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arxiv: 2605.20270 · v1 · pith:IKRKQWDInew · submitted 2026-05-18 · 💻 cs.LG · cs.AI· stat.ML

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

Hamed Khosravi , Xiaoming Huo This is my paper

Pith reviewed 2026-05-21 07:27 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords conformal predictionanytime validityselective risk controlRLVRLLM deploymente-processrisk bounds
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The pith

Conformal Selective Acting wraps RLVR-trained LLMs to deliver anytime-pathwise selective risk control at every round.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Conformal Selective Acting as a deployment wrapper for specialist LLMs fine-tuned with reinforcement learning from verifiable rewards. It addresses the need for per-deployment safety certificates in regulated settings without waiting for long-run averages or pooling data across deployments. The method maintains a Ville-type e-process for each threshold on a Bonferroni grid and evaluates it against the RLVR filtration. Under the assumptions of predictable updates and isotonic-calibrated monotone risk, it establishes bounds on selective risk that hold pathwise at every time step. This enables operators to certify and release decisions with controlled error at each round while maintaining high release rates.

Core claim

Conformal Selective Acting fills an empty cell in the (test statistic, validity guarantee, deployment rule) framework by using a per-round wrapper that maintains a Ville-type e-process per threshold on a Bonferroni grid evaluated against the RLVR filtration. It proves an anytime-pathwise selective-risk bound R_T^act ≤ α + O(N_T^{-1/2}), rate-optimal certification matching Θ(η̄^{-2} log(1/δ)), and a horizon-independent release-rate gap.

What carries the argument

The central mechanism is the Conformal Selective Acting wrapper that constructs and evaluates a Ville-type e-process per threshold on a Bonferroni grid to achieve selective risk control.

If this is right

  • The selective risk stays bounded by alpha plus a term that decreases like one over square root of rounds.
  • Certification reaches the optimal rate in terms of average step size.
  • The release rate gap stays independent of the time horizon.
  • It satisfies pathwise validity and non-refusing deployment on all tested benchmark and shift cells.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This wrapper could apply to other online updating models that satisfy predictable updates.
  • Regulated operators could adopt it to meet per-deployment error budgets while keeping release rates high.
  • Relaxing the monotone risk assumption might allow similar bounds for wider classes of risk functions.

Load-bearing premise

The central claim relies on the model updates being predictable and the risk function being isotonic-calibrated and monotone with respect to the threshold.

What would settle it

Observing a sequence of decisions where the empirical selective risk exceeds alpha plus a term that shrinks like one over square root of the number of rounds, despite satisfying predictable updates and monotone risk, would falsify the bound.

Figures

Figures reproduced from arXiv: 2605.20270 by Hamed Khosravi, Xiaoming Huo.

Figure 1
Figure 1. Figure 1: CSA as a plug-and-play deployment wrapper. Top (blue): the RLVR system is unchanged. Middle (green): CSA computes a surrogate score, updates one e-process per candidate threshold, certifies when the e-process crosses δ −1 q , and gates release via the largest certified threshold. Bottom (red): the anytime-valid guarantee holds simultaneously for all T under predictable updates and monotone risk, without ex… view at source ↗
Figure 2
Figure 2. Figure 2: Empirical validation of the RLVR structural layer on the live LoRA experiment (K=8 SFT rounds, 100 MATH problems each). (a) Estimated oracle frontier q ⋆ k ; red dashed lines mark drop rounds (DT =3). (b) Per-round slack ξk; nonzero only at drop rounds. (c) Cumulative slack BT = Pξk ≈ 0.40. Verifying the structural conditions in practice. All structural conditions are empirically falsifiable from the deplo… view at source ↗
Figure 3
Figure 3. Figure 3: Per-benchmark, per-α phase-budget view. Each panel is a benchmark; x-axis is the 6-α grid; each point is one (method, α) cell with Risk on the y-axis and AR encoded by point size. The y=α diagonal (dotted) is the pathwise-safety boundary; the shaded region above is the violation zone. CSA stays strictly at or below the diagonal on every (benchmark, α) cell. F.2.2 Prompts and answer extraction Each benchmar… view at source ↗
Figure 4
Figure 4. Figure 4: Risk vs. nominal budget α across all 8 benchmarks (10 replications per cell). Dotted diagonal y = α: pathwise-safety boundary. Shaded red: violation zone. CSA is the only method whose Risk stays at or below the diagonal on every benchmark at every α [PITH_FULL_IMAGE:figures/full_fig_p028_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Safe-Coverage radar, one mini-radar per method with at least one nonzero vertex. Vertex at benchmark b is Cov at α ⋆ b if the method is pathwise-safe, else 0 [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Live RLVR + online LoRA on Qwen2.5-Math-7B (MATH cell, T=4,000, 20 replications). Top: running selective risk Ract t for all ten methods; dashed: y=α; red: violation zone. Bottom: running action rate ARt restricted to methods whose final risk is at or below α. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
read the original abstract

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 $\alpha$. 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 $R_T^{\mathrm{act}}\le\alpha+O(N_T^{-1/2})$, (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 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Conformal Selective Acting (CSA), a per-round wrapper for RLVR-trained LLMs that maintains a Ville-type e-process per threshold on a Bonferroni grid, evaluated against the RLVR filtration, and deploys via a max-certified-threshold rule. Under the assumptions of predictable updates and isotonic-calibrated monotone risk, it proves (i) an anytime-pathwise selective-risk bound R_T^{act} ≤ α + O(N_T^{-1/2}), (ii) rate-optimal certification matching Θ(η̄^{-2} log(1/δ)), and (iii) a horizon-independent release-rate gap. Across 480 benchmark streams, 160 adversarial-shift cells, and 10,300 live Expert-Iteration rounds with online LoRA, CSA is the only method among ten comparators that satisfies pathwise validity and non-refusing deployment on every cell.

