.. _method-approximate_control_variate-convergence_tolerance:

"""""""""""""""""""""
convergence_tolerance
"""""""""""""""""""""


Stopping criterion based on relative error reduction



**Topics**


method_independent_controls


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* REAL

- *Default:* 1.e-4


**Description**


The ``convergence_tolerance`` specification provides a real value for
controlling the termination of iteration through satisfaction of a
specified accuracy at minimum total cost.

For multilevel and multifidelity sampling methods, it is a *relative
convergence tolerance* on the mean squared error (MSE), where the
MSE is typically comprised of known estimator variance (stochastic
error), neglecting unknown residual bias (deterministic error).

The reference estimator variance is then defined as follows:

- Multilevel approaches ( ``multilevel_sampling`` and ``multilevel_multifidelity_sampling``): tolerance relative to initial multilevel Monte Carlo (MLMC) error after pilot sample
- Control variate approaches ( ``multifidelity_sampling`` and ``approximate_control_variate``): relative to Monte Carlo (MC) error from pilot sample where these are all initial estimator variances fot the algorithm, recognizing that control variate approaches can extract no benefit from low-fidelity pilot samples prior to the definition of corresponding sample increments.

Permissible values are between 0 and 1, non-inclusive.
Default value is 1.e-4.