Optimal stopping policy slashes costs of AI self-refinement

Foundation models often improve outputs by looping through generate-feedback-refine cycles, using external verifiers and in-context learning. But every extra iteration burns compute, and knowing when to stop is a blind spot. In a new paper accepted at the 65th IEEE Conference on Decision and Control (CDC 2026), Kim Hammar, Tansu Alpcan, and Emil C. Lupu treat this as an optimal stopping problem: decide the number of refinement iterations based on expected improvement versus cost. The authors derive optimal stopping policies that can be efficiently computed using stochastic approximation, offering a principled alternative to heuristics or fixed iteration counts.

They evaluated their approach on a coding benchmark for foundation models, where the policies consistently outperformed prior stopping strategies in cost-efficiency. The key insight is that the value of each refinement step diminishes—sometimes sharply—so dynamically stopping early on easy tasks and pushing further on hard ones yields better overall economics. This work bridges control theory and AI deployment, giving practitioners a rigorous way to balance quality and compute spend. With self-refinement becoming standard in agentic and reasoning-heavy workflows, such policies could directly reduce inference costs at scale while preserving task performance.