Dashboard
Signal #165875POSITIVE

Signed Sensitivity of Expected Hitting Time to Mutation Rate in the (1+1) EA: Per-State Sign Theorems and Verifiable Certificates for Non-Lumpable Families

100

arXiv:2609.12510v1 Announce Type: new Abstract: For the (1+1) evolutionary algorithm with standard bit mutation, we study the sensitivity of the expected hitting time $H_p=\mathbb{E}_x T$ to the mutation rate. We first point out an easily overlooked formalization pitfall: the improvement event is not monotone in the mutation mask, so the unsigned (total-influence) form of the Margulis-Russo formula does not apply; the correct object is the signed endpoint difference. Second, we give an exact three-dimensional separation: two fitness functions share the entire one-step success-rate curve, yet their expected hitting times are two different exact rational numbers; hence one-step success-rate quantities do not determine the expected hitting time. Building on the runtime derivative $H'_p=(I-Q_p)^{-1}Q'_p H_p$, we construct computable double-residual sign certificates, prove a per-initial-state sign theorem on OneMax (for every non-optimal initial state, $\partial_c H<0$ on $0<1$, where $p=c...

arXiv Neural/NEabout 9 hours ago
Read Full Article

Explore with AI-Powered Tools

View All Signals

Explore more AI intelligence

Want to discover more AI signals like this?

Explore Steek
Signed Sensitivity of Expected Hitting Time to Mutation Rate in the (1+1) EA: Per-State Sign Theorems and Verifiable Certificates for Non-Lumpable Families | Steek AI Signal | Steek