torch.optim
===================================

.. automodule:: torch.optim

How to use an optimizer
-----------------------

To use :mod:`torch.optim` you have to construct an optimizer object, that will hold
the current state and will update the parameters based on the computed gradients.

Constructing it
^^^^^^^^^^^^^^^

To construct an :class:`Optimizer` you have to give it an iterable containing the
parameters (all should be :class:`~torch.autograd.Variable` s) to optimize. Then,
you can specify optimizer-specific options such as the learning rate, weight decay, etc.

Example::

    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
    optimizer = optim.Adam([var1, var2], lr=0.0001)

Per-parameter options
^^^^^^^^^^^^^^^^^^^^^

:class:`Optimizer` s also support specifying per-parameter options. To do this, instead
of passing an iterable of :class:`~torch.autograd.Variable` s, pass in an iterable of
:class:`dict` s. Each of them will define a separate parameter group, and should contain
a ``params`` key, containing a list of parameters belonging to it. Other keys
should match the keyword arguments accepted by the optimizers, and will be used
as optimization options for this group.

.. note::

    You can still pass options as keyword arguments. They will be used as
    defaults, in the groups that didn't override them. This is useful when you
    only want to vary a single option, while keeping all others consistent
    between parameter groups.


For example, this is very useful when one wants to specify per-layer learning rates::

    optim.SGD([
                    {'params': model.base.parameters()},
                    {'params': model.classifier.parameters(), 'lr': 1e-3}
                ], lr=1e-2, momentum=0.9)

This means that ``model.base``'s parameters will use the default learning rate of ``1e-2``,
``model.classifier``'s parameters will use a learning rate of ``1e-3``, and a momentum of
``0.9`` will be used for all parameters.

Taking an optimization step
^^^^^^^^^^^^^^^^^^^^^^^^^^^

All optimizers implement a :func:`~Optimizer.step` method, that updates the
parameters. It can be used in two ways:

