Path-level error control for greedy admission

Establish path-level error control for greedy admission of forecasters, together with corresponding selective-inference adjustments that account for the data-dependent incumbent, initial forecaster, and candidate family at successive selection steps.

Background

The paper develops a three-way admission rule with simultaneous heteroskedasticity- and autocorrelation-consistent bounds for a fixed incumbent pool and candidate family. Under a central limit theorem and consistent HAC estimation, those bounds provide asymptotic control conditional on the incumbent pool.

However, the proposed procedure applies greedy selection sequentially: the incumbent pool, starting forecaster, and candidate family at later steps depend on the observed data. The paper explicitly notes that the fixed-incumbent guarantee does not propagate along this adaptive path and that no selective-inference correction is imposed. A general theorem providing valid path-level error control, together with suitable selective-inference adjustments, is therefore left unresolved.

References

A theorem establishing path-level error control for greedy admission, together with selective-inference adjustments, remains for future work.

— Target alignment, dilution and forecast selection when cross-sectional forecasts share a common target  (2609.26303 - Soleimani, 22 Sep 2026) in Section Discussion, paragraph “Limitations”

Two open questions are central here: (i) power, namely the resolution limit $\Delta_{\min}(n,\hat\sigma)$ of a finite held-out set, which is what actually binds late-training improvement (our Proposition~D companion); and (ii) multi-candidate selection bias, since planners proposing 5--8 pipelines per round break the single-candidate assumption, and the Vovk--Wang merge must be invoked (made explicit in our gate).

— A Kinetic Theory of the Gated Self-Evolving LLM Agent  (2610.03243 - Wang, 2 Oct 2026) in Section 2, Related Work, subsection “Statistical gating”