optax.projections.projection_l1_sphere

optax.projections.projection_l1_sphere(tree: Any, scale: jax.typing.ArrayLike = 1) → Any

Projection onto the l1 sphere.

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

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

Parameters:

• tree – tree to project.

• scale – radius of the sphere.

Returns:

projected tree, with the same structure as tree.