Conformal Selective Acting: Anytime-Valid Risk Control for RLVR-Trained LLMs

A local specialist LLM, fine-tuned with reinforcement learning from verifiable rewards (RLVR) on operator-local data, is installed inside a single regulated organization under a per-deployment error budget $\alpha$. The operator needs a safety certificate that holds on *this* deployment's stream, simultaneously at every wall-clock round: no pooling across deployments, no waiting for a long-run average. Existing wrappers cannot deliver this on these adaptive, online-updated streams: offline conformal-risk methods require exchangeability; online-conformal methods bound only long-run averages; non-exchangeable extensions are marginally valid; and the closest anytime wrapper, A-RCPS, controls marginal rather than selective risk. Through a (test statistic, validity guarantee, deployment rule) framework we identify one empty cell forced by the deployment requirements (e-process per threshold, selective risk, anytime-pathwise validity, max-certified-threshold rule); **Conformal Selective Acting** (CSA) fills it as a per-round wrapper maintaining a Ville-type e-process per candidate score threshold on a Bonferroni grid, evaluated against the RLVR filtration. Under predictable updates and isotonic-calibrated monotone risk we prove (i) an anytime-pathwise selective-risk bound $R_T^{\mathrm{act}} \le \alpha + O(N_T^{-1/2})$, (ii) rate-optimal certification matching $\Theta(\bar\eta^{-2} \log(1/\delta))$, and (iii) a horizon-independent release-rate gap. Across eight specialist benchmarks (480 streams), sixteen adversarial distribution-shift cells (160 streams), and five live Expert-Iteration RLVR cells with online LoRA over four base models in three architecture families (10,300 rounds), CSA is the only method among ten directly compared that satisfies both pathwise validity and non-refusing deployment on every cell. We do not propose a new LLM, training algorithm, or policy class; CSA is the deployment-side complement, orthogonal to the model itself, for operators who cannot use a frontier API.