Online coordinate-structure estimation during CBO

Develop an online estimation procedure that jointly estimates the coordinate transformation associated with a linearly separable objective during the consensus-based optimization run, replacing the current two-stage procedure.

Background

The method estimates the vectors defining the linearly separable structure in a separate Hessian-sampling stage and subsequently uses those estimates in one of three consensus-based optimization modifications. This separation requires a preliminary estimation budget and prevents the optimization dynamics from adapting the coordinate system as new function evaluations are collected.

The paper explicitly leaves unresolved whether the estimation can be integrated into the consensus-based optimization process itself.

References

Second, instead of a two-stage method, can we perform the estimation step online during the CBO run?

— Consensus-based optimization for linearly separable functions  (2609.01317 - Fiedler et al., 1 Sep 2026) in Section 5, Conclusion

Our experiments demonstrate how powerful a well-chosen noise model can be for CBO schemes, however, unlike CMA-ES it is a two-stage procedure. A combined adaptation scheme for CBO is left for future work.

— Consensus-based optimization for linearly separable functions  (2609.01317 - Fiedler et al., 1 Sep 2026) in Section 3.2, Noise modification through change of variables