arXiv subjects

Ricardo J. Sandoval

Publications and source records attributed to Ricardo J. Sandoval.

4 recordsLinked to original sources

arXiv2026

Always-On Experimentation

Generative AI has dramatically accelerated the rate at which new treatments---from novel pharmaceuticals to online marketing campaigns---can be conceived and deployed. As a result, modern experimentation platforms often run continuously, with treatments added as they are ready and removed when they underperform. We formalize this "Always-On" experimental setting, in which treatments can be dynamically generated, added to, and removed from a running experiment, and study the statistical problem of deciding whether to accept or reject each treatment while controlling for the false discovery rate. We develop sequential tests that achieve time-uniform Type-I error control under arbitrary stopping times and "predictable" treatment schedules. Our approach builds on the testing-by-betting framework: we construct test supermartingales for testing the average treatment effect of each treatment, and show that the construction of these test supermartingales is growth-rate optimal in an almost-sure sense.

stat.ME↗

arXiv2026

Instance-Log-Optimality of Portfolio-Based E-Processes and their Sequential Hypothesis Tests

We consider the problem of sequential hypothesis testing using $e$-processes. For a rich class of composite testing problems---which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of two-sample and independence testing as special cases---we show that any $e$-process satisfying a certain sublinear regret bound is asymptotically and almost surely instance-log-optimal for a composite alternative. This is a strong notion of optimality that has not previously been established for the aforementioned problems, and we provide explicit test supermartingales and $e$-processes satisfying this notion in a more general case. Furthermore, we derive matching lower and upper bounds on the expected rejection time in the high-confidence regime for the resulting sequential tests in all of these cases. The proofs of these results make weak, algorithm-agnostic moment assumptions and rely on a proof technique involving the aforementioned regret and a family of numeraire portfolios. Finally, we discuss how all of these theorems hold in a distribution-uniform sense, a notion of log-optimality that is stronger still and seems to be new to the literature.

math.ST↗

arXiv2026

Multi-Armed Sequential Hypothesis Testing by Betting

We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms. We consider the composite global null hypothesis $\mathscr{P}$ that all arms are null in a certain sense (e.g. all dosages of a treatment are ineffective) and we are interested in rejecting $\mathscr{P}$ in favor of a composite alternative $\mathscr{Q}$ where at least one arm is non-null (e.g. there exists an effective treatment dosage). We posit an optimality desideratum that we describe informally as follows: even if several arms are non-null, we seek $e$-processes and sequential tests whose performance are as strong as the ones that have oracle knowledge about which arm generates the most evidence against $\mathscr{P}$. Formally, we generalize notions of log-optimality and expected rejection time optimality to more than one arm, obtaining matching lower and upper bounds for both. A key technical device in this optimality analysis is a modified upper-confidence-bound-like algorithm for unobservable but sufficiently "estimable" rewards. In the design of this algorithm, we derive nonasymptotic concentration inequalities for optimal wealth growth rates in the sense of Kelly [1956]. These may be of independent interest.

stat.ME↗

arXiv2026

On Nonasymptotic Confidence Intervals for Treatment Effects in Randomized Experiments

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves systematic exploitation of negative dependence or variance adaptivity (or both). We also show that the nonasymptotic rates that we achieve are unimprovable in an information-theoretic sense.

stat.ME↗