Anytime-Valid Inference

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4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Oct 1, 2026cs.LG

Evidence-Gated Research: Statistically Controlled Model Adoption in Adaptive Search

Adaptive model search is path dependent: once a challenger is adopted, it becomes the reference from which later candidates are generated. A statistically unsupported replacement can therefore alter hypotheses that have not yet been proposed. We introduce Evidence-Gated Research (EGR), a statistical adoption layer for moving-incumbent search. EGR freezes each challenger before decision evidence is revealed, builds anytime-valid evidence across a predeclared set of environments, routes evidence predictably toward unresolved components, composes a persistent candidate e-value, and passes that e-value to an online controller. Under explicit conditional-validity and predictability conditions, the resulting procedure controls false discovery rate for the declared all-environment adoption target even though earlier adoptions change later challengers. In a 5,000-trajectory closed-loop benchmark, development-only e-LOND attains persistent FDR 0.621, whereas no persistent false-adoption path is observed for the audited EGR variants in that finite run. In matched replay over 600 challenger--incumbent pairs, Stagewise EGR preserves fixed-anytime alternative crossing decisions while using 56.1% less decision evidence at the representative threshold. A three-environment public-data study and a 40,000-sample controlled neural benchmark reproduce the evidence-efficiency pattern. These results identify model replacement as a distinct statistical control point in adaptive model development.

Yifan Guo

Department of Applied Mathematics and Statistics Stony Brook University

FDR Control Anytime-Valid Inference E-Values

Sep 30, 2026cs.LG

Prequential E-Values for Selected-GP Near-Optimality Certificates

When optimizing an expensive black-box function sequentially, as in hyperparameter optimization, we may want to stop once the best evaluated value is certified within

\varepsilon

of the global optimum. Such a certificate needs two ingredients: a lower confidence bound for the selected value and an upper confidence envelope over the domain, typically supplied by a Gaussian process (GP). GP-UCB-style stopping rules are valid when the kernel and constants defining this envelope are fixed before the run, but the practical temptation is to tune the envelope from the same adaptive evaluations and then certify as if it had been fixed. We use prequential e-values to make this selection auditable: starting from a predeclared set of fully specified GP/RKHS envelopes, each candidate is tested by its own one-step-ahead e-process, contradicted candidates are deleted, and certification uses the largest upper bound among the survivors. With a valid selected-point lower bound and one declared candidate having valid latent coverage and noise calibration, the rule is anytime-valid. On a 512-seed noisy RBF stress sweep, it roughly halves false-certification risk at comparable power versus fit-then-certify. Relative to random fixed GP precommitment on smooth

d=3,4

objectives, each additional false certificate is accompanied by 3.0 and 13.5 additional correct certificates, respectively.

Ami Tavory, Noa Cohen

Meta Platforms

Black-Box Optimization Anytime-Valid Inference E-Values Sequential Hypothesis Testing

Sep 27, 2026cs.CR

The Price of Peeking: Anytime-Valid Leakage Detection on ML-KEM EM Traces

Side-channel evaluators routinely inspect leakage tests while acquisition is still running, and extend or stop the campaign based on what they see. Fixed-horizon screening such as the Welch

t

-test with threshold

|t|>4.5

gives no error guarantee for this monitored decision rule. We study anytime-valid leakage detection based on testing by betting: SKIT-type swap-pair e-processes whose false-alarm probability is controlled uniformly over time under an explicit conditional symmetry null. In matched comparisons that share the frozen witness, rows and payoff, first-crossing detection needed 1.68-2.00

\times

the traces of a fixed-horizon randomization test at 80% detection on synthetic streams, and 1.68-2.38

\times

on degraded recordings from an open ML-KEM electromagnetic dataset with the primary Ridge witness at

α=0.05

. With the same primary witness and level, on undegraded reference and pqm4 recordings the monitored procedure stopped early: its median stopping point was 62-72 and 146-316 evaluation traces, i.e. 2-8% of a conservative 4096-trace budget. Under exact designed nulls on the recorded backgrounds, repeated-look

|t|>4.5

screening over all 13000-20000 samples raised a false alarm in 2.7-12.9% of replicates, against 0.0-4.7% for terminal-only screening and no rejection by a sample-wise e-Bonferroni process, which in a prespecified follow-up detected natural-label associations in 4 of 4 backgrounds after 840-3288 traces. All recordings come from one device, and natural-label results are descriptive; we state the assumptions each claim requires.

