optax.projections.projection_l1_ball

optax.projections.projection_l1_ball#

optax.projections.projection_l1_ball(tree: Any, scale: jax.typing.ArrayLike = 1) → Any[source]#

Projection onto the l1 ball.

This function solves the following constrained optimization problem, where x is the input tree.

\[\underset{y}{\text{argmin}} ~ \|x - y\|_2^2 \quad \textrm{subject to} \quad \|y\|_1 \le \text{scale}\]
Parameters:

  • tree – tree to project.

  • scale – radius of the ball.

Returns:

projected tree, with the same structure as tree.

Example

>>> import jax.numpy as jnp
>>> from optax import tree, projections
>>> data = {"w": jnp.array([2.5, 3.2]), "b": 0.5}
>>> print(tree.norm(data, ord=1))
6.2
>>> new_data = projections.projection_l1_ball(data)
>>> print(tree.norm(new_data, ord=1))
1.0000002

Added in version 0.2.4.