``optimizer.step()``
~~~~~~~~~~~~~~~~~~~~

This is a simplified version supported by most optimizers. The function can be
called once the gradients are computed using e.g.
:func:`~torch.autograd.Variable.backward`.

Example::

    for input, target in dataset:
        optimizer.zero_grad()
        output = model(input)
        loss = loss_fn(output, target)
        loss.backward()
        optimizer.step()

``optimizer.step(closure)``
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Some optimization algorithms such as Conjugate Gradient and LBFGS need to
reevaluate the function multiple times, so you have to pass in a closure that
allows them to recompute your model. The closure should clear the gradients,
compute the loss, and return it.

Example::

    for input, target in dataset:
        def closure():
            optimizer.zero_grad()
            output = model(input)
            loss = loss_fn(output, target)
            loss.backward()
            return loss
        optimizer.step(closure)

.. _optimizer-algorithms:

Base class
----------

.. autoclass:: Optimizer

.. autosummary::
    :toctree: generated
    :nosignatures:

    Optimizer.add_param_group
    Optimizer.load_state_dict
    Optimizer.state_dict
    Optimizer.step
    Optimizer.zero_grad

Algorithms
----------

.. autosummary::
    :toctree: generated
    :nosignatures:

    Adadelta
    Adagrad
    Adam
    AdamW
    SparseAdam
    Adamax
    ASGD
    LBFGS
    NAdam
    RAdam
    RMSprop
    Rprop
    SGD

How to adjust learning rate
---------------------------

:mod:`torch.optim.lr_scheduler` provides several methods to adjust the learning
rate based on the number of epochs. :class:`torch.optim.lr_scheduler.ReduceLROnPlateau`
allows dynamic learning rate reducing based on some validation measurements.

Learning rate scheduling should be applied after optimizer's update; e.g., you
should write your code this way:

Example::

    model = [Parameter(torch.randn(2, 2, requires_grad=True))]
    optimizer = SGD(model, 0.1)
    scheduler = ExponentialLR(optimizer, gamma=0.9)

    for epoch in range(20):
        for input, target in dataset:
            optimizer.zero_grad()
            output = model(input)
            loss = loss_fn(output, target)
            loss.backward()
            optimizer.step()
        scheduler.step()

Most learning rate schedulers can be called back-to-back (also referred to as
chaining schedulers). The result is that each scheduler is applied one after the
other on the learning rate obtained by the one preceding it.

Example::

    model = [Parameter(torch.randn(2, 2, requires_grad=True))]
    optimizer = SGD(model, 0.1)
    scheduler1 = ExponentialLR(optimizer, gamma=0.9)
    scheduler2 = MultiStepLR(optimizer, milestones=[30,80], gamma=0.1)

    for epoch in range(20):
        for input, target in dataset:
            optimizer.zero_grad()
            output = model(input)
            loss = loss_fn(output, target)
            loss.backward()
            optimizer.step()
        scheduler1.step()
        scheduler2.step()

In many places in the documentation, we will use the following template to refer to schedulers
algorithms.

    >>> scheduler = ...
    >>> for epoch in range(100):
    >>>     train(...)
    >>>     validate(...)
    >>>     scheduler.step()

.. warning::
  Prior to PyTorch 1.1.0, the learning rate scheduler was expected to be called before
  the optimizer's update; 1.1.0 changed this behavior in a BC-breaking way.  If you use
  the learning rate scheduler (calling ``scheduler.step()``) before the optimizer's update
  (calling ``optimizer.step()``), this will skip the first value of the learning rate schedule.
  If you are unable to reproduce results after upgrading to PyTorch 1.1.0, please check
  if you are calling ``scheduler.step()`` at the wrong time.


.. autosummary::
    :toctree: generated
    :nosignatures:

    lr_scheduler.LambdaLR
    lr_scheduler.MultiplicativeLR
    lr_scheduler.StepLR
    lr_scheduler.MultiStepLR
    lr_scheduler.ConstantLR
    lr_scheduler.LinearLR
    lr_scheduler.ExponentialLR
    lr_scheduler.PolynomialLR
    lr_scheduler.CosineAnnealingLR
    lr_scheduler.ChainedScheduler
    lr_scheduler.SequentialLR
    lr_scheduler.ReduceLROnPlateau
    lr_scheduler.CyclicLR
    lr_scheduler.OneCycleLR
    lr_scheduler.CosineAnnealingWarmRestarts

Stochastic Weight Averaging
---------------------------

:mod:`torch.optim.swa_utils` implements Stochastic Weight Averaging (SWA). In particular,
:class:`torch.optim.swa_utils.AveragedModel` class implements SWA models,
:class:`torch.optim.swa_utils.SWALR` implements the SWA learning rate scheduler and
:func:`torch.optim.swa_utils.update_bn` is a utility function used to update SWA batch
normalization statistics at the end of training.

SWA has been proposed in `Averaging Weights Leads to Wider Optima and Better Generalization`_.

.. _`Averaging Weights Leads to Wider Optima and Better Generalization`: https://arxiv.org/abs/1803.05407

Constructing averaged models
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

`AveragedModel` class serves to compute the weights of the SWA model. You can create an
averaged model by running:

>>> swa_model = AveragedModel(model)

Here the model ``model`` can be an arbitrary :class:`torch.nn.Module` object. ``swa_model``
will keep track of the running averages of the parameters of the ``model``. To update these
averages, you can use the :func:`update_parameters` function:

>>> swa_model.update_parameters(model)


SWA learning rate schedules
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Typically, in SWA the learning rate is set to a high constant value. :class:`SWALR` is a
learning rate scheduler that anneals the learning rate to a fixed value, and then keeps it
constant. For example, the following code creates a scheduler that linearly anneals the
learning rate from its initial value to 0.05 in 5 epochs within each parameter group:

>>> swa_scheduler = torch.optim.swa_utils.SWALR(optimizer, \
>>>         anneal_strategy="linear", anneal_epochs=5, swa_lr=0.05)

You can also use cosine annealing to a fixed value instead of linear annealing by setting
``anneal_strategy="cos"``.


Taking care of batch normalization
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

:func:`update_bn` is a utility function that allows to compute the batchnorm statistics for the SWA model
on a given dataloader ``loader`` at the end of training:

>>> torch.optim.swa_utils.update_bn(loader, swa_model)

:func:`update_bn` applies the ``swa_model`` to every element in the dataloader and computes the activation
statistics for each batch normalization layer in the model.

.. warning::
    :func:`update_bn` assumes that each batch in the dataloader ``loader`` is either a tensors or a list of
    tensors where the first element is the tensor that the network ``swa_model`` should be applied to.
    If your dataloader has a different structure, you can update the batch normalization statistics of the
    ``swa_model`` by doing a forward pass with the ``swa_model`` on each element of the dataset.


Custom averaging strategies
^^^^^^^^^^^^^^^^^^^^^^^^^^^

By default, :class:`torch.optim.swa_utils.AveragedModel` computes a running equal average of
the parameters that you provide, but you can also use custom averaging functions with the
``avg_fn`` parameter. In the following example ``ema_model`` computes an exponential moving average.

Example:

>>> ema_avg = lambda averaged_model_parameter, model_parameter, num_averaged:\
>>>         0.1 * averaged_model_parameter + 0.9 * model_parameter
>>> ema_model = torch.optim.swa_utils.AveragedModel(model, avg_fn=ema_avg)


Putting it all together
^^^^^^^^^^^^^^^^^^^^^^^

In the example below, ``swa_model`` is the SWA model that accumulates the averages of the weights.
We train the model for a total of 300 epochs and we switch to the SWA learning rate schedule
and start to collect SWA averages of the parameters at epoch 160:

>>> loader, optimizer, model, loss_fn = ...
>>> swa_model = torch.optim.swa_utils.AveragedModel(model)
>>> scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=300)
>>> swa_start = 160
>>> swa_scheduler = SWALR(optimizer, swa_lr=0.05)
>>>
>>> for epoch in range(300):
>>>       for input, target in loader:
>>>           optimizer.zero_grad()
>>>           loss_fn(model(input), target).backward()
>>>           optimizer.step()
>>>       if epoch > swa_start:
>>>           swa_model.update_parameters(model)
>>>           swa_scheduler.step()
>>>       else:
>>>           scheduler.step()
>>>
>>> # Update bn statistics for the swa_model at the end
>>> torch.optim.swa_utils.update_bn(loader, swa_model)
>>> # Use swa_model to make predictions on test data
>>> preds = swa_model(test_input)