Georgios Feretzakis, Alexandros Papaspyridis

Anytime-Valid Inference Sequential Hypothesis Testing

Sep 21, 2026cs.CL

Human-LLM Deliberation as Interactive Proof: Conditions for Verifiability Without Transparency

When an LLM supplies an argument that a user could not readily construct, how can the user decide whether to accept its claim? Inspired by interactive proofs, we model human-LLM deliberation as an interaction between a prover with unrestricted internal search and a resource-bounded human verifier. The verifier requests and checks supporting details without access to the LLM's internal state. Passed checks accumulate evidence toward an acceptance threshold. We prove anytime-valid soundness against adaptive provers: the probability of ever accepting a false claim is at most a chosen error level, provided the task supplies bounds on false passes and human checking errors that remain valid after every relevant history. A finite-horizon completeness bound additionally requires bounds on the adequacy of honest responses and sufficient diagnostic progress. Further checks can strengthen the evidence for acceptance, but each requires another adequate response and reliable human effort. Whether this tradeoff permits certification depends on the verifier's effort budget, cognitive load, expertise, and fatigue. We identify conditions under which the supplied bounds certify a specified sequence of local checks but not a specified global check under the same resource budgets.

Baotong Zhang, Dean Foster, João Sedoc

Stern School of Business New York University New York, NY, USA · Amazon New York, NY, USA

LLM Answer Verification Anytime-Valid Inference

Aug 31, 2026cs.LG

When the Martingale Never Stops Firing: Anytime-Valid Gating on Real Forecast Streams

Machine learning systems are increasingly corrected while they run, and the decision of when to intervene is increasingly delegated to statistical monitors. Anytime-valid inference promises evidence that can be acted on at any moment, exactly the guarantee this setting needs, and it is moving from theory into deployed monitoring. Conformal test martingales are the change-detection instrument, and Ville's inequality caps their false-alarm probability on exchangeable data. The guarantee is conditional. A deployment inherits it only if the stream it monitors behaves exchangeably. The premise is hardest to satisfy where these monitors are most useful, on dependent data and inside loops where the monitor modifies the learner whose scores it reads. It is also rarely measured. We measure it in a pre-specified case study, where such a monitor gates the online updates of a Kalman adapter correcting frozen time-series foundation models on five forecasting streams. On exchangeable synthetic streams, the same implementation fires in at most 1 of 60 runs. On the real streams, at alpha = 0.05, 135 of 135 clean-stream runs fired. The construction does not explain the firing; the failure comes from the deployed score stream itself. Repeated fires hold the gate's drift response active, and the gated filter amplifies the very transient it was designed to prevent. The component worth keeping makes no validity claim. Huber-style gating of the filter's own updates cuts isolated-spike degradation by an order of magnitude with no dataset specific tuning. Anytime-valid methods proposed for dependent data should therefore be accompanied by null-calibration controls and mechanism traces.

Weijia Han, Lisha Qu

University of Washington · Seattle, USA

Anytime-Valid Inference Conformal Prediction Change-Point Detection

Aug 8, 2026cs.CR

Private Anytime Selective-Risk Certification for Federated Retrieval-Augmented Generation: Guarantees and Empirical Limits

Selective-risk certificates promise that accepted outputs meet a declared error target. We develop Fed-SRC, a score-agnostic certificate for federated, differentially private, adaptively monitored retrieval-augmented generation. Clients release only Gaussian-perturbed score and loss histograms. Record-indexed and noise-variance-indexed martingales jointly bound target-risk contrast and accepted mass over all registered thresholds and rounds, permitting predictable recruitment, dropout, threshold selection, and optional stopping. A range-one total-variation term transfers the calibration mixture to a declared deployment mixture. The contribution is this private, federated, anytime combination, rather than the contrast statistic or acceptance floor individually. Empirically, no simultaneous-bound violation occurs in any evaluated cell, privacy level, or policy. Operational power depends on the score and population: the primary target r*=0.10 never certifies, and on RAGTruth the secondary target r*=0.20 never certifies either, whereas on HaluEval question answering it certifies in all 200 non-private trials, with held-out risk below the target. Naively privatized non-private certificates violate their bounds in 146 to 198 of 200 trials. As an exploratory comparison, we also evaluate a private betting-capital heuristic for which we do not establish e-process validity. This heuristic stops certifying at epsilon <= 4, where Fed-SRC still certifies. Certification nevertheless consumes roughly 30 times more stream events than unique calibration items.

