arXiv subjects

Xiaocheng Li

Publications and source records attributed to Xiaocheng Li.

At least 19 recordsLinked to original sources

arXiv2026

Understanding Uncertainty Sampling via Equivalent Loss

Uncertainty sampling is a classical active-learning strategy, yet the statistical objective induced by its query rule is often implicit. We introduce the equivalent loss, whose gradient is the original loss gradient multiplied by the query probability. This construction places probabilistic, margin-based, and threshold-based uncertainty rules within a common framework. For binary classification, concrete equivalent losses and surrogate link functions show how uncertainty weighting preserves calibration while reshaping optimization geometry. When the equivalent loss is convex, we derive a finite-sample excess-risk bound with a fixed learning rate and an explicit constant controlling the tradeoff between initial error and query-weighted gradient variance. A feasible choice based only on maximal uncertainty yields a leading classification-risk upper bound no larger than the corresponding passive-learning bound at the same expected label budget; knowledge of the average query rate sharpens this comparison. We also analyze pool-based sampling, characterize the integrability obstruction beyond scalar prediction, and examine the query-clock dynamics of momentum methods. Together, these results provide a reusable route from a classical acquisition rule to its induced objective, statistical guarantees, and optimization behavior.

cs.LG↗

arXiv2026

Users as Annotators: LLM Preference Learning from Comparison Mode

Pairwise preference data have played an important role in the alignment of large language models (LLMs). Each sample of such data consists of a prompt, two different responses to the prompt, and a binary label indicating which of the two responses is better. The labels are usually annotated by professional human annotators. In this paper, we consider an alternative approach to collect pairwise preference data -- user annotation from comparison mode. With the increasingly wider adoption of LLMs among the population, users are contributing more and more of their preference labels through their daily interactions with the LLMs. The upside of such labels is that users are the best experts in judging the responses to their own queries/prompts, but the downside is the lack of quality control in these labels. In this paper, we consider a new idea of generating two responses from two different models or two different versions of the same model. The asymmetry allows us to make an inference of the user's data quality through our proposed user behavior model. We develop an expectation-maximization algorithm to estimate a latent quality factor of the user, and filter users' annotation data accordingly. The downstream task shows the effectiveness of our approach in both capturing the user behavior and data filtering for LLM alignment.

cs.CL↗

arXiv2026

Calibrating conditional risk

We introduce and study the problem of calibrating conditional risk, which involves estimating the expected loss of a prediction model conditional on input features. We analyze this problem in both classification and regression settings and show that it is fundamentally equivalent to a standard regression task. For classification settings, we further establish a connection between conditional risk calibration and individual/conditional probability calibration, and develop theoretical insights for the performance metric. This reveals that while conditional risk calibration is related to existing uncertainty quantification problems, it remains a distinct and standalone machine learning problem. Empirically, we validate our theoretical findings and demonstrate the practical implications of conditional risk calibration in the learning to defer (L2D) framework. Our systematic experiments provide both qualitative and quantitative assessments, offering guidance for future research in uncertainty-aware decision-making.

cs.LG↗

arXiv2026

Incentivizing High-Quality Human Annotations with Golden Questions

Human-annotated data plays a vital role in training large language models (LLMs), such as supervised fine-tuning and human preference alignment. However, it is not guaranteed that paid human annotators produce high-quality data. In this paper, we study how to incentivize human annotators to do so. We start from a principal-agent model to model the dynamics between the company (the principal) and the annotator (the agent), where the principal can only monitor the annotation quality by examining $n$ samples. We investigate the maximum likelihood estimators (MLE) and the corresponding hypothesis testing to incentivize annotators: the agent is given a bonus if the MLE passes the test. By analyzing the variance of the outcome, we show that the strategic behavior of the agent makes the hypothesis testing very different from traditional ones: Unlike the exponential rate proved by the large deviation theory, the principal-agent model's hypothesis testing rate is of $Θ(1/\sqrt{n \log n})$. Our theory implies two criteria for the \emph{golden questions} to monitor the performance of the annotators: they should be of (1) high certainty and (2) similar format to normal ones. In that light, we select a set of golden questions in human preference data. By doing incentive-compatible experiments, we find out that the annotators' behavior is better revealed by those golden questions, compared to traditional survey techniques such as instructed manipulation checks.

