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

Many of our algorithms have various implementations optimized for performance,
readability and/or generality, so we attempt to default to the generally fastest
implementation for the current device if no particular implementation has been
specified by the user.

We have 3 major categories of implementations: for-loop, foreach (multi-tensor), and
fused. The most straightforward implementations are for-loops over the parameters with
big chunks of computation. For-looping is usually slower than our foreach
implementations, which combine parameters into a multi-tensor and run the big chunks
of computation all at once, thereby saving many sequential kernel calls. A few of our
optimizers have even faster fused implementations, which fuse the big chunks of
computation into one kernel. We can think of foreach implementations as fusing
horizontally and fused implementations as fusing vertically on top of that.

In general, the performance ordering of the 3 implementations is fused > foreach > for-loop.
So when applicable, we default to foreach over for-loop. Applicable means the foreach
implementation is available, the user has not specified any implementation-specific kwargs
(e.g., fused, foreach, differentiable), and all tensors are native and on CUDA. Note that
while fused should be even faster than foreach, the implementations are newer and we would
like to give them more bake-in time before flipping the switch everywhere. You are welcome
to try them out though!

Below is a table showing the available and default implementations of each algorithm:

.. csv-table::
    :header: "Algorithm", "Default", "Has foreach?", "Has fused?"
    :widths: 25, 25, 25, 25
    :delim: ;

    :class:`Adadelta`;foreach;yes;no
    :class:`Adagrad`;foreach;yes;no
    :class:`Adam`;foreach;yes;yes
    :class:`AdamW`;foreach;yes;yes
    :class:`SparseAdam`;for-loop;no;no
    :class:`Adamax`;foreach;yes;no
    :class:`ASGD`;foreach;yes;no
    :class:`LBFGS`;for-loop;no;no
    :class:`NAdam`;foreach;yes;no
    :class:`RAdam`;foreach;yes;no
    :class:`RMSprop`;foreach;yes;no
    :class:`Rprop`;foreach;yes;no
    :class:`SGD`;foreach;yes;no

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::

    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
    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::

    optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
    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

Weight Averaging (SWA and EMA)
------------------------------

:mod:`torch.optim.swa_utils` implements Stochastic Weight Averaging (SWA) and Exponential Moving Average (EMA). In particular,
the :class:`torch.optim.swa_utils.AveragedModel` class implements SWA and EMA 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/EMA batch
normalization statistics at the end of training.

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

EMA is a widely known technique to reduce the training time by reducing the number of weight updates needed. It is a variation of `Polyak averaging`_, but using exponential weights instead of equal weights across iterations.

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

.. _`Polyak averaging`: https://paperswithcode.com/method/polyak-averaging

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

The `AveragedModel` class serves to compute the weights of the SWA or EMA model.

You can create an SWA averaged model by running:

>>> averaged_model = AveragedModel(model)

EMA models are constructed by specifying the ``multi_avg_fn`` argument as follows:

>>> decay = 0.999
>>> averaged_model = AveragedModel(model, multi_avg_fn=get_ema_multi_avg_fn(decay))

Decay is a parameter between 0 and 1 that controls how fast the averaged parameters are decayed. If not provided to ``get_ema_multi_avg_fn``, the default is 0.999.

``get_ema_multi_avg_fn`` returns a function that applies the following EMA equation to the weights:

.. math:: W^\textrm{EMA}_{t+1} = \alpha W^\textrm{EMA}_{t} + (1 - \alpha) W^\textrm{model}_t

where alpha is the EMA decay.

Here the model ``model`` can be an arbitrary :class:`torch.nn.Module` object. ``averaged_model``
will keep track of the running averages of the parameters of the ``model``. To update these
averages, you should use the :func:`update_parameters` function after the `optimizer.step()`:

>>> averaged_model.update_parameters(model)

For SWA and EMA, this call is usually done right after the optimizer ``step()``. In the case of SWA, this is usually skipped for some numbers of steps at the beginning of the training.

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`` or ``multi_avg_fn`` parameters:

- ``avg_fn`` allows defining a function operating on each parameter tuple (averaged parameter, model parameter) and should return the new averaged parameter.
- ``multi_avg_fn`` allows defining more efficient operations acting on a tuple of parameter lists, (averaged parameter list, model parameter list), at the same time, for example using the ``torch._foreach*`` functions. This function must update the averaged parameters in-place.

In the following example ``ema_model`` computes an exponential moving average using the ``avg_fn`` parameter:

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


In the following example ``ema_model`` computes an exponential moving average using the more efficient ``multi_avg_fn`` parameter:

>>> ema_model = AveragedModel(model, multi_avg_fn=get_ema_multi_avg_fn(0.9))


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.




Putting it all together: SWA
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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)


Putting it all together: EMA
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In the example below, ``ema_model`` is the EMA model that accumulates the exponentially-decayed averages of the weights with a decay rate of 0.999.
We train the model for a total of 300 epochs and start to collect EMA averages immediately.

>>> loader, optimizer, model, loss_fn = ...
>>> ema_model = torch.optim.swa_utils.AveragedModel(model, \
>>>             multi_avg_fn=torch.optim.swa_utils.get_ema_multi_avg_fn(0.999))
>>>
>>> for epoch in range(300):
>>>       for input, target in loader:
>>>           optimizer.zero_grad()
>>>           loss_fn(model(input), target).backward()
>>>           optimizer.step()
>>>           ema_model.update_parameters(model)
>>>
>>> # Update bn statistics for the ema_model at the end
>>> torch.optim.swa_utils.update_bn(loader, ema_model)
>>> # Use ema_model to make predictions on test data
>>> preds = ema_model(test_input)
