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Yunbei Xu

Yunbei Xu contributes to research discovery and scholarly infrastructure.

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Machine Learning cond-mat.stat-mech math.FA math.OC math.PR math.ST

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preprint2026arXiv

Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds

We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize how the sequence horizon $H$ affects both approximation and estimation errors in this joint-distribution, sequence-level regime. By establishing matching upper and lower bounds, we provide, to our knowledge, the first complete characterization of long-horizon error behavior under the natural joint KL objective, with improved rates and optimality justification relative to existing work. On the approximation side, we show that joint KL admits a horizon-free approximation factor, in sharp contrast to Hellinger-based analyses that exhibit an $Ω(H)$ dependence for computationally efficient methods; this isolates the choice of divergence as the source of approximation amplification. On the estimation side, we prove a fundamental information-theoretic lower bound of order $Ω(H)$ that holds for both decomposable policy classes and fully shared policies, matching the $\widetilde O(H)$ upper bounds achieved by computationally efficient algorithms. Our analysis clarifies the landscape of recent autoregressive learning results by aligning the log-loss training objective, the sequence-level evaluation metric, and the approximation metric {\color{black}through a sharp joint-KL oracle theory}. We further show that these joint-KL guarantees imply policy learning regret bounds at rates matching prior imitation learning literature.

preprint2026arXiv

In-Context Learning for Data-Driven Censored Inventory Control

We study inventory control with decision-dependent censoring, focusing on the censored or repeated newsvendor (R-NV), where each order quantity determines whether demand is fully observed or censored by sales. Existing approaches based on parametric Thompson sampling (TS) can be brittle under prior mismatch, while offline imputation methods need not transfer to online learning. Motivated by the predictive view of decision making, we combine these ideas by taking oracle actions on learned completions of latent demand. We propose in-context generative posterior sampling (ICGPS), which uses modern generative models that are meta-trained offline and deployed online by in-context autoregressive generation. Theoretically, we show that the Bayesian regret of ICGPS with a learned completion kernel is bounded by the Bayesian regret of a TS benchmark with the ideal completion kernel plus a deployment penalty scaling as $\sqrt{T}$ times the square root of the completion mismatch. This yields a plug-in template for operational problems with known TS regret bounds. For R-NV, we derive sublinear Bayesian regret by reducing censored feedback to bandit convex optimization feedback. We also show that, under reasonable coverage and stability assumptions, the online completion mismatch is controlled by the offline censored predictive mismatch, so offline predictive quality transfers to online performance. Practically, we instantiate ICGPS with ChronosFlow, which combines a frozen time-series transformer backbone with a trainable conditional normalizing-flow head for fast censoring-consistent sampling. In benchmark experiments, ChronosFlow-ICGPS matches correctly specified TS, outperforms myopic and UCB-style baselines, and is robust to prior mismatch and distribution shift. ChronosFlow-ICGPS also performs well for the real-world SuperStore dataset, especially under heavy censoring.

preprint2026arXiv

On the Blessing of Pre-training in Weak-to-Strong Generalization

The paradigm of Weak-to-Strong Generalization (W2SG) suggests that a pre-trained strong model can surpass its weak supervisor, yet the decisive role of pre-training remains theoretically and empirically under-explored. In this work, we identify pre-training as the essential prerequisite for the emergence of W2SG. Theoretically, we formalize the W2SG problem within a high-dimensional single-index model framework using spiked Gaussian data, modeling pre-training as a spectral initialization step. Building upon prior impossibility results regarding the failure of learning under random initialization, we prove that W2SG is achievable when pre-training provides a geometric warm start that places the model within an "effective region" characterized by a perturbed strong-convexity geometry. Within this region, we derive a rigorous generalization bound that naturally captures the optimization dynamics: an initial performance improvement followed by a saturation bottleneck dictated by the weak supervisor's bias. Empirically, we first validate all our assumptions and theoretical insights through controlled synthetic simulations. Finally, through a massive-scale evaluation of hundreds of intermediate pre-training checkpoints from large language models, we demonstrate that W2SG is not an innate capability but emerges via a phase transition tightly coupled with the progression of pre-training.

preprint2026arXiv

On the Power of Adaptivity for $\varepsilon$-Best Arm Identification in Linear Bandits

We study the minimax sample complexity of $\varepsilon$-best arm identification in linear bandits. Given a compact action set $\mathcal{X}$ that spans $\mathbb{R}^d$ and an unknown reward vector $θ\in\mathbb{R}^d$, the goal is to output an arm $\widehat{x}\in\mathcal{X}$ such that $\langle \widehat{x},θ\rangle \ge \max_{x\in\mathcal{X}} \langle x,θ\rangle - \varepsilon$ with probability at least $1-δ$, using as few samples as possible. First, we present a non-adaptive fixed-design method with sample complexity $\mathcal{O}\!\left(\frac{d\log(1/δ)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$, where $w(\mathcal{X})$ is a Gaussian width term dependent on $\mathcal{X}$, and we prove a matching lower bound $Ω\!\left(\frac{d\log(1/δ)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$ for all non-adaptive fixed-design methods. We then turn to adaptive sampling. We raise an important structural question: beyond the canonical basis, are there structured action sets for which adaptivity yields only logarithmic-factor improvements over the optimal non-adaptive rate? We answer in the affirmative for several natural action sets, namely the hypercube, the $\ell_2$ ball, $m$-sets, and multi-task multi-armed bandits. Finally, we provide the first construction of an action set $\mathcal{X}$ for which adaptivity yields a polynomial-factor improvement over every non-adaptive algorithm. A key ingredient behind this separation is an $\ell_2$-norm estimation subroutine: we design an adaptive algorithm that uses $\mathcal{O}\!\left(\frac{d\log(1/δ)}{\varepsilon^2}\right)$ samples from the unit $\ell_2$ ball in $\mathbb{R}^d$ and outputs an estimate $\widehat r$ satisfying $|\widehat r-\|θ\|_2|\le \varepsilon$ with probability at least $1-δ$, where $θ$ is the unknown reward vector.

preprint2026arXiv

Pointwise Generalization in Deep Neural Networks

We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear feature-learning regime and builds a new statistical foundation for representation learning. For each trained model, we characterize the hypothesis via a pointwise Riemannian Dimension, derived from the eigenvalues of the learned feature representations across layers. This establishes a principled framework for deriving hypothesis-dependent, representation-aware generalization bounds. These bounds offer a systematic upgrade over approaches based on model size, products of norms, and infinite-width linearizations, yielding guarantees that are orders of magnitude tighter in both theory and experiment. Analytically, we identify the structural properties and mathematical principles that explain the tractability of deep networks. Empirically, the pointwise Riemannian Dimension exhibits substantial feature compression, decreases with increased over-parameterization, and captures the implicit bias of optimizers. Taken together, our results indicate that deep networks are mathematically tractable in practical regimes and that their generalization is sharply explained by pointwise, feature-spectrum-aware complexity.

preprint2026arXiv

Thompson Sampling for Repeated Newsvendor

In this paper, we investigate the performance of Thompson Sampling (TS) for online learning with censored feedback, focusing primarily on the classic repeated newsvendor model--a foundational framework in inventory management--and demonstrating how our techniques can be naturally extended to a broader class of problems. We first model demand using a Weibull distribution and initialize TS with a Gamma prior to dynamically adjust order quantities. Our analysis establishes optimal (up to logarithmic factors) frequentist regret bounds for TS without imposing restrictive prior assumptions. More importantly, it yields novel and highly interpretable insights on how TS addresses the exploration-exploitation trade-off in the repeated newsvendor setting. Specifically, our results show that when past order quantities are sufficiently large to overcome censoring, TS accurately estimates the unknown demand parameters, leading to near-optimal ordering decisions. Conversely, when past orders are relatively small, TS automatically increases future order quantities to gather additional demand information. Then, we extend our analysis to general parametric distribution family and provide proof for Bayesian regret. Extensive numerical simulations further demonstrate that TS outperforms more conservative and widely-used approaches such as online convex optimization, upper confidence bounds, and myopic Bayesian dynamic programming.

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