PMDIteration

class deepinv.optim.optim_iterators.PMDIteration(bregman_potential=None, **kwargs)

Bases: OptimIterator

Iterator for Proximal Mirror Descent (PMD).

Class for a single iteration of the Proximal Mirror Descent (PMD) algorithm for minimizing \(f(x) + \lambda \regname(x)\).

For a given Bregman convex potential \(h\), the iteration is given by

\[\begin{split}\begin{equation*} \begin{aligned} u_{k} &= \nabla h^*(\nabla h(x_k) - \gamma \nabla f(x_k)) \\ x_{k+1} &= \operatorname{prox^h}_{\gamma \lambda \regname}(u_k) \end{aligned} \end{equation*}\end{split}\]

where \(\gamma\) is a stepsize that should satisfy \(\gamma \leq 2/L\) with \(L\) verifying \(Lh-f\) is convex. The potential \(h\) should be specified in the cur_params dictionary.