We study nonparametric estimation of Schrödinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schrödinger bridge time-series (SBTS) drift formula, we analyze a direct Nadaraya--Watson plug-in estimator built from kernelized numerator and denominator terms. Unlike recent SB analyses based on entropic-OT potentials, Sinkhorn iterations, or iterative bridge solvers, our approach works directly at the drift level and isolates \emph{statistical error} from optimization, approximation, and discretization error. Under Hölder regularity, a marginal-density floor, and bounded support, we prove a uniform non-asymptotic bound for admissible bandwidth pairs, a pointwise CLT under genuine undersmoothing, and an adaptive bandwidth selector satisfying an oracle inequality. We also prove a pivot-local minimax lower bound which, through an explicit uniform pivot, yields a global minimax lower bound under transparent compatibility conditions; hence the adaptive selector is minimax-rate optimal up to logarithmic factors. Synthetic experiments provide theorem-targeted diagnostics for finite-sample scaling, Gaussian approximation, and adaptive behavior.

Machine learning models are often personalized by using group attributes that encode personal characteristics (e.g., sex, age group, HIV status). In such settings, individuals expect to receive more accurate predictions in return for disclosing group attributes to the personalized model. We study when we can tell that a personalized model upholds this principle for every group who provides personal data. We introduce a metric called the benefit of personalization (BoP) to measure the smallest gain in accuracy that any group expects to receive from a personalized model. We describe how the BoP can be used to carry out basic routines to audit a personalized model, including: (i) hypothesis tests to check that a personalized model improves performance for every group; (ii) estimation procedures to bound the minimum gain in personalization. We characterize the reliability of these routines in a finite-sample regime and present minimax bounds on both the probability of error for BoP hypothesis tests and the mean-squared error of BoP estimates. Our results show that we can only claim that personalization improves performance for each group who provides data when we explicitly limit the number of group attributes used by a personalized model. In particular, we show that it is impossible to reliably verify that a personalized classifier with k 19 binary group attributes will benefit every group who provides personal data using a dataset of n = 8 109 samples - one for each person in the world.

Neural Information Processing Systems http://nips.cc/

We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound $\widetilde{O}\left(SA\frac{\mathsf{H}}{\varepsilon^2} \right)$, where $\mathsf{H}$ is the span of the bias function of the optimal policy and $SA$ is the cardinality of the state-action space. Our result is the first that is minimax optimal (up to log factors) in all parameters $S,A,\mathsf{H}$, and $\varepsilon$, improving on existing work that either assumes uniformly bounded mixing times for all policies or has suboptimal dependence on the parameters. We also initiate the study of sample complexity in general (multichain) average-reward MDPs.