The PyCmaSampler

[fsmosca]

optuna.integration.PyCmaSampler
https://optuna.readthedocs.io/en/stable/reference/generated/optuna.integration.PyCmaSampler.html#optuna-integration-pycmasampler

OGPT (Optuna Game Parameter Tuner) so far support sigma0 parameter as option.

What is sigma0?

sigma0 – Initial standard deviation of CMA-ES. By default, sigma0 is set to min_range / 6,
where min_range denotes the minimum range of the distributions in the search space.
If distribution is categorical, min_range is len(choices) - 1.
Please refer to cma.CMAEvolutionStrategy for further details of sigma0.

Further in cma api:

sigma0
initial standard deviation. The problem variables should have been scaled, such that a
single standard deviation on all variables is useful and the optimum is expected to
lie within about x0 +- 3*sigma0. Often one wants to check for solutions close to the initial point.
This allows, for example, for an easier check of consistency of the objective function
and its interfacing with the optimizer. In this case, a much smaller sigma0 is advisable.

Be smart when using cmaes sampler

Imagine you are optimizing the value of a parameter with initial value of 75 and you are confident that the optimal value lies in [50, 100].

range or param_space = 100-50 = 50
default_sigma0 = range/6 = 50/6 = 8.3

The optimizer would then make more samples close to 75 - 3x8.3 and 75 + 3x8.3, or in the window [50, 100] to be tried by the objective function.

An example where we have 2 parameters to optimize

param_a={init=75, min=50, max=100}
param_b={init=10, min=0, max=20}

range_a = 100-50 = 50
range_b = 20-10 = 10

default_sigma0 = range_b/6 = 1.67
we use range_b because it is the minimum of the ranges as per Optuna framework.

Now cmaes would think that the best:

param_a lies within [75 - 3x1.67, 75 + 3x1.67] or [70, 80]  
param_b lies within [10 - 3x1.67, 10 + 3x1.67] or [5, 15]  

Here is the problem, what if the best param_a is actually 90, in this case more sampling are tried in the range [70, 80] thereby wasting time, it might get to 90 eventually as the sigma0 is just an initial sigma that cmaes would use.

To solve such issue OGPT now supports the sigma0 parameter overriding the default min_range/6.
We can try to use sigma0=6 for example.
--sampler name=cmaes sigma0=6

The best:

param_a lies within [75 - 3x6, 75 + 3x6] or [57, 93]  
param_b lies within [10 - 3x6, 10 + 3x6] or [-8, 28]  

In the future, OGPT will expose the param to the user where sigma0 can be controlled by the user per parameter.

At the moment avoid mixing param with very high and very low parameter range or else try to apply sigma0=value.

Note sigma0 should not exceed the minimum range. In our example it should not be more than 10.