recursive_factor
For under-relaxation of shared sample increments, apply a recursive factor on each iteration that advances the relaxation factor toward 1
Specification
Alias: None
Arguments: REAL
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 recursive_factor option, an updated relaxation factor is
applied on each online iteration, where the value of the relaxation
factor \(r\) is determined from the recursive factor \(\gamma\)
by the following recursion:
where \(r^0 = 0\), or equivalently, \(r^1 = \gamma\). In words, the relaxation factor is advanced by applying the recursive factor to the remainder separating the previous relaxation factor from unity.
Usage Tips
Even through the under-relaxation factor approaches but never reaches the value of 1, the sample increments will generally decay toward an integer truncation of zero, terminating the online iteration.
As for other relaxation specification options, the one case where the
relaxation factor will be automatically advanced to 1 is the case
where a max_iterations constraint will force early termination of
the iteration. This advancement avoids polluting the final results
with an anticipated variance reduction that was not fully realized due
to increment throttling.
The example below corresponds to a sequence of relaxation factors equal to .5, .75, .875, .9375, .96875, .984375, etc. The larger the recursive factor specification, the faster the sequence decays toward 1.
Examples
method,
multilevel_blue
solution_mode online_pilot
relaxation recursive_factor = .5
pilot_samples = 25
seed = 8674132
max_function_evaluations = 500
