SQwash: Distributionally Robust Learning in PyTorch with 1 Additional Line of Code

This package implements the superquantile a.k.a. Conditional Value at Risk (CVaR) for distributionally robust learning in PyTorch with GPU support. The superquantile achieves distributional robustness by averaging over some fraction of the worst losses on the minibatch in each step, as illustrated in this figure:

For details, see the complete documentation

Installation

Once you have PyTorch >=1.7, you can grab SQwash from pip:

pip install sqwash

The only dependency of SQwash is PyTorch, version 1.7 or higher. See here for install instructions.

Quick Start

As the name suggests, it requires only a one-line modification to the usual PyTorch training loops.

from sqwash import SuperquantileReducer
criterion = torch.nn.CrossEntropyLoss(reduction='none')  # Note: must set `reduction='none'`
reducer = SuperquantileReducer(superquantile_tail_fraction=0.5)  # define the reducer

# Training loop
for x, y in dataloader:
    y_hat = model(x)
    batch_losses = criterion(y_hat, y)  # shape: (batch_size,)
    loss = reducer(batch_losses)  # Additional line to use the superquantile reducer
    loss.backward()  # Proceed as usual from here
    ...

The package also gives a functional version of the reducers, similar to torch.nn.functional:

import torch.nn.functional as F
from sqwash import reduce_superquantile

for x, y in dataloader:
    y_hat = model(x)
    batch_losses = F.cross_entropy(y_hat, y, reduction='none')  # must set `reduction='none'`
    loss = reduce_superquantile(batch_losses, superquantile_tail_fraction=0.5)  # Additional line
    loss.backward()  # Proceed as usual from here
    ...

The package can also be used for distributionally robust learning over pre-specified groups of data. Simply obtain a tensor of losses for each element of the batch and use the reducers in this pacakge as follows:

loss_per_group = ...  # shape: (num_groups,)
reducer = reduce_superquantile(loss_per_group, superquantile_tail_fraction=0.6)

Functionality

This package provides 3 reducers, which take a tensor of losses on a minibatch and reduce them to a single value.

• MeanReducer: the usual reduction, which is equivalent to specifying reduction='mean' in your criterion.
• SuperquantileReducer: computes the superquantile/CVaR of the batch losses.
• SuperquantileSmoothReducer: computes a smooth counterpart of the superquantile/CVaR of the batch losses.

The reducers take in a batch of losses, so make sure you set the the flag reduction='none' in your criterion to get all the losses of your batch.

These reducers are also available via the functional interface, similar to torch.nn.functional:

• reduce_mean
• reduce_superquantile
• reduce_superquantile_smooth

Setting the parameters

Both the SuperquantileReducer and the SuperquantileSmoothReducer take a parameter called the superquantile_tail_fraction. This fraction of the worst losses on a batch are taken by the reducer. When superquantile_tail_fraction is taken to be 1, it is equivalent to taking the mean of the batch losses. When superquantile_tail_fraction is 0, it is equivalent to the maximum of the batch losses. For typical applications, we find that values between 0.3 and 0.7 work reasonably. If it is smaller than 0.3, you end up throwing away most of the information in your batch, while values close to 1 are effectively equivalent to the mean.

The SuperquantileSmoothReducer takes an additional argument smoothing_parameter, which controls how smooth the resulting function is. The smoothing parameter is internally scaled by the batch size due to theoretical considerations (see qp_solve.py for details). The extreme regimes for the smoothing parameter are:

• smoothing_parameter is close to 0: we recover exactly the superquantile (i.e., the output of SuperquantileReducer),
• smoothing_parameter is very large (tending to infinity): we recover the mean (the output of MeanReducer).

Implementation Details

The SuperquantileReducer requires computing a quantile of the batch losses, which has a computational cost of O(batch_size). One the other hand, the SuperquantileSmoothReducer requires solving a quadratic program. By using the special structure of this quadratic program, we can solve it algorithmically by just sorting a vector of size 2*batch_size. The algorithm also requires creating a matrix of shape (2*batch_size, batch_size), which can be done very efficiently on the GPU with a < 2% increase in running time for moderate batch sizes.

Authors

Krishna Pillutla
Yassine Laguel
Jérôme Malick
Zaid Harchaoui

License

SQwash is available under the GPLv3 license. Please see the license for details.

Citation

If you found this package useful, please cite the following paper

@inproceedings{DBLP:conf/ciss/LPMH21,
  author    = {Yassine Laguel and
               Krishna Pillutla and
               J{\'{e}}r{\^{o}}me Malick and
               Zaid Harchaoui},
  title     = {{A Superquantile Approach to Federated Learning with Heterogeneous
               Devices}},
  booktitle = {55th Annual Conference on Information Sciences and Systems, {CISS}
               2021, Baltimore, MD, USA, March 24-26, 2021},
  pages     = {1--6},
  publisher = {{IEEE}},
  year      = {2021},
}

Acknowledgements

We acknowledge support from NSF DMS 2023166, DMS 1839371, CCF 2019844, the CIFAR program "Learning in Machines and Brains", faculty research awards, and a JP Morgan PhD fellowship. This work has been partially supported by MIAI – Grenoble Alpes, (ANR-19-P3IA-0003).