Significance. If the central claims hold, the work supplies a practical, theoretically grounded deployment complement for regulated operators who require per-stream safety certificates without pooling across deployments or waiting for long-run averages. It receives credit for identifying an empty cell in the (test statistic, validity guarantee, deployment rule) framework, for applying standard e-process and conformal ingredients to the online RLVR setting, and for the scale of the empirical evaluation (480 + 160 + 10,300 streams) that directly tests pathwise validity.

major comments (2)
  1. [§3.2] §3.2 (Assumption on isotonic-calibrated monotone risk): The proofs of the pathwise selective-risk bound and the supermartingale property of the per-threshold Ville e-process rest on this assumption when the risk is evaluated against the filtration induced by online LoRA updates. The manuscript invokes the assumption for the 10,300 live Expert-Iteration rounds and the 160 adversarial-shift cells, yet reports no diagnostic (e.g., empirical risk-vs-threshold plots or isotonic regression residuals) confirming that monotonicity and calibration hold under the actual RLVR updates. If violated on even a positive fraction of rounds, the claimed pathwise control does not follow.
  2. [Theorem 1 / §4.1] Theorem 1 / §4.1 (derivation of R_T^{act} ≤ α + O(N_T^{-1/2})): The rate term and the horizon-independent release-rate gap are derived under the predictable-updates assumption. No sensitivity analysis or empirical check of this assumption is provided for the live streams, leaving the applicability of the bound to the reported RLVR experiments conditional on an unverified modeling choice.
minor comments (2)
  1. [§3] The Bonferroni grid construction and the precise definition of the max-certified-threshold rule would benefit from an explicit algorithmic pseudocode block in §3.
  2. [Experiments section] Table captions for the 10,300-round experiments should list the four base models and three architecture families to allow direct replication of the reported coverage numbers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comments highlight important points regarding the empirical support for our modeling assumptions. We address each major comment below and will revise the manuscript accordingly to include additional diagnostics and analyses.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Assumption on isotonic-calibrated monotone risk): The proofs of the pathwise selective-risk bound and the supermartingale property of the per-threshold Ville e-process rest on this assumption when the risk is evaluated against the filtration induced by online LoRA updates. The manuscript invokes the assumption for the 10,300 live Expert-Iteration rounds and the 160 adversarial-shift cells, yet reports no diagnostic (e.g., empirical risk-vs-threshold plots or isotonic regression residuals) confirming that monotonicity and calibration hold under the actual RLVR updates. If violated on even a positive fraction of rounds, the claimed pathwise control does not follow.

    Authors: We agree that direct empirical verification of the isotonic-calibrated monotone risk assumption strengthens the applicability of the pathwise selective-risk bound to the reported RLVR experiments. In the revised manuscript we will add risk-versus-threshold plots together with isotonic regression residual diagnostics for the 10,300 live Expert-Iteration rounds and the 160 adversarial-shift cells. These plots will be generated from the same streams used in the original experiments and will confirm that monotonicity and calibration hold under the online LoRA updates, thereby supporting the supermartingale property and the claimed pathwise control. revision: yes

  2. Referee: [Theorem 1 / §4.1] Theorem 1 / §4.1 (derivation of R_T^{act} ≤ α + O(N_T^{-1/2})): The rate term and the horizon-independent release-rate gap are derived under the predictable-updates assumption. No sensitivity analysis or empirical check of this assumption is provided for the live streams, leaving the applicability of the bound to the reported RLVR experiments conditional on an unverified modeling choice.

    Authors: The predictable-updates assumption is a natural modeling choice for online LoRA updates, which are performed using data observed up to the preceding round. We acknowledge that the original submission did not contain a sensitivity analysis. In the revision we will add a sensitivity study that perturbs the degree of predictability (e.g., by introducing controlled lag in the update schedule) and reports the resulting effect on the O(N_T^{-1/2}) rate term and the horizon-independent release-rate gap. This analysis will demonstrate robustness while preserving the theoretical derivation under the stated assumption. revision: yes

Circularity Check

0 steps flagged

No circularity: bounds derived from e-process and conformal methods under explicit external assumptions

full rationale

The paper applies standard Ville-type e-processes and conformal risk control to the RLVR online-update setting. The central claims (anytime-pathwise selective-risk bound R_T^act ≤ α + O(N_T^{-1/2}), rate-optimal certification, horizon-independent release-rate gap) are proven under the stated assumptions of predictable updates and isotonic-calibrated monotone risk with respect to the RLVR filtration. These assumptions are introduced as conditions on the data-generating process rather than quantities defined or fitted inside the derivation; the selective-risk bound is not obtained by renaming a fitted parameter or by self-referential construction. No load-bearing self-citation, ansatz smuggling, or uniqueness theorem imported from the authors' prior work appears in the provided abstract or description. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions required for the filtration and the risk bound; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption predictable updates
    Invoked when the method is evaluated against the RLVR filtration for online streams.
  • domain assumption isotonic-calibrated monotone risk
    Required to obtain the selective-risk bound R_T^{act} ≤ α + O(N_T^{-1/2}).

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