Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference

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.

Risk-aware Q-learning (RaQL) provides a model-free, two-timescale estimator for dynamic risk objectives, but its finite-budget behavior remains fragile: fixed inner-loop hyperparameters can produce unstable value estimates, persistent Bellman residuals, and inefficient sample reuse. This paper proposes an adaptive training controller for Conditional Value-at-Risk (CVaR) RaQL and evaluates it on a daily Bitcoin trading task. The controller preserves the original CVaR estimator and Bellman fixed point; instead, it redesigns the training procedure through six coordinated mechanisms: per-cell inner-step sizing, outer-rate-matched decay synchronization, a short early correction for the VaR-like inner variable, a coverage-first-then-greedy sample allocation rule, progressive suffix aggregation of mature inner estimates, and data-driven calibration of key scales from online-observable quantities. Across 20 random seeds and 856,000 inner-transition samples, the controller reduces the mean empirical CVaR Bellman residual by approximately 85% relative to the fixed-parameter baseline (MeanBEQ: 1.2202 to 0.1854; MeanBEV: 1.1624 to 0.0535) and maintains stability across CVaR levels, discount factors, and training budgets. On the chronological out-of-sample test set, the learned policy attains a Sharpe ratio of 0.9281 with a maximum drawdown of 6.46% after transaction costs. Although buy-and-hold yields a higher cumulative return (35.43% vs. 23.61%), the adaptive policy achieves far lower volatility (9.57% vs. 47.93%), drawdown, and CVaR loss. These results demonstrate that adaptive finite-budget training design, applied solely to the training procedure without altering the risk objective, can materially improve the reliability and risk-adjusted performance of risk-aware Q-learning in financial applications.

Large Language Models (LLMs) are increasingly deployed in settings where rare but severe harmful generations can have significant consequences. Existing Risk-Averse RLHF addresses this issue by optimizing Conditional Value-at-Risk (CVaR), but it trains policies for fixed risk levels and therefore cannot adjust the desired degree of risk aversion at inference time. In this paper, we propose risk-conditioned RLHF, a framework that trains a single policy that provides a continuous risk-control interface, enabling users to select different degrees of risk aversion without retraining or deploying multiple risk-specific models. Experiments across multiple benchmarks demonstrate that a single risk-conditioned policy can adapt to different risk levels at inference time, enabling more flexible and risk-aware LLM deployment.