.mean_square_name,
+                MomentOut=self.moment_name,
+                epsilon=self.epsilon,
+                decay=self.decay,
+                momentum=self.momentum,
+                centered=False)
+
+        rmsprop_op.run(scope, place)
+
+        atol = 1e-5
+        equal_nan = False
+
+        if self.centered:
+            atol = 1e-3
+            equal_nan = True
+
+        self.check(
+            np.array(mean_square), self.ms_out, place, self.mean_square_name)
+        self.check(
+            np.array(moment),
+            self.moment_out,
+            place,
+            self.moment_name,
+            atol=atol,
+            equal_nan=equal_nan)
+        self.check(
+            np.array(param),
+            self.param_out,
+            place,
+            self.param_name,
+            atol=atol,
+            equal_nan=equal_nan)
+
+        if self.centered:
+            self.check(
+                np.array(mean_grad), self.mg_out, place, self.mean_grad_name)
+
+    def test_rmsprop(self):
+        places = [core.CPUPlace()]
+        if core.is_compiled_with_cuda():
+            places.append(core.CUDAPlace(0))
+        for place in places:
+            self.check_with_place(place, False, 1e-6)
+            self.check_with_place(place, False, 1e-10)
+            self.check_with_place(place, True, 1e-6)
+            self.check_with_place(place, True, 1e-10)
 
 
 if __name__ == "__main__":