arXiv subjects

Yangchun Zhang

Publications and source records attributed to Yangchun Zhang.

8 recordsLinked to original sources

arXiv2025

On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices

This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to determine the convergence rate of spiked eigenvalue estimates.

math.ST↗

arXiv2025

The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models

Standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the framework of Elliptical Factor Models (EFM), which accommodate both heavy tails and potential non-linear dependencies common in real-world data. We demonstrate, both theoretically and empirically, that heavy-tailed noise generates spurious eigenvalues that mimic true factor signals. To distinguish these, we propose a novel methodology based on a fluctuation magnification algorithm. Under mild conditions, we show that, by magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) than spurious eigenvalues arising from heavy-tailed effects. We develop a formal testing procedure based on this principle and apply it to the problem of accurately selecting the number of common factors in heavy-tailed EFMs. Simulation studies and real data analysis confirm the effectiveness of our approach, particularly in scenarios with pronounced heavy-tailedness.

stat.ME↗

arXiv2025

On Generalization and Distributional Update for Mimicking Observations with Adequate Exploration

Learning from observations (LfO) replicates expert behavior without needing access to the expert's actions, making it more practical than learning from demonstrations (LfD) in many real-world scenarios. However, directly applying the on-policy training scheme in LfO worsens the sample inefficiency problem, while employing the traditional off-policy training scheme in LfO magnifies the instability issue. This paper seeks to develop an efficient and stable solution for the LfO problem. Specifically, we begin by exploring the generalization capabilities of both the reward function and policy in LfO, which provides a theoretical foundation for computation. Building on this, we modify the policy optimization method in generative adversarial imitation from observation (GAIfO) with distributional soft actor-critic (DSAC), and propose the Mimicking Observations through Distributional Update Learning with adequate Exploration (MODULE) algorithm to solve the LfO problem. MODULE incorporates the advantages of (1) high sample efficiency and training robustness enhancement in soft actor-critic (SAC), and (2) training stability in distributional reinforcement learning (RL). Extensive experiments in MuJoCo environments showcase the superior performance of MODULE over current LfO methods.

stat.ML↗

arXiv2024

TestAgent: Automatic Benchmarking and Exploratory Interaction for Evaluating LLMs in Vertical Domains

As Large Language Models (LLMs) are increasingly deployed in highly specialized vertical domains, the evaluation of their domain-specific performance becomes critical. However, existing evaluations for vertical domains typically rely on the labor-intensive construction of static single-turn datasets, which present two key limitations: (i) manual data construction is costly and must be repeated for each new domain, and (ii) static single-turn evaluations are misaligned with the dynamic multi-turn interactions in real-world applications, limiting the assessment of professionalism and stability. To address these, we propose TestAgent, a framework for automatic benchmarking and exploratory dynamic evaluation in vertical domains. TestAgent leverages retrieval-augmented generation to create domain-specific questions from user-provided knowledge sources, combined with a two-stage criteria generation process, thereby enabling scalable and automated benchmark creation. Furthermore, it introduces a reinforcement learning-guided multi-turn interaction strategy that adaptively determines question types based on real-time model responses, dynamically probing knowledge boundaries and stability. Extensive experiments across medical, legal, and governmental domains demonstrate that TestAgent enables efficient cross-domain benchmark generation and yields deeper insights into model behavior through dynamic exploratory evaluation. This work establishes a new paradigm for automated and in-depth evaluation of LLMs in vertical domains.

cs.AI↗

arXiv2024

On Reward Transferability in Adversarial Inverse Reinforcement Learning: Insights from Random Matrix Theory

