ott.solvers.linear.sinkhorn.Sinkhorn.output_from_state

Sinkhorn.output_from_state(ot_prob, state)

Create an output from a loop state.

Note

When differentiating the regularized OT cost, and assuming Sinkhorn has run to convergence, Danskin’s (or the envelope) theorem [Bertsekas, 1971, Danskin, 1967] states that the resulting OT cost as a function of the inputs (geometry, a, b) behaves locally as if the dual optimal potentials were frozen and did not vary with those inputs.

Notice this is only valid, as when using implicit_differentiation mode, if the Sinkhorn algorithm outputs potentials that are near optimal. namely when the threshold value is set to a small tolerance.

The flag use_danskin controls whether that assumption is made. By default, that flag is set to the value of implicit_differentiation if not specified. If you wish to compute derivatives of order 2 and above, set use_danskin to False.

Parameters:

• ot_prob (LinearProblem) – the transport problem.

• state (SinkhornState) – a SinkhornState.

Return type:

SinkhornOutput

Returns:

A SinkhornOutput.