Fully adaptive cross-entropy optimization

⚠️ Curated Limitations & Negative Results

• The dedicated top-K level on PDF p. 35 is S_(N-K+1), but Algorithm 4.1 refers back to Equation 20, whose ceil((1-rho)N) index becomes N-K at rho=K/N. With distinct scores and 1<=K<N, an inclusive threshold at that latter index selects K+1 occurrences; at K=N it gives index zero in one-based notation. Boundary ties add another selection ambiguity. This description retains the dedicated top-K convention and the discrepancy, without claiming to repair an author implementation.
• The flowchart advances the outer iteration and resets its sample size after fitting, whereas numbered Step 4 returns to Step 2 without an explicit new outer sample or iteration advance. Equation 55 compares d+1 indexed maxima although the prose calls them the last d iterations; the cap-history range has a similar inclusive-count convention. Earlier-history initialization and some sampling/recalculation details remain underspecified. The record is a source-scoped mechanism description, not a certified executable reconstruction.
• Finite stagnation or repeated sample-cap exhaustion can occur away from even a local optimum. Under a fixed proposal with improvement probability p in (0,1), an independent budget N_max misses every improving candidate with probability (1-p)^N_max>0; zero support on improvements is a further boundary. These elementary qualifications do not compute the failure probability of an entire adaptive run. Reliable, hard and high-probability improvement language must not be promoted to general guarantees, especially for noisy scores or finite-precision equality tests.
• The fixed elite count must be an integer compatible with N_min and N_max. Suggested proportional elite sizes need a rounding convention; an admissible likelihood maximizer, parameter support, tie ordering and numerical safeguards also require explicit choices. Although alpha is listed among FACE’s supplied parameters, Algorithm 4.1 does not specify a complete smoothing schedule. The separate Section 4.1 performance-weighted CE modification is not a mandatory FACE operation.
• This identity selects the named adaptive CE optimization controller. It does not replace generic CrossEntropyOptimization, the rare-event CE estimator or the full EDA family. Particular unweighted product-distribution fits can overlap with UMDA, and some smoothing steps can overlap with PBIL, without establishing whole-method equivalence. The source’s reduction to fixed-size CE requires matched selection and control conventions; it is not literal equivalence between the conflicting printed indices.
• The retained published 2005 tutorial is the defining evidence here, with Section 4.2 and its flowchart read directly. The earlier manuscript, cited proofs, applications outside the recorded reading scope and author software are not silently imported. Reported timing gains and parameter suggestions are empirical and problem-specific, not universal speed or convergence results. No author-code execution, optimizer run or benchmark reproduction underlies these claims. Historical owner 245 and the dated identity assessment do not assert absence beyond the inspected repository snapshot.