Sanjeda Akter, Ibne Farabi Shihab, Anuj Sharma

Department of Computer Science, Iowa State University · Department of Civil, Construction & Environmental Engineering, Iowa State University

Anytime-Valid Inference RAG Evaluation

Aug 6, 2026cs.GT

AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Games

Deciding which of two agents is stronger means playing games until skill outweighs luck, and every game costs money, model inference, or expert time. Since the number of games needed is unknown, fixed-budget evaluations either keep paying after the result is settled or stop before the agents can be told apart, while naive optional stopping with an ordinary confidence interval invalidates the stated level. We make such an evaluation stop as soon as its evidence suffices, with the guarantee intact. The Action-Informed Value Assessment Tool (AIVAT) reduces variance in imperfect-information games through conditional mean-zero corrections, by a median

54\times

across 15 LLM agent configurations spanning 71,439 paired Heads-Up No-Limit Hold'em (HUNL) hands, but does not say when to stop. We combine AIVAT with continuously monitored Confidence Sequences (CSs) into anytime-valid AIVAT (AV-AIVAT), whose online value model learns only from past games so that no game scores its own correction. At the nominal 95% level and a target precision of

\pm1

Big Blind, raw outcomes need a median

74\times

as many hands as AIVAT-corrected outcomes to stop under the Asymptotic CS (AsympCS). Exact finite-sample certification uses the Empirical-Bernstein CS (EB-CS), which needs an independently justified bound on corrected payoffs. We establish such a bound structurally for Leduc hold'em and characterize a width floor set by the CS's bet cap and that bound, which governs how much of a variance gain becomes earlier stopping; the descriptive HUNL EB-CS runs show a median

1.37\times

stopping-time ratio. AV-AIVAT turns variance reduction into efficient, auditable early stopping while separating asymptotic screening from exact certification, so an evaluation can stop the moment its evidence suffices and hand a third party everything needed to recheck the verdict at that very stopping time.

Boning Li, Yu Chen, Longbo Huang

IIIS, Tsinghua University

Early Stopping Imperfect-Information Games Anytime-Valid Inference LLM Agent Evaluation

Jul 9, 2026cs.RO

On Exploring Input Resolution Scaling For Anytime LiDAR Object Detection

Making tradeoffs between execution latency and result utility (i.e., anytime computing) for adapting to dynamic operational requirements has been shown to enhance the performance of cyber-physical systems. In this work, we focus on enabling anytime computing for deep neural networks (DNNs) that process LiDAR point clouds for 3D object detection. We propose a novel method that enables multi-resolution inference for models that process point clouds as pillars or voxels, allowing the input to be dynamically scaled and processed at the resolution needed to meet timing requirements. Importantly, our memory-efficient approach requires the deployment of only a single DNN model, avoiding the need to deploy multiple models, each trained for a different input resolution. We also introduce a deadline-aware scheduler that selects the highest possible resolution for any given input by accurately predicting the execution time for all possible resolutions at runtime, which is challenging due to the irregularity of LiDAR point clouds. Experimental results on the nuScenes autonomous driving dataset demonstrate that our method significantly outperforms existing anytime computing approaches for LiDAR object detection. Finally, we deploy our approach in a simulated autonomous driving system, where it consistently enables collision-free navigation while avoiding unnecessary stalls caused by environmental complexity.

Ahmet Soyyigit, Shuochao Yao, Heechul Yun

The National Defense University, Istanbul, Turkiye · George Mason University, Fairfax, VA, USA · The University of Kansas, Lawrence, KS, USA

Adaptive Inference Lidar-Based 3D Object Detection Anytime-Valid Inference Memory-Efficient Inference 3D Object Detection

Jun 26, 2026cs.LG

Halt Fast! Early Stopping for Certified Robustness

Randomized Smoothing (RS) provides rigorous robustness guarantees for neural networks without architectural constraints, yet its adoption is limited by extreme computational costs. Standard RS requires tens of thousands of model evaluations per input and forces practitioners to commit to fixed sample sizes a priori. In this work, we present a novel meta-learning framework for anytime-valid certified robustness that adaptively deploys computational resources. By using a lightweight meta-learner to predict image-specific priors for a sequential E-process, we achieve a 20-fold reduction in sample complexity compared to traditional methods while maintaining rigorous statistical guarantees. Beyond raw efficiency, we demonstrate how anytime-validity enables adaptively allocating compute based upon application-specific risk thresholds, a form of resource triage impossible under classic certification frameworks. That this is achievable while also providing similar certification performance demonstrates that our approach provides a pathway for real-time, safety-critical certification deployments.

