Adaptation sampling

⚠️ Curated Limitations & Negative Results

• The weighted normal approximation is not established as calibrated for reused importance-weighted groups. In the equal-law case with finite ratios equal to one, both groups contain the same n quality values. Pair symmetry, including ties, makes U=n²/2 deterministically, whereas the displayed substituted variance is n²*(2*n+1)/12>0 for n>0. This bounded curator derivation refutes that expression as the actual variance in this paired case; it is not an author-issued erratum, a general error-rate calculation or a claim that every independent direct-sampling test is invalid.
• The thesis Appendix B gives half credit for equal values but displays no tie-adjusted variance. Integer weights as repeated observations explain the pair-count identity, not independence or valid variance. Adaptive choice of the hypothetical law, repeated comparisons and dependence between the reused groups require separate calibration. Empirical rho is not asserted to be a valid nominal significance level.
• The thesis and journal prose attach weights to unchanged quality values. The 2012 Algorithm 2 and 2014 Algorithm 4 instead write a set containing weight times rank, which must not silently be implemented as altered rank values. Their weighted-Mann-Whitney return value and rank/tail convention are not fully specified; the threshold branch is not certified as a literal implementation of the thesis’s directional normal comparisons. No repaired pseudocode or author-code behavior is claimed.
• Ratios need finite, positive sampling densities at reused observations and defined finite hypothetical densities. Representing hypothetical-law expectations also requires suitable proposal coverage and integrability; positivity only at observed points does not establish global support coverage or stable weights. Large distribution changes can create large as well as small ratios. A weighted finite batch need not reveal an improvement, and no automatic effective-sample-size or numerical safeguard is supplied.
• Direct mode spends fresh evaluations, while virtual mode reuses expensive quality observations and still needs hypothetical-density evaluation and comparison work. The optional interpolation using fresh samples is not required in every mode. No cost-free controller, general variance reduction, monotonic progress, convergence, universal noise robustness or benchmark advantage is asserted.
• The concrete NES rule concerns the global-scale learning rate and empirical defaults. It is distinct from xNES or SNES themselves, natural-gradient geometry, IGO flow, CMA-ES evolution-path control, Rprop gradient-sign updates and population-based model copying. The source’s increase/decrease analogy with Rprop does not establish an exact alias. Underlying full-covariance NES formulas are not re-certified by this controller description.
• Primary reading is limited to the declared methods and context: the thesis Section 2.4.4 and Appendix B, journal Section 3.2, and the 2012 Section 2.2/Algorithm 2 and defaults. The thesis body incorrectly points to Appendix A; the acquired 134-page author copy places the weighted test in Appendix B, PDF p. 121 / printed p. 97. Its cover dates and the separately inspected TUM repository metadata are retained without claiming byte equivalence to the repository PDF. The full thesis and empirical figures/tables were not audited.
• The 2012 proceedings paper notes that its use of the known target fitness for restart decisions was outside the BBOB guidelines; its numerical comparisons are not imported here. Its initial sandbox DNS download failure and separate successful retry remain in the research provenance. An author BibTeX fetch was unsupported by the web tool. No author implementation, benchmark, statistical test or calculator was executed for this controller assessment.