arXiv subjects

Han Shao

Publications and source records attributed to Han Shao.

At least 19 recordsLinked to original sources

arXiv