Andrew C. Cullen, Paul Montague, Benjamin I. P. Rubinstein

University of Melbourne · DST Group, Adelaide

Efficient Neural Network Inference Early Stopping Randomized Smoothing Anytime-Valid Inference Neural Network Robustness Certified Robustness

Jun 23, 2026cs.RO

Sim-to-Real Betting on the E-Process: Bringing "simulators" to anytime-valid confidence sequences

This note describes an integration of the sim-to-real performance estimate with betting (from Chen et al.) and the safe anytime-valid inference (from Ramdas et al.). Using the scaled simulators. The method produces efficient, reliable certificates for the mean estimate, an approach that is especially valuable in robot performance testing. This note gives a primary, self-contained account of the construction; preliminaries of the respective methods are kept at a minimum, and one shall refer to the original works for full detail. Some synthetic examples demonstrating the proposed algorithm can be found at https://github.com/ISUSAIL/Bet4Sim2Real-EProcess.

Yujia Chen, Bowen Weng

Department of Computer Science, Iowa State University

Anytime-Valid Inference

Jun 18, 2026cs.LG

CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes

Can we trust evaluation scores to capture an LLM's true real-world performance? Certifiable evaluation answers this question by providing guarantee for LLM evaluation. In particular, existing methods sequentially curate evaluation samples and keep updating confidence intervals (CIs) that cover the true performance with high probability (e.g., 95%) until some conditions are satisfied, e.g., the CI width reaches a target precision. However, existing methods are not generally anytime-valid: the claimed coverage (e.g., 95%) may fail when CIs are repeatedly updated and used to decide when to stop, leaving a gap between theoretical rigor and practice. This paper bridges this gap by proposing Celeus, a Certifiable framework for Efficient LLM evaluation, which leverages E-processes to build anytime-valid CIs. Concretely, we propose signals that combine two ingredients: (i) Uncertainty-guided sampling to select informative samples for evaluation, and (ii) Surrogate-assisted approximations for unevaluated samples. We prove that such signals remain unbiased for the evaluation score conditional on the past, enabling statistically-grounded and anytime-valid

e

-process CIs. More importantly, the two ingredients reduce estimation variance and help reach the target precision with fewer evaluated samples. We also prove that CIs obtained by Celeus can shrink at a near-parametric rate up to logarithmic factors and analyze the oracle variance-optimal sampling rule that motivates the empirical uncertainty-guided one. Experiments show that Celeus reaches the target precision using 54-62% fewer evaluated samples than baselines, while preserving anytime-valid coverage.

Zhijian Zhou, Zesheng Ye, Zhaorun Chen +2

The University of Melbourne · Department of Computer Science, University of Chicago · Department of Computer Science, University of Illinois Urbana-Champaign

LLM Evaluation Anytime-Valid Inference Adaptive Sampling Uncertainty Sampling

Jun 13, 2026cs.AI

Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelines

Continuous evaluation of LLM products relies on a strong LLM judge treated as ground truth: a cheap monitor scores every interaction and a team is paged when the score drifts down. But the judge is itself a model behind an API, and a silent version bump or scoring-prompt update changes how it scores -- so every drift alarm is ambiguous between a worse product and a changed judge. We resolve the ambiguity with a fixed, human-labeled anchor set that the current judge re-scores at a steady interleave, a second betting e-process on the judge-versus-human gap, and a guard-window rule returning a verdict in {none, system, judge}. We prove anytime-validity, one-way identification (only the judge can move the anchors), an attribution race whose design law is that the anchors must out-run the main process they guard, and process orthogonality. On two real judge changes, a silent version bump is detected as judge drift in 60/60 runs with zero judge-to-system misattribution, and a contaminating strict-prompt change is correctly attributed on 110 of 120 runs at guard width 300 -- while the industry-default rolling z-test false-alarms on 75% of drift-free streams. Every experiment replicates on a second domain (TL;DR summarization) with nothing re-tuned, and where the domains differ the differences are the ones the race predicts: the strict-prompt change shifts scores harder there, so the anchors fire faster and attribution becomes perfect (240/240). The monitor runs at approximately 0.64 of the cost of strong-judging every item, or 0.21 in a cheaper-but-deafer regime.