cs.GT↗

arXiv2026

How Humans Help LLMs: Assessing and Incentivizing Human Preference Annotators

Human-annotated preference data play an important role in aligning large language models (LLMs). In this paper, we study two connected questions: how to monitor the quality of human preference annotators and how to incentivize them to provide high-quality annotations. In current practice, expert-based monitoring is a natural workhorse for quality control, but it performs poorly in preference annotation because annotators are heterogeneous and downstream model performance is an indirect and noisy proxy for annotation quality. We therefore propose a self-consistency monitoring scheme tailored to preference annotation, and analyze the statistical sample complexity of both methods. This practitioner-facing analysis identifies how many inspected samples are needed to reliably assess an annotator and shows when self-consistency monitoring can outperform expert-based monitoring. We then use the resulting monitoring signal as the performance measure in a principal-agent model, which lets us study a second sample-complexity question: how many monitored samples are needed before simple contracts perform close to the ideal benchmark in which annotation quality is perfectly observable. Under this continuous action space, we show that this shortfall scales as $Θ(1/\sqrt{\mathcal{I} n \log n})$ for binary contracts and $Θ(1/(\mathcal{I}n))$ for linear contracts, where $\mathcal{I}$ is the Fisher information and $n$ is the number of samples; we further show that the linear contracts are rate-optimal among general contracts. This contrasts with the known result that binary contracts are optimal and of $\exp(-Θ(n))$ when the action space is discrete \citep{frick2023monitoring}.

cs.LG↗

arXiv2026

Towards Better Statistical Understanding of Watermarking LLMs

In this paper, we study the problem of watermarking large language models (LLMs). We consider the trade-off between model distortion and detection ability and formulate it as a constrained optimization problem based on the red-green list watermarking algorithm. We show that the optimal solution to the optimization problem enjoys a nice analytical property which provides a better understanding and inspires the algorithm design for the watermarking process. We develop an online dual gradient ascent watermarking algorithm in light of this optimization formulation and prove its asymptotic Pareto optimality between model distortion and detection ability. Such a result guarantees an averaged increased green list probability and henceforth detection ability explicitly (in contrast to previous results). Moreover, we provide a systematic discussion on the choice of the model distortion metrics for the watermarking problem. We justify our choice of KL divergence and present issues with the existing criteria of ``distortion-free'' and perplexity. Finally, we empirically evaluate our algorithms on extensive datasets against benchmark algorithms.

cs.LG↗

arXiv2025

Quantile Markov Decision Process

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific quantile of the cumulative reward instead of its expectation. In this paper we consider the problem of optimizing the quantiles of the cumulative rewards of a Markov decision process (MDP), which we refer to as a quantile Markov decision process (QMDP). We provide analytical results characterizing the optimal QMDP value function and present a dynamic programming-based algorithm to solve for the optimal policy. The algorithm also extends to the MDP problem with a conditional value-at-risk (CVaR) objective. We illustrate the practical relevance of our model by evaluating it on an HIV treatment initiation problem, where patients aim to balance the potential benefits and risks of the treatment.

cs.AI↗

arXiv2025

Exploration-free Algorithms for Multi-group Mean Estimation

We address the problem of multi-group mean estimation, which seeks to allocate a finite sampling budget across multiple groups to obtain uniformly accurate estimates of their means. Unlike classical multi-armed bandits, whose objective is to minimize regret by identifying and exploiting the best arm, the optimal allocation in this setting requires sampling every group on the order of $Θ(T)$ times. This fundamental distinction makes exploration-free algorithms both natural and effective. Our work makes three contributions. First, we strengthen the existing results on subgaussian variance concentration using the Hanson-Wright inequality and identify a class of strictly subgaussian distributions that yield sharper guarantees. Second, we design exploration-free non-adaptive and adaptive algorithms, and we establish tighter regret bounds than the existing results. Third, we extend the framework to contextual bandit settings, an underexplored direction, and propose algorithms that leverage side information with provable guarantees. Overall, these results position exploration-free allocation as a principled and efficient approach to multi-group mean estimation, with potential applications in experimental design, personalization, and other domains requiring accurate multi-group inference.

cs.LG↗

arXiv2025

Risk Profiling and Modulation for LLMs

Large language models (LLMs) are increasingly used for decision-making tasks under uncertainty; however, their risk profiles and how they are influenced by prompting and alignment methods remain underexplored. Existing studies have primarily examined personality prompting or multi-agent interactions, leaving open the question of how post-training influences the risk behavior of LLMs. In this work, we propose a new pipeline for eliciting, steering, and modulating LLMs' risk profiles, drawing on tools from behavioral economics and finance. Using utility-theoretic models, we compare pre-trained, instruction-tuned, and RLHF-aligned LLMs, and find that while instruction-tuned models exhibit behaviors consistent with some standard utility formulations, pre-trained and RLHF-aligned models deviate more from any utility models fitted. We further evaluate modulation strategies, including prompt engineering, in-context learning, and post-training, and show that post-training provides the most stable and effective modulation of risk preference. Our findings provide insights into the risk profiles of different classes and stages of LLMs and demonstrate how post-training modulates these profiles, laying the groundwork for future research on behavioral alignment and risk-aware LLM design.

cs.AI↗

arXiv2025

Online-Optimized RAG for Tool Use and Function Calling

In many applications, retrieval-augmented generation (RAG) drives tool use and function calling by embedding the (user) queries and matching them to pre-specified tool/function descriptions. In this paper, we address an embedding misalignment issue that often arises in practical applications due to imperfect embedding models or noisy descriptions; such misalignment may lead to incorrect retrieval and task failure. We introduce Online-Optimized RAG, a deployment-time framework that continually adapts retrieval embeddings from live interactions using minimal feedback (e.g., task success). Online-Optimized RAG applies lightweight online gradient updates with negligible per-query latency and requires no changes to the underlying LLM. The method is plug-and-play: it supports both single- and multi-hop tool use, dynamic tool inventories, and $K$-retrieval with re-ranking. We provide a problem-dependent theoretical analysis that quantifies how the method's performance depends on the initialization quality of the embeddings and other related quantities. Across diverse tool-use and document-retrieval scenarios, our Online-Optimized RAG consistently improves tool selection accuracy and end-task success, thus providing a simple, practical path to robust, self-improving RAG systems.

cs.SE↗

arXiv2025

Algebraic and analytic properties of invariant differential operators on a homogeneous space of complexity $1$

Denote by $SL_3(\mathbb R)$ the special linear group of degree 3 over the real numbers, $A$ the subgroup consisting of the diagonal matrices with positive entries. In this paper, we study the algebraic and analytic properties of the invariant differential operators on the homogeneous space $SL_3(\mathbb R)/A$. Firstly, we specify the noncommutative algebra of invariant differential operators in terms of generators and their relations. Secondly, we describe the center of this algebra and prove that all of its symmetric elements are essentially self-adjoint. Thirdly, for the first time on homogeneous spaces, we identify several essentially self-adjoint invariant differential operators which do not lie in the center of the algebra of invariant differential operators.

math.RT↗

arXiv2025

Collaborative Prediction: To Join or To Disjoin Datasets

With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even for simple prediction models. In this work, we study the problem of developing practical algorithms that select appropriate dataset to minimize population loss of our prediction model with high probability. Broadly speaking, we investigate when datasets from different sources can be effectively merged to enhance the predictive model's performance, and propose a practical algorithm with theoretical guarantees. By leveraging an oracle inequality and data-driven estimators, the algorithm reduces population loss with high probability. Numerical experiments demonstrate its effectiveness in both standard linear regression and broader machine learning applications. Code is available at https://github.com/kkrokii/collaborative_prediction.

stat.ML↗

arXiv2025

Out-of-distribution Robust Optimization

In this paper, we consider the contextual robust optimization problem under an out-of-distribution setting. The contextual robust optimization problem considers a risk-sensitive objective function for an optimization problem with the presence of a context vector (also known as covariates or side information) capturing related information. While the existing works mainly consider the in-distribution setting, and the resultant robustness achieved is in an out-of-sample sense, our paper studies an out-of-distribution setting where there can be a difference between the test environment and the training environment where the data are collected. We propose methods that handle this out-of-distribution setting, and the key relies on a density ratio estimation for the distribution shift. We show that additional structures such as covariate shift and label shift are not only helpful in defending distribution shift but also necessary in avoiding non-trivial solutions compared to other principled methods such as distributionally robust optimization. We also illustrate how the covariates can be useful in this procedure. Numerical experiments generate more intuitions and demonstrate that the proposed methods can help avoid over-conservative solutions.

math.OC↗

arXiv2025

OMGPT: A Sequence Modeling Framework for Data-driven Operational Decision Making

We build a Generative Pre-trained Transformer (GPT) model from scratch to solve sequential decision making tasks arising in contexts of operations research and management science which we call OMGPT. We first propose a general sequence modeling framework to cover several operational decision making tasks as special cases, such as dynamic pricing, inventory management, resource allocation, and queueing control. Under the framework, all these tasks can be viewed as a sequential prediction problem where the goal is to predict the optimal future action given all the historical information. Then we train a transformer-based neural network model (OMGPT) as a natural and powerful architecture for sequential modeling. This marks a paradigm shift compared to the existing methods for these OR/OM tasks in that (i) the OMGPT model can take advantage of the huge amount of pre-trained data; (ii) when tackling these problems, OMGPT does not assume any analytical model structure and enables a direct and rich mapping from the history to the future actions. Either of these two aspects, to the best of our knowledge, is not achieved by any existing method. We establish a Bayesian perspective to theoretically understand the working mechanism of the OMGPT on these tasks, which relates its performance with the pre-training task diversity and the divergence between the testing task and pre-training tasks. Numerically, we observe a surprising performance of the proposed model across all the above tasks.

cs.LG↗

arXiv2024

Reward Modeling with Ordinal Feedback: Wisdom of the Crowd

Learning a reward model (RM) from human preferences has been an important component in aligning large language models (LLMs). The canonical setup of learning RMs from pairwise preference data is rooted in the classic Bradley-Terry (BT) model that accepts binary feedback, i.e., the label being either Response 1 is better than Response 2, or the opposite. Such a setup inevitably discards potentially useful samples (such as "tied" between the two responses) and loses more fine-grained information (such as "slightly better"). In this paper, we propose a framework for learning RMs under ordinal feedback which generalizes the case of binary preference feedback to any arbitrary granularity. Specifically, we first identify a marginal unbiasedness condition, which generalizes the assumption of the BT model in the existing binary feedback setting. The condition validates itself via the sociological concept of the wisdom of the crowd. Under the condition, we develop a natural probability model for pairwise preference data under ordinal feedback and analyze its properties. We prove the statistical benefits of ordinal feedback in terms of reducing the Rademacher complexity compared to the case of binary feedback. The proposed learning objective and the theory also extend to hinge loss and direct policy optimization (DPO). In particular, the theoretical analysis may be of independent interest when applying to a seemingly unrelated problem of knowledge distillation to interpret the bias-variance trade-off therein. The framework also sheds light on writing guidance for human annotators. Our numerical experiments validate that fine-grained feedback leads to better reward learning for both in-distribution and out-of-distribution settings. Further experiments show that incorporating a certain proportion of samples with tied preference boosts RM learning.

cs.LG↗

arXiv2024

Personalized Playback Technology: How Short Video Services Create Excellent User Experience

Short-form video content has become increasingly popular and influential in recent years. Its concise yet engaging format aligns well with todays' fast-paced and on-the-go lifestyles, making it a dominating trend in the digital world. As one of the front runners in the short video platform space, ByteDance has been highly successful in delivering a one-of-a-kind short video experience and attracting billions of users worldwide. One key contributing factor is its advanced end-to-end personalized short video playback technology, where we pioneered and developed the new technical field over the past five years to optimize user experience. This paper introduces the major concepts and methodologies of this personalized video playback technology that distinguish it from traditional multimedia technologies. More details, including goal setting, iterative process, modeling, experimental methods and required supporting systems, are also provided to encourage deeper research in this area.

cs.MM↗

arXiv2024

Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach

In this paper, we study the problem of uncertainty estimation and calibration for LLMs. We begin by formulating the uncertainty estimation problem, a relevant yet underexplored area in existing literature. We then propose a supervised approach that leverages labeled datasets to estimate the uncertainty in LLMs' responses. Based on the formulation, we illustrate the difference between the uncertainty estimation for LLMs and that for standard ML models and explain why the hidden neurons of the LLMs may contain uncertainty information. Our designed approach demonstrates the benefits of utilizing hidden activations to enhance uncertainty estimation across various tasks and shows robust transferability in out-of-distribution settings. We distinguish the uncertainty estimation task from the uncertainty calibration task and show that better uncertainty estimation leads to better calibration performance. Furthermore, our method is easy to implement and adaptable to different levels of model accessibility including black box, grey box, and white box.

cs.LG↗

arXiv2024

Understanding the Training and Generalization of Pretrained Transformer for Sequential Decision Making

In this paper, we consider the supervised pre-trained transformer for a class of sequential decision-making problems. The class of considered problems is a subset of the general formulation of reinforcement learning in that there is no transition probability matrix; though seemingly restrictive, the subset class of problems covers bandits, dynamic pricing, and newsvendor problems as special cases. Such a structure enables the use of optimal actions/decisions in the pre-training phase, and the usage also provides new insights for the training and generalization of the pre-trained transformer. We first note the training of the transformer model can be viewed as a performative prediction problem, and the existing methods and theories largely ignore or cannot resolve an out-of-distribution issue. We propose a natural solution that includes the transformer-generated action sequences in the training procedure, and it enjoys better properties both numerically and theoretically. The availability of the optimal actions in the considered tasks also allows us to analyze the properties of the pre-trained transformer as an algorithm and explains why it may lack exploration and how this can be automatically resolved. Numerically, we categorize the advantages of pre-trained transformers over the structured algorithms such as UCB and Thompson sampling into three cases: (i) it better utilizes the prior knowledge in the pre-training data; (ii) it can elegantly handle the misspecification issue suffered by the structured algorithms; (iii) for short time horizon such as $T\le50$, it behaves more greedy and enjoys much better regret than the structured algorithms designed for asymptotic optimality.

cs.LG↗