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fc0f7bd | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | Projections
===========
.. currentmodule:: optax.projections
Projections can be used to perform constrained optimization.
The Euclidean projection onto a set :math:`\mathcal{C}` is:
.. math::
\text{proj}_{\mathcal{C}}(u) :=
\underset{v}{\text{argmin}} ~ ||u - v||^2_2 \textrm{ subject to } v \in \mathcal{C}.
For instance, here is an example how we can project parameters to the non-negative orthant::
>>> import optax
>>> import jax
>>> import jax.numpy as jnp
>>> num_weights = 2
>>> xs = jnp.array([[-1.8, 2.2], [-2.0, 1.2]])
>>> ys = jnp.array([0.5, 0.8])
>>> optimizer = optax.adam(learning_rate=1e-3)
>>> params = {'w': jnp.zeros(num_weights)}
>>> opt_state = optimizer.init(params)
>>> loss = lambda params, x, y: jnp.mean((params['w'].dot(x) - y) ** 2)
>>> grads = jax.grad(loss)(params, xs, ys)
>>> updates, opt_state = optimizer.update(grads, opt_state)
>>> params = optax.apply_updates(params, updates)
>>> params = optax.projections.projection_non_negative(params)
Available projections
~~~~~~~~~~~~~~~~~~~~~
.. autosummary::
projection_box
projection_hypercube
projection_non_negative
projection_simplex
Projection onto a box
~~~~~~~~~~~~~~~~~~~~~
.. autofunction:: projection_box
Projection onto a hypercube
~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. autofunction:: projection_hypercube
Projection onto the non-negative orthant
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. autofunction:: projection_non_negative
Projection onto a simplex
~~~~~~~~~~~~~~~~~~~~~~~~~
.. autofunction:: projection_simplex
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