.. _method-multilevel_blue-solution_mode-online_pilot-relaxation-factor_sequence:

"""""""""""""""
factor_sequence
"""""""""""""""


For under-relaxation of shared sample increments, apply a sequence of factors, one per iteration



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



**Specification**

- *Alias:* None

- *Arguments:* REALLIST


**Description**


When initial correlation / covariance approximations are inaccurate,
iterated sample updates can be overly aggressive, such that it becomes
advisable to only accept a portion of this suggested increment through
use of an under-relaxation factor.

In the ``factor_sequence`` option, a sequence of relaxation factors is
specified, one for each online iteration. Once the sequence is
exhausted, all subsequent online iterations will continue to employ
the final sequence value.

**Usage Tips**

While not required or enforced, it is often a good idea to end the
sequence with a value of 1, corresponding to retirement of the
relaxation process.

The one case where the relaxation factor is automatically advanced to
1 is the case where a ``max_iterations`` constraint will force early
termination of the iteration. This avoids polluting the final results
with an anticipated variance reduction that was not fully realized due
to increment throttling.

The need for under-relaxation is usually highest on the initial
iteration, corresponding to a smaller relaxation factor in the
sequence (e.g., initial factor of .5 below).  This need then decays as
the shared samples approach the optimal allocation and the covariances
approach their final values (e.g., subsequent factors of .75 and
1. below).




**Examples**



.. code-block::

    method,
	multilevel_blue
	  solution_mode  online_pilot
	    relaxation factor_sequence = .5 .75 1.
	  pilot_samples = 25
	  seed = 8674132
	  max_function_evaluations = 500