diff --git a/_doc/sphinxdoc/source/api/training.rst b/_doc/sphinxdoc/source/api/training.rst
index b5e33d8c..698032b4 100644
--- a/_doc/sphinxdoc/source/api/training.rst
+++ b/_doc/sphinxdoc/source/api/training.rst
@@ -11,6 +11,12 @@ BaseEstimator
 .. autosignature:: onnxcustom.training.optimizers.BaseEstimator
     :members:
 
+LearingRate
++++++++++++
+
+.. autosignature:: onnxcustom.training.sgd_learning_rate.LearningRateSGDRegressor
+    :members:
+
 OrtGradientOptimizer
 ++++++++++++++++++++
 
diff --git a/_doc/sphinxdoc/source/onnxmd/index.rst b/_doc/sphinxdoc/source/onnxmd/index.rst
index d0434296..19ec9cef 100644
--- a/_doc/sphinxdoc/source/onnxmd/index.rst
+++ b/_doc/sphinxdoc/source/onnxmd/index.rst
@@ -8,6 +8,6 @@ The documentation can be searched.
 
 .. toctree::
     :maxdepth: 1
-    
+
     index_onnx
     index_onnxruntime
diff --git a/_unittests/ut_training/test_optimizers.py b/_unittests/ut_training/test_optimizers.py
index fb0e49f9..967149b7 100644
--- a/_unittests/ut_training/test_optimizers.py
+++ b/_unittests/ut_training/test_optimizers.py
@@ -13,6 +13,7 @@
 from sklearn.linear_model import LinearRegression
 from mlprodict.onnx_conv import to_onnx
 from onnxcustom import __max_supported_opset__ as opset
+from onnxcustom.training.sgd_learning_rate import LearningRateSGDRegressor
 try:
     from onnxruntime import TrainingSession
 except ImportError:
@@ -136,7 +137,8 @@ def test_ort_gradient_optimizers_optimal_use_numpy(self):
         onx_loss = add_loss_output(onx)
         inits = ['intercept', 'coef']
         train_session = OrtGradientOptimizer(
-            onx_loss, inits, learning_rate='optimal', max_iter=10)
+            onx_loss, inits, max_iter=10,
+            learning_rate=LearningRateSGDRegressor(learning_rate='optimal'))
         self.assertRaise(lambda: train_session.get_state(), AttributeError)
         train_session.fit(X, y, use_numpy=True)
         state_tensors = train_session.get_state()
@@ -164,7 +166,8 @@ def test_ort_gradient_optimizers_optimal_use_ort(self):
         onx_loss = add_loss_output(onx)
         inits = ['intercept', 'coef']
         train_session = OrtGradientOptimizer(
-            onx_loss, inits, learning_rate='optimal', max_iter=10)
+            onx_loss, inits, max_iter=10,
+            learning_rate=LearningRateSGDRegressor(learning_rate='optimal'))
         self.assertRaise(lambda: train_session.get_state(), AttributeError)
         train_session.fit(X, y, use_numpy=False)
         state_tensors = train_session.get_state()
diff --git a/onnxcustom/training/optimizers.py b/onnxcustom/training/optimizers.py
index e3ea35c9..d9c56f26 100644
--- a/onnxcustom/training/optimizers.py
+++ b/onnxcustom/training/optimizers.py
@@ -8,14 +8,21 @@
     OrtValue, TrainingParameters,
     SessionOptions, TrainingSession)
 from .data_loader import OrtDataLoader
+from .sgd_learning_rate import BaseLearningRate
 
 
 class BaseEstimator:
     """
     Base class for optimizers.
     Implements common methods such `__repr__`.
+
+    :param learning_rate: learning rate class,
+        see module :mod:`onnxcustom.training.sgd_learning_rate`
     """
 
+    def __init__(self, learning_rate):
+        self.learning_rate = BaseLearningRate.select(learning_rate)
+
     @classmethod
     def _get_param_names(cls):
         init = getattr(cls.__init__, "deprecated_original", cls.__init__)
@@ -32,7 +39,9 @@ def __repr__(self):
             if k not in self.__dict__:
                 continue  # pragma: no cover
             ov = getattr(self, k)
-            if v is not inspect._empty or ov != v:
+            if isinstance(ov, BaseLearningRate):
+                ps.append("%s=%s" % (k, repr(ov)))
+            elif v is not inspect._empty or ov != v:
                 ro = repr(ov)
                 if len(ro) > 50 or "\n" in ro:
                     ro = ro[:10].replace("\n", " ") + "..."
@@ -53,24 +62,16 @@ class OrtGradientOptimizer(BaseEstimator):
     :param max_iter: number of training iterations
     :param training_optimizer_name: optimizing algorithm
     :param batch_size: batch size (see class *DataLoader*)
-    :param eta0: initial learning rate for the `'constant'`, `'invscaling'`
-        or `'adaptive'` schedules.
-    :param alpha: constant that multiplies the regularization term,
-        the higher the value, the stronger the regularization.
-        Also used to compute the learning rate when set to *learning_rate*
-        is set to `'optimal'`.
-    :param power_t: exponent for inverse scaling learning rate
-    :param learning_rate: learning rate schedule:
-        * `'constant'`: `eta = eta0`
-        * `'optimal'`: `eta = 1.0 / (alpha * (t + t0))` where *t0* is chosen
-            by a heuristic proposed by Leon Bottou.
-        * `'invscaling'`: `eta = eta0 / pow(t, power_t)`
+    :param learning_rate: a name or a learning rate instance,
+        see module :mod:`onnxcustom.training.sgd_learning_rate`
     :param device: `'cpu'` or `'cuda'`
     :param device_idx: device index
     :param warm_start: when set to True, reuse the solution of the previous
         call to fit as initialization, otherwise, just erase the previous
         solution.
     :param verbose: use :epkg:`tqdm` to display the training progress
+    :param validation_every: validation with a test set every
+        *validation_every* iterations
 