In the context of inverse reinforcement learning (IRL) with a single expert, adversarial inverse reinforcement learning (AIRL) serves as a foundational approach to providing comprehensive and transferable task descriptions. However, AIRL faces practical performance challenges, primarily stemming from the framework's overly idealized decomposability condition, the unclear proof regarding the potential equilibrium in reward recovery, or questionable robustness in high-dimensional environments. This paper revisits AIRL in \textbf{high-dimensional scenarios where the state space tends to infinity}. Specifically, we first establish a necessary and sufficient condition for reward transferability by examining the rank of the matrix derived from subtracting the identity matrix from the transition matrix. Furthermore, leveraging random matrix theory, we analyze the spectral distribution of this matrix, demonstrating that our rank criterion holds with high probability even when the transition matrices are unobservable. This suggests that the limitations on transfer are not inherent to the AIRL framework itself, but are instead related to the training variance of the reinforcement learning algorithms employed within it. Based on this insight, we propose a hybrid framework that integrates on-policy proximal policy optimization in the source environment with off-policy soft actor-critic in the target environment, leading to significant improvements in reward transfer effectiveness.

stat.ML↗

arXiv2024

Rethinking Adversarial Inverse Reinforcement Learning: Policy Imitation, Transferable Reward Recovery and Algebraic Equilibrium Proof

Adversarial inverse reinforcement learning (AIRL) stands as a cornerstone approach in imitation learning, yet it faces criticisms from prior studies. In this paper, we rethink AIRL and respond to these criticisms. Criticism 1 lies in Inadequate Policy Imitation. We show that substituting the built-in algorithm with soft actor-critic (SAC) during policy updating (requires multi-iterations) significantly enhances the efficiency of policy imitation. Criticism 2 lies in Limited Performance in Transferable Reward Recovery Despite SAC Integration. While we find that SAC indeed exhibits a significant improvement in policy imitation, it introduces drawbacks to transferable reward recovery. We prove that the SAC algorithm itself is not feasible to disentangle the reward function comprehensively during the AIRL training process, and propose a hybrid framework, PPO-AIRL + SAC, for a satisfactory transfer effect. Criticism 3 lies in Unsatisfactory Proof from the Perspective of Potential Equilibrium. We reanalyze it from an algebraic theory perspective.

cs.LG↗

arXiv2023

Exploring Gradient Explosion in Generative Adversarial Imitation Learning: A Probabilistic Perspective

Generative Adversarial Imitation Learning (GAIL) stands as a cornerstone approach in imitation learning. This paper investigates the gradient explosion in two types of GAIL: GAIL with deterministic policy (DE-GAIL) and GAIL with stochastic policy (ST-GAIL). We begin with the observation that the training can be highly unstable for DE-GAIL at the beginning of the training phase and end up divergence. Conversely, the ST-GAIL training trajectory remains consistent, reliably converging. To shed light on these disparities, we provide an explanation from a theoretical perspective. By establishing a probabilistic lower bound for GAIL, we demonstrate that gradient explosion is an inevitable outcome for DE-GAIL due to occasionally large expert-imitator policy disparity, whereas ST-GAIL does not have the issue with it. To substantiate our assertion, we illustrate how modifications in the reward function can mitigate the gradient explosion challenge. Finally, we propose CREDO, a simple yet effective strategy that clips the reward function during the training phase, allowing the GAIL to enjoy high data efficiency and stable trainability.

cs.LG↗

arXiv2023

Sampling without replacement from a high-dimensional finite population

It is well known that most of the existing theoretical results in statistics are based on the assumption that the sample is generated with replacement from an infinite population. However, in practice, available samples are almost always collected without replacement. If the population is a finite set of real numbers, whether we can still safely use the results from samples drawn without replacement becomes an important problem. In this paper, we focus on the eigenvalues of high-dimensional sample covariance matrices generated without replacement from finite populations. Specifically, we derive the Tracy-Widom laws for their largest eigenvalues and apply these results to parallel analysis. We provide new insight into the permutation methods proposed by Buja and Eyuboglu in [Multivar Behav Res. 27(4) (1992) 509--540]. Simulation and real data studies are conducted to demonstrate our results.

math.ST↗