Conformal Risk Certificates for Portfolio Optimization Under Uncertainty: A Gated Reinforcement-Learning Approach

Large language models (LLMs) can generate plausible-sounding ETF portfolios while silently violating basic KYC-style constraints on risk, fees, and diversification. This is especially problematic in agentic multi-turn advisory systems, where each draft recommendation can become an action unless guarded by an auditable enforcement layer. We study a model-agnostic, asset-agnostic post-generation guardrail pipeline: (i) enforce a strict JSON allocation schema, (ii) validate allocations against numeric caps, and (iii) when violations occur, deterministically project the output to the nearest feasible portfolio via a convex quadratic program (QCQP). We introduce BiasMix-Finance (Mini), a compact stress-test benchmark for constrained decision-making under biased LLM generations, with a 16-ETF universe, three investor profiles, and eight bias prompts. Across three models and three inference modes (direct, critique, self-consistency), first-pass generations violate at least one cap in 47.6-85.7% of test cases (67.2% pooled), but the convex projection layer reduces final feasibility violations to 0% while requiring only a small correction distance (test pooled median D=||w*-w0||_2=0.066), indicating that the guardrail typically preserves the intent of the original allocation. We report violation rates and correction distances with confidence intervals, and paired model comparisons with multiple-testing correction. To support reproducibility, we release the dataset, prompts, caps, and code in our public GitHub repository.

Large language models (LLMs) deployed for structured generation (NER, JSON extraction, QA, and classification) lack formal reliability guarantees, and standard heuristic abstention policies miss user-specified risk targets by 7.5--12.5%. We characterize when conformal risk control (CRC) can certify structured LLM outputs and when it provably cannot. First, we prove an impossibility result: when the base risk (μ> α), any distribution-free method must abstain on at least ((μ-α)/(1-α)) examples, yielding a closed-form feasibility test: one can check whether CRC will work before running it. Second, we analyze a certification hierarchy across Hoeffding, empirical Bernstein, and a betting-based e-CRC bound, with strict gains in low-variance/large-sample regimes: the Hoeffding-to-Bernstein step delivers the largest gain (+37% certified configurations), while e-CRC adds value when calibration data is scarce (10% certification at 20% data versus 0% for Hoeffding). Third, we validate adaptive conformal inference (ACI) under cross-dataset shift, reducing risk-target violations from 71% to 21%, with residual failures concentrated exactly where the impossibility bound predicts. Across six open-weight models (3B--72B parameters), eight datasets, four tasks, and six nonconformity scores, hard NER/QA/CLS configurations are uncertifiable at (α= 0.10); relaxing to (α= 0.30--0.40) unlocks practical certification (47% NER, 40% QA, 60% CLS). The framework gives a three-step deployment recipe: check feasibility, select the bound and score, then mitigate shift.

A local specialist LLM, fine-tuned with reinforcement learning from verifiable rewards (RLVR) on operator-local data, is installed in a regulated organization with per-deployment error budget $α$. The operator needs a safety certificate for this deployment's stream at every round: no pooling across deployments, no waiting for a long-run average. Existing wrappers cannot deliver this on 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. Using a (test statistic, validity guarantee, deployment rule) framework, we identify one empty cell forced by 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 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 $R_T^{\mathrm{act}}\leα+O(N_T^{-1/2})$, (ii) rate-optimal certification matching $Θ(\barη^{-2}\log(1/δ))$, 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 compared that satisfies 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, for operators who cannot use a frontier API.