Yitao Li

LLM Evaluation LLM-as-a-Judge Language Model Generation Evaluation Anytime-Valid Inference Change-Point Detection Drifting Models

Jun 12, 2026stat.ML

Anytime-Valid Confirmation of Label-Shift Corrections

In small-batch scientific deployments, labeled target outcomes may be too scarce for reliable shift estimation even when unlabeled target inputs are available. We address the complementary setting where the practitioner has a pre-specified label-shift correction from domain knowledge and asks whether incoming labeled outcomes support it. We show that the per-observation likelihood ratio between a label-shift-corrected predictive and the source predictive is a conditional e-value, so its running product is a nonnegative martingale and Ville's inequality yields an anytime-valid confirmation rule. The log martingale equals the cumulative negative log-predictive density (NLPD) gap between the source and the corrected predictive, converting routine model monitoring into a formal sequential test. Rejection means the incoming data support the posited correction relative to the source predictive, but it is not a precise estimate of the degree of shift. Closed forms are available for GP sources with Gaussian label-shift ratios. GP regression simulations validate Type I control, finite-sample power, miscalibration sensitivity, and the small-batch advantage of a reliable prior over label-based re-estimation.

Seungjin Choi

CROID Research and aSSIST University, Seoul, Korea.

Label Shift Anytime-Valid Inference E-Values

May 29, 2026stat.ML

Correcting Split Selection in Online Decision Trees via Anytime-Valid Inference

Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow decision trees incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on anytime-valid inference. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d. data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.

Salim I. Amoukou, Saumitra Mishra, Manuela Veloso

J.P. Morgan AI Research.

Anytime-Valid Inference Decision Tree Learning Random Forest Sequential Hypothesis Testing

May 27, 2026stat.ML

Anytime-Valid Federated Conformal RAG for LLM Swarms

Federated Conformal RAG (FC-RAG) provides distribution-free coverage for a bandwidth-limited swarm of weak language models, but only at a fixed horizon. We extend it to anytime-valid sequential coverage: validity at every stopping time, preserved under predictable adaptive control (recalibration, per-node bandwidth escalation, distilled-student refresh), at no extra cost in assumptions over fixed-horizon FC-RAG. Naive composition fails because FC-RAG's marginal coverage bound makes the betting e-process a non-supermartingale on adverse calibration draws, and Ville's inequality cannot be invoked. We give Anytime-FC-RAG, a sequential extension built on a summable per-step calibration-deviation budget that converts the marginal bound into a strict conditional bound on a calibration-good event, paired with a truncated betting e-process that is a nonnegative supermartingale on the entire probability space. From these two ingredients, we obtain four guarantees: time-uniform alarm validity

\mathbb{P}(\sup_t E_t \ge 1/δ_e) \le δ_e + δ_{\mathrm{cal}}

, a Hoeffding-stitched cumulative-miscoverage envelope at the same total budget, safety under any predictable controller (recalibration, bandwidth escalation, student refresh), and training-side error propagation across an unbounded sequence of Federated Probe-Logit Distillation (FPLD) refreshes via a summable training budget. As a practical consequence, an adaptive controller that escalates retrieval bandwidth only when the e-process crosses a warning threshold matches the alarm rate of a fixed-high-bandwidth schedule at substantially lower communication cost. Experiments on a GPT-2-small + MiniLM swarm across MMLU, DBpedia, and AG News verify the predicted alarm rate, detection delay, envelope coverage, and

14

-

57\%

bandwidth savings; the alarm fires when and only when coverage genuinely breaks.

Prasanjit Dubey, Xiaoming Huo

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Retrieval-Augmented Generation Anytime-Valid Inference Conformal Prediction Federated Learning

May 18, 2026cs.LG

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 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.

Hamed Khosravi, Xiaoming Huo

Georgia Institute of Technology

Selective Prediction Anytime-Valid Inference Conformal Risk Control LLM Safety

May 13, 2026stat.ML

When Should an AI Workflow Release? Always-Valid Inference for Black-Box Generate-Verify Systems

LLM-enabled AI workflows increasingly produce outputs through iterative generate-evaluate-revise loops. Each iteration can improve the candidate, but it also creates a release decision: when to stop and output the current result? This raises a statistical challenge because deployment-time evaluator scores are adaptively generated and repeatedly monitored, yet the likelihood models or exchangeability assumptions typically used for calibration are unavailable. We propose an always-valid release wrapper for existing generator-evaluator pipelines. The wrapper builds a hard-negative reference pool of high-scoring failures, calibrates deployment-time evaluator scores against this pool, and accumulates the resulting evidence with an e-process. This separates two roles: the reference pool turns black-box scores into conservative evidence, while the e-process provides validity under optional stopping. In theory, we show that a conservative reference pool yields finite-sample control of the probability of releasing on infeasible tasks, that is, tasks for which the given workflow is not capable of producing a reliable solution. We also characterize conditions under which the same conservative rule still achieves nontrivial release on feasible tasks. In an MBPP+ coding-agent case study, the wrapper reduces premature incorrect release relative to baseline stopping rules while still releasing on tasks for which the workflow repeatedly accumulates moderate supporting evidence.