     Once initialized, the class creates the attribute
     `session_` which holds an instance of `onnxruntime.TrainingSession`.
@@ -96,11 +97,12 @@ class OrtGradientOptimizer(BaseEstimator):
 
     def __init__(self, model_onnx, weights_to_train, loss_output_name='loss',
                  max_iter=100, training_optimizer_name='SGDOptimizer',
-                 batch_size=10, eta0=0.01, alpha=0.0001, power_t=0.25,
-                 learning_rate='invscaling', device='cpu', device_idx=0,
+                 batch_size=10, learning_rate='SGDRegressor',
+                 device='cpu', device_idx=0,
                  warm_start=False, verbose=0, validation_every=0.1):
         # See https://scikit-learn.org/stable/modules/generated/
         # sklearn.linear_model.SGDRegressor.html
+        BaseEstimator.__init__(self, learning_rate)
         self.model_onnx = model_onnx
         self.batch_size = batch_size
         self.weights_to_train = weights_to_train
@@ -108,10 +110,6 @@ def __init__(self, model_onnx, weights_to_train, loss_output_name='loss',
         self.training_optimizer_name = training_optimizer_name
         self.verbose = verbose
         self.max_iter = max_iter
-        self.eta0 = eta0
-        self.alpha = alpha
-        self.power_t = power_t
-        self.learning_rate = learning_rate.lower()
         self.device = device
         self.device_idx = device_idx
         self.warm_start = warm_start
@@ -133,23 +131,6 @@ def __setstate__(self, state):
             setattr(self, att, v)
         return self
 
-    def _init_learning_rate(self):
-        self.eta0_ = self.eta0
-        if self.learning_rate == "optimal":
-            typw = numpy.sqrt(1.0 / numpy.sqrt(self.alpha))
-            self.eta0_ = typw / max(1.0, (1 + typw) * 2)
-            self.optimal_init_ = 1.0 / (self.eta0_ * self.alpha)
-        else:
-            self.eta0_ = self.eta0
-        return self.eta0_
-
-    def _update_learning_rate(self, t, eta):
-        if self.learning_rate == "optimal":
-            eta = 1.0 / (self.alpha * (self.optimal_init_ + t))
-        elif self.learning_rate == "invscaling":
-            eta = self.eta0_ / numpy.power(t + 1, self.power_t)
-        return eta
-
     def fit(self, X, y, X_val=None, y_val=None, use_numpy=False):
         """
         Trains the model.
@@ -186,7 +167,7 @@ def fit(self, X, y, X_val=None, y_val=None, use_numpy=False):
                 X_val, y_val, batch_size=X_val.shape[0], device=self.device)
         else:
             data_loader_val = None
-        lr = self._init_learning_rate()
+        self.learning_rate.init_learning_rate()
         self.input_names_ = [i.name for i in self.train_session_.get_inputs()]
         self.output_names_ = [
             o.name for o in self.train_session_.get_outputs()]
@@ -202,13 +183,14 @@ def fit(self, X, y, X_val=None, y_val=None, use_numpy=False):
 
