An agent design with goal reaching guarantees for enhancement of learning

Both the paper and the model prove that Algorithm 1 preserves the η-improbable goal-reaching property by showing: (i) only finitely many random “relax” actions occur (paper: Markov inequality on E[∑ξt]; model: union bound/Borel–Cantelli on ∑λt), (ii) only finitely many critic-feasible updates occur (paper: a monotone bound via Λ̂; model: a monotone bound via V̂ ≤ 0), and hence (iii) after a finite random time the trajectory follows π0 forever, yielding P[lim inf dG(St)=0] ≥ 1−η by π0’s assumption. The arguments align step-for-step with minor stylistic differences (Markov vs. BC1; Λ̂ vs. V̂ sign convention). See Theorem statement, Algorithm 1, and the proof skeleton in the paper (A.9–A.12 and the T̂/T̃ construction) .