# Differentiable convex optimization layers

## cvxpylayers

cvxpylayers is a Python library for constructing differentiable convex optimization layers in PyTorch and TensorFlow using CVXPY. A convex optimization layer solves a parametrized convex optimization problem in the forward pass to produce a solution. It computes the derivative of the solution with respect to the parameters in the backward pass.

This library accompanies our NeurIPS 2019 paper on differentiable convex optimization layers. For an informal introduction to convex optimization layers, see our blog post.

Our package uses CVXPY for specifying parametrized convex optimization problems.

## Installation

Use the package manager pip to install

cvxpylayers.

```
pip install cvxpylayers
```

Our package includes convex optimization layers for PyTorch and TensorFlow 2.0;

the layers are functionally equivalent. You will need to install

PyTorch or TensorFlow

separately, which can be done by following the instructions on their websites.

cvxpylayers has the following dependencies:

- Python 3
- NumPy
- CVXPY >= 1.1.a1
- TensorFlow >= 2.0 or PyTorch >= 1.0
- diffcp >= 1.0.13

## Usage

Below are usage examples of our PyTorch and TensorFlow layers. Note that

the parametrized convex optimization problems must be constructed in CVXPY,

using DPP.

### PyTorch

```
import cvxpy as cp
import torch
from cvxpylayers.torch import CvxpyLayer
n, m = 2, 3
x = cp.Variable(n)
A = cp.Parameter((m, n))
b = cp.Parameter(m)
constraints = [x >= 0]
objective = cp.Minimize(0.5 * cp.pnorm(A @ x - b, p=1))
problem = cp.Problem(objective, constraints)
assert problem.is_dpp()
cvxpylayer = CvxpyLayer(problem, parameters=[A, b], variables=[x])
A_tch = torch.randn(m, n, requires_grad=True)
b_tch = torch.randn(m, requires_grad=True)
# solve the problem
solution, = cvxpylayer(A_tch, b_tch)
# compute the gradient of the sum of the solution with respect to A, b
solution.sum().backward()
```

### TensorFlow 2.0

```
import cvxpy as cp
import tensorflow as tf
from cvxpylayers.tensorflow import CvxpyLayer
n, m = 2, 3
x = cp.Variable(n)
A = cp.Parameter((m, n))
b = cp.Parameter(m)
constraints = [x >= 0]
objective = cp.Minimize(0.5 * cp.pnorm(A @ x - b, p=1))
problem = cp.Problem(objective, constraints)
assert problem.is_dpp()
cvxpylayer = CvxpyLayer(problem, parameters=[A, b], variables=[x])
A_tf = tf.Variable(tf.random.normal((m, n)))
b_tf = tf.Variable(tf.random.normal((m,)))
with tf.GradientTape() as tape:
# solve the problem, setting the values of A, b to A_tf, b_tf
solution, = cvxpylayer(A_tf, b_tf)
summed_solution = tf.math.reduce_sum(solution)
# compute the gradient of the summed solution with respect to A, b
gradA, gradb = tape.gradient(summed_solution, [A_tf, b_tf])
```

## Examples

Our examples subdirectory contains simple applications of convex optimization

layers in IPython notebooks.

## Contributing

Pull requests are welcome. For major changes, please open an issue first to

discuss what you would like to change.

Please make sure to update tests as appropriate.

Please lint the code with `flake8`

.

```
pip install flake8 # if not already installed
flake8
```

## Running tests

cvxpylayers uses the `pytest`

framework for running tests.

To install `pytest`

, run:

```
pip install pytest
```

### PyTorch

To run the tests for `torch`

, in the main directory of this repository, run:

```
pytest cvxpylayers/torch
```

### TensorFlow

To run the tests for `tensorflow`

, in the main directory of this repository, run:

```
pytest cvxpylayers/tensorflow
```

## License

cvxpylayers carries an Apache 2.0 license.

## Citing

If you use cvxpylayers for research, please cite our accompanying NeurIPS paper:

```
@inproceedings{cvxpylayers2019,
author={Agrawal, A. and Amos, B. and Barratt, S. and Boyd, S. and Diamond, S. and Kolter, Z.},
title={Differentiable Convex Optimization Layers},
booktitle={Advances in Neural Information Processing Systems},
year={2019},
}
```