Young Hyun Cho, Will Wei Sun

Department of Statistics, Purdue University. · Mitch Daniels School of Business, Purdue University.

Anytime-Valid Inference Sequential Hypothesis Testing LLM Agent Reliability

May 8, 2026stat.ML

Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on the choice of martingale updates, and many existing constructions do not exploit prior information about plausible data-generating distributions or mean values. We propose a Bayes-assisted framework that uses a Bayesian working predictive model to adaptively construct confidence sequences. For each candidate mean and time point, the predictive distribution selects, among valid one-step martingale factors, the update maximising predictive expected log-growth; validity is therefore preserved even when the prior or working model is misspecified. We prove that if the predictive distribution is Wasserstein-consistent, the resulting procedure is asymptotically log-optimal, matching the per-sample log-growth of an oracle procedure with access to the true distribution. We instantiate the framework using robust predictives based on Dirichlet-process mixtures and Bayesian exponentially tilted empirical likelihood. Experiments on synthetic data, sequential best-arm identification for LLM evaluation, and prediction-powered inference show that informative priors can substantially reduce confidence-sequence width and sampling effort while retaining anytime-valid coverage.

Valentin Kilian, Stefano Cortinovis, François Caron

Department of Statistics, University of Oxford

Anytime-Valid Inference Bayesian Inference

May 7, 2026cs.AI

Adaptive auditing of AI systems with anytime-valid guarantees

A major bottleneck in characterizing the failure modes of generative AI systems is the cost and time of annotation and evaluation. Consequently, adaptive testing paradigms have gained popularity, where one opportunistically decides which cases and how many to annotate based on past results. While this framework is highly practical, its extreme flexibility makes it difficult to draw statistically rigorous conclusions, as it violates classical assumptions: the number of observations is typically limited (often 10 to 50 cases) and decisions regarding sampling and stopping are made in the midst of data collection rather than based a pre-specified rule. To characterize what statistical inferences can be drawn from highly adaptive audits, we introduce a hypothesis testing framework from two 'dueling' perspectives: (i) the model's null that asserts there is no failure mode with performance below a target threshold versus (ii) the auditor's null that asserts they have a sampling strategy that will uncover a failure mode. Leveraging Safe Anytime-Valid Inference (SAVI), we formalize the auditor as conducting 'testing by betting', which translates into simultaneous e-processes for testing the dueling null hypotheses. Furthermore, if the auditor is sufficiently powerful, we prove that these two hypotheses are asymptotically inverses of each other, in that passage of a stringent audit does in fact certify the AI system as being globally robust. Empirically, we demonstrate that our proposed testing procedures maintain anytime-valid type-I error control, outperform pre-specified testing methods, and can reach statistically rigorous conclusions sometimes with as few as 20 observations.

Siyu Zhou, Patrick Vossler, Venkatesh Sivaraman +2

University of California, San Francisco · Stanford University

Algorithmic Auditing Anytime-Valid Inference Sequential Hypothesis Testing

May 7, 2026stat.ML

CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency

Large language models often improve reasoning by sampling multiple outputs and aggregating their final answers, but precise and efficient control of error levels remains a challenging task. In particular, deciding when to stop sampling remains difficult when the stopping rule is data-dependent and the set of possible answers is not known in advance. We study anytime-valid certification of a prespecified target answer as the unique mode of the model's response distribution, a guarantee distinct from answer correctness. We propose the Certification by Intersection-union Testing with E-processes (CITE) algorithm, which provably controls false certification at any prescribed level under arbitrary data-driven stopping, without requiring prior knowledge of the answer category set. We also prove an category-set-size-free stopping-time rate, establish matching minimax lower bounds up to constants in the main regime, and extend the construction to confidence-weighted voting. Simulations and LLM self-consistency experiments show empirical error control and improved certification in diffuse-tail settings.

Hirofumi Ota, Naoto Iwase, Yuki Ichihara +2

arXiv:2605.05873v1

LLM Evaluation Anytime-Valid Inference Sequential Hypothesis Testing Statistical Hypothesis Testing