GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at any time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.

Efficient Adaptive Experimentation with Non-Compliance

We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV--an \textbf{A}daptive, \textbf{M}ultiply-\textbf{R}obust estimator for \textbf{I}nstrumental-\textbf{V}ariable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.

CSPI-MT: Calibrated Safe Policy Improvement with Multiple Testing for Threshold Policies

When modifying existing policies in high-risk settings, it is often necessary to ensure with high certainty that the newly proposed policy improves upon a baseline, such as the status quo. In this work, we consider the problem of safe policy improvement, where one only adopts a new policy if it is deemed to be better than the specified baseline with at least pre-specified probability. We focus on threshold policies, a ubiquitous class of policies with applications in economics, healthcare, and digital advertising. Existing methods rely on potentially underpowered safety checks and limit the opportunities for finding safe improvements, so too often they must revert to the baseline to maintain safety. We overcome these issues by leveraging the most powerful safety test in the asymptotic regime and allowing for multiple candidates to be tested for improvement over the baseline. We show that in adversarial settings, our approach controls the rate of adopting a policy worse than the baseline to the pre-specified error level, even in moderate sample sizes. We present CSPI and CSPI-MT, two novel heuristics for selecting cutoff(s) to maximize the policy improvement from baseline. We demonstrate through both synthetic and external datasets that our approaches improve both the detection rates of safe policies and the realized improvement, particularly under stringent safety requirements and low signal-to-noise conditions.