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name: path_covariance_adaptation description: Update CMA-ES cumulative step-size paths and covariance matrix from selected normalized steps.

CSA and Covariance Adaptation

Use this skill after a CMA-ES generation has produced selected normalized steps. It updates the sigma evolution path, global step-size, covariance evolution path, and covariance matrix.

Inputs

• Current p_sigma, p_c, sigma, covariance matrix, weighted step y_w, selected y vectors, selected z vectors, and strategy parameters.

Outputs

• Updated paths, sigma, covariance, eigenvalues, condition number, and booleans showing whether sigma and covariance changed.

Workflow

1. Update the isotropic path from selected z steps.
2. Compare its norm to the expected norm of a standard normal vector and update sigma on the log scale.
3. Update the covariance path from the weighted y step.
4. Apply rank-one and rank-mu covariance terms, symmetrize, and floor eigenvalues for numerical safety.

Validation

Run the included tests or validate_skill_tree.py --run-tests.

Limitations

The reduced recovery uses positive recombination weights; active negative weights are not required for the selected proxy target.