         train_losses = []
         val_losses = []
+        lr = self.learning_rate.value
         for it in loop:
             bind_lr = OrtValue.ortvalue_from_numpy(
                 numpy.array([lr / self.batch_size], dtype=numpy.float32),
                 self.device, self.device_idx)
             loss = self._iteration(data_loader, bind_lr,
                                    bind, use_numpy=use_numpy)
-            lr = self._update_learning_rate(it, lr)
+            lr = self.learning_rate.update_learning_rate(it).value
             if self.verbose > 1:  # pragma: no cover
                 loop.set_description(
                     "loss=%1.3g lr=%1.3g" % (  # pylint: disable=E1101,E1307
diff --git a/onnxcustom/training/sgd_learning_rate.py b/onnxcustom/training/sgd_learning_rate.py
new file mode 100644
index 00000000..5a565ff5
--- /dev/null
+++ b/onnxcustom/training/sgd_learning_rate.py
@@ -0,0 +1,153 @@
+"""
+@file
+@brief Helper for :epkg:`onnxruntime-training`.
+"""
+import inspect
+import numpy
+
+
+class BaseLearningRate:
+    """
+    Class handling the learning rate update after every
+    iteration of a gradient.
+    """
+
+    def __init__(self):
+        pass
+
+    def init_learning_rate(self):
+        """
+        Initializes the learning rate at the beginning of the training.
+        :return: self
+        """
+        raise NotImplementedError(
+            "This method must be overwritten.")
+
+    def update_learning_rate(self, t):
+        """
+        Updates the learning rate at the end of an iteration.
+        :param t: iteration number
+        :return: self
+        """
+        raise NotImplementedError(
+            "This method must be overwritten.")
+
+    @property
+    def value(self):
+        "Returns the current learning rate."
+        raise NotImplementedError(
+            "This method must be overwritten.")
+
+    @staticmethod
+    def select(class_name, **kwargs):
+        """
+        Returns an instance of a given initialized with
+        *kwargs*.
+        :param class_name: an instance of @see cl BaseLearningRate
+            or a string among the following class names (see below)
+        :return: instance of @see cl BaseLearningRate
+
+        Possible values for *class_name*:
+        * `'LearningRateSGDRegressor'`: see @see cl LearningRateSGDRegressor
+        """
+        if isinstance(class_name, BaseLearningRate):
+            return class_name
+        cls = {LearningRateSGDRegressor: ['SGDRegressor']}
+        for cl, aliases in cls.items():
+            if class_name == cl.__class__.__name__ or class_name in aliases:
+                return cl(**kwargs)
+        raise ValueError(
+            "Unexpected class name %r. It should be one of %r." % (
+                class_name, list(map(lambda c: c.__name__, cls))))
+
+    @classmethod
+    def _get_param_names(cls):
+        init = getattr(cls.__init__, "deprecated_original", cls.__init__)
+        init_signature = inspect.signature(init)
+        parameters = [
+            p for p in init_signature.parameters.values()
+            if p.name != "self" and p.kind != p.VAR_KEYWORD]
+        return [(p.name, p.default) for p in parameters]
+
+    def __repr__(self):
+        """
+        Usual
+        """
+        param = self._get_param_names()
+        ps = []
+        for k, v in param:
+            if k not in self.__dict__:
+                continue  # pragma: no cover
+            ov = getattr(self, k)
+            if v is not inspect._empty or ov != v:
+                ro = repr(ov)
+                ps.append("%s=%s" % (k, ro))
+        return "%s(%s)" % (self.__class__.__name__, ", ".join(ps))
+
+
+class LearningRateSGDRegressor(BaseLearningRate):
+    """
+    Implements the learning the same way as
+    :class:`sklearn.linear_model.SGDRegressor`.
+
+    :param eta0: initial learning rate for the `'constant'`, `'invscaling'`
+        or `'adaptive'` schedules.
+    :param alpha: constant that multiplies the regularization term,
+        the higher the value, the stronger the regularization.
+        Also used to compute the learning rate when set to *learning_rate*
+        is set to `'optimal'`.
+    :param power_t: exponent for inverse scaling learning rate
+    :param learning_rate: learning rate schedule:
+        * `'constant'`: `eta = eta0`
+        * `'optimal'`: `eta = 1.0 / (alpha * (t + t0))` where *t0* is chosen
+            by a heuristic proposed by Leon Bottou.
+        * `'invscaling'`: `eta = eta0 / pow(t, power_t)`
+
+    Created attributes:
+    * `eta0_`: initial eta0
+    * `optimal_init_`: use when `learning_rate=='optimal'`
+    * `value_`: value to be returned by property `value`
+    """
+
+    def __init__(self, eta0=0.01, alpha=0.0001, power_t=0.25,
+                 learning_rate='invscaling'):
+        BaseLearningRate.__init__(self)
+        self.eta0 = eta0
+        self.alpha = alpha
+        self.power_t = power_t
+        self.learning_rate = learning_rate.lower()
+        self.value_ = None
+
+    def init_learning_rate(self):
+        """
+        Updates the learning rate at the end of an iteration.
+        :return: self
+        """
+        self.eta0_ = self.eta0
+        if self.learning_rate == "optimal":
+            typw = numpy.sqrt(1.0 / numpy.sqrt(self.alpha))
+            self.eta0_ = typw / max(1.0, (1 + typw) * 2)
+            self.optimal_init_ = 1.0 / (self.eta0_ * self.alpha)
+        else:
+            self.eta0_ = self.eta0
+        self.value_ = self.eta0_
+        return self
+
+    def update_learning_rate(self, t):
+        """
+        Updates the learning rate at the end of an iteration.
+        :param t: iteration number
+        :return: self
+        """
+        eta = self.value_
+        if self.learning_rate == "optimal":
+            eta = 1.0 / (self.alpha * (self.optimal_init_ + t))
+        elif self.learning_rate == "invscaling":
+            eta = self.eta0_ / numpy.power(t + 1, self.power_t)
+        self.value_ = eta
+        return self
+
+    @property
+    def value(self):
+        "Returns the current learning rate."
+        return self.value_