Xiaocong Xu

Yingying Fan, Yuxuan Han, Jinchi Lv et al.

We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=μ_\ast(\mathsf c_t)+ξ_t$, with an unknown utility map $μ_\ast$ and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map $u\mapsto p^\ast(u)$ induced by the scalar index $u=μ_\ast(\mathsf c)$ and the noise tail. Under the $β$-Hölder smoothness of the tail function for $β\geq 2$ and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself $(β-1)$-smooth. We exploit such structure through $\mathsf{ORBIT}$, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model $μ_\ast(\mathsf c)=\mathsf c^\topθ_\ast$, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret $\widetilde{O}\big(T^{\frac{2β-1}{4β-3}}+\sqrt{dT}\big)$. For fixed $d$, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Hölder utility.

Yingying Fan, Lan Gao, Jinchi Lv et al.

We propose a unified theoretical framework for studying the robustness of the model-X knockoffs framework by investigating the asymptotic false discovery rate (FDR) control of the practically implemented approximate knockoffs procedure. This procedure deviates from the model-X knockoffs framework by substituting the true covariate distribution with a user-specified distribution that can be learned using in-sample observations. By replacing the distributional exchangeability condition of the model-X knockoff variables with three conditions on the approximate knockoff statistics, we establish that the approximate knockoffs procedure achieves the asymptotic FDR control. Using our unified framework, we further prove that an arguably most popularly used knockoff variable generation method--the Gaussian knockoffs generator based on the first two moments matching--achieves the asymptotic FDR control when the two-moment-based knockoff statistics are employed in the knockoffs inference procedure. For the first time in the literature, our theoretical results justify formally the effectiveness and robustness of the Gaussian knockoffs generator. Simulation and real data examples are conducted to validate the theoretical findings.

Yingying Fan, Yuxuan Han, Jinchi Lv et al.

In this paper, we study the behavior of the Upper Confidence Bound-Variance (UCB-V) algorithm for the Multi-Armed Bandit (MAB) problems, a variant of the canonical Upper Confidence Bound (UCB) algorithm that incorporates variance estimates into its decision-making process. More precisely, we provide an asymptotic characterization of the arm-pulling rates for UCB-V, extending recent results for the canonical UCB in Kalvit and Zeevi (2021) and Khamaru and Zhang (2024). In an interesting contrast to the canonical UCB, our analysis reveals that the behavior of UCB-V can exhibit instability, meaning that the arm-pulling rates may not always be asymptotically deterministic. Besides the asymptotic characterization, we also provide non-asymptotic bounds for the arm-pulling rates in the high probability regime, offering insights into the regret analysis. As an application of this high probability result, we establish that UCB-V can achieve a more refined regret bound, previously unknown even for more complicate and advanced variance-aware online decision-making algorithms.

Qian Shi, Xiaolei Qin, Lingyu Sun et al.

Global forest cover is critical to the provision of certain ecosystem services. With the advent of the google earth engine cloud platform, fine resolution global land cover mapping task could be accomplished in a matter of days instead of years. The amount of global forest cover (GFC) products has been steadily increasing in the last decades. However, it's hard for users to select suitable one due to great differences between these products, and the accuracy of these GFC products has not been verified on global scale. To provide guidelines for users and producers, it is urgent to produce a validation sample set at the global level. However, this labeling task is time and labor consuming, which has been the main obstacle to the progress of global land cover mapping. In this research, a labor-efficient semi-automatic framework is introduced to build a biggest ever Forest Sample Set (FSS) contained 395280 scattered samples categorized as forest, shrubland, grassland, impervious surface, etc. On the other hand, to provide guidelines for the users, we comprehensively validated the local and global mapping accuracy of all existing 30m GFC products, and analyzed and mapped the agreement of them. Moreover, to provide guidelines for the producers, optimal sampling strategy was proposed to improve the global forest classification. Furthermore, a new global forest cover named GlobeForest2020 has been generated, which proved to improve the previous highest state-of-the-art accuracies (obtained by Gong et al., 2017) by 2.77% in uncertain grids and by 1.11% in certain grids.