optim.ADMMBlock#

class bartorch.optim.ADMMBlock#

Bases: Module

One iteration of the alternating direction method of multipliers, BART’s admm.

For \(\min_x \tfrac12 \| A x - y \|^2 + \sum_j g_j(G_j x - b_j)\), a step solves the x-update \(\bigl(M (A^H A + \lambda) + \rho \sum_j G_j^H G_j\bigr) x = M A^H y + \rho \sum_j G_j^H (z_j - u_j + b_j)\) by conjugate gradients from the previous \(x\), then updates each term’s split \(z_j\) and scaled dual \(u_j\). The state’s done is the residual stopping test, and invokes counts the conjugate-gradient iterations spent, the quantity ADMM’s maxiter budgets.

Parameters:

priors (Regularizer or ImplicitPrior, or an iterable of them) – The terms \(g_j\), with any transform \(G_j\).
rho (float or sequence of float, default=0.5) – Penalty parameter \(\rho\). A sequence is a schedule, one value per iteration and the last repeated beyond its end; the scaled duals are rescaled at each change so the unscaled ones carry over (annealed plug-and-play, \(\rho_k = \lambda / \sigma_k^2\)).
alpha (float, default=1.6) – Over-relaxation parameter.
cg_maxiter (int, default=10) – Conjugate-gradient iterations per x-update.
cg_maxiter_first (int, default=None) – Conjugate-gradient iterations of the first x-update; cg_maxiter when omitted.
cclambda (float, default=0.0) – \(\lambda\), the weight of an identity added to the normal operator.
biases (sequence of tensor, default=None) – The \(b_j\), one per term, each of its term’s prox_shape().
dynamic_rho (bool, default=False) – Multiply \(\rho\) by tau when the primal residual exceeds mu times the dual, divide it in the opposite case.
dynamic_tau (bool, default=False) – Set tau from the residuals, \(\sqrt{r / s}\) or its inverse, clipped to tau_max.
relative_norm (bool, default=False) – Compare the residuals each relative to its scaling.
fast (bool, default=False) – Skip the residuals and the stopping test.
hogwild (bool, default=False) – Double \(\rho\) after iteration 1, 3, 7, 15, …
mu (float, default=3.0) – Residual ratio beyond which dynamic_rho rescales \(\rho\).
tau_max (float, default=20.0) – Upper bound of tau.
abstol (float, default=0.0) – Absolute tolerance of the residual stopping test.
reltol (float, default=0.0) – Relative tolerance of the residual stopping test.
precond (LinearOperator, default=None) – Left preconditioner \(M\) from A.ishape to itself, positive definite (lsqr2_create’s precond_op).

Raises:

ValueError – hogwild or fast with dynamic_rho; a rho schedule with dynamic_rho or hogwild; not one bias per term; at start(), biases with a term with auxiliary variables.

Notes

With dynamic_rho or hogwild the state carries \(\rho\). With a term that has auxiliary variables the state’s x is the image followed by those variables, and output() returns the image alone.

start()#

Initial state of a run.

Parameters: