[Feature description] A Noisifier for objective functions

[nikohansen]

Since Feb 2025, the module cocoex.noiser provides a small Python wrapper, the Noisifier, whos noisify method can be used to wrap any objective function, and in particular a coco function.

import cocoex

suite = cocoex.Suite('bbob', '', '')
noisifier = cocoex.noiser.Noisifier()
problem = suite[0]
noised_problem = noisifier.noisify(problem)
print(noisifier.parameters)

{'p_add': 0.2, 'p_subtract': 0.0, 'p_epsilon': 0, 'epsilon': 0.0001}

A more complete usage example can be found in the api documentation (also accessibly with help(noisifier) or help(cocoex.noiser.Noisifier)) or in the file example_experiment_parameter_sweep.py in this folder. When benchmarking, noisifier.noisify must be applied after the problem is observed. The handling by the postprocessing is described here.

The Noisifier is mainly meant to model outliers by adding pseudorandom noise to $f(x)$. The "noise" deterministically depends on $x$ and is modelled from

• adding a positive heavy tail number,
• adding a negative heavy tail number,
• adding a Gaussian number with variance $\varepsilon^2$

each with a certain "probability" ratio only. Formally, the "noise" can be written as

$$I(U_h < p_1) \times |H_1| - I(U_h > 1 - p_2) \times |H_2| + I(U_n < p_3) \times \varepsilon N$$

where

• $I$ is the indicator function,
• $U_h$ and $U_n$ are realizations from a uniform distribution in $[0,1]$,
• $H_i$ are (heavy tail) Cauchy random numbers with scale parameter $\pi/2$ and hence obey $P(|H_i| &gt; \alpha) \approx 1/\alpha$ when $\alpha\ge 5$,
• $N$ is a standard normally distributed number

The code accepts only values with $p_1 + p_2 \le 1$.

Parameters are

• $p_1=$p_add: probability of seeing a worse than the true value, $[0.01\dots 0.75]$ seems a reasonable range to explore
• $p_2=$p_subtract: probability of seeing a better than the true value, $[0 \dots0.5]$ seems a reasonable range to explore
• $p_3=$p_epsilon: probability of seeing additional Gaussian noise, $[0 \dots1]$ seems a reasonable range to explore
• $\varepsilon=$epsilon: scaling of the Gaussian noise, $[10^{-7} \dots 1]$ seems a reasonable range.

Update: since v2.7.2, the Noisifier adds a different noise realization on each objective.

Acknowledgements

This work was inspired by discussions during the Dagstuhl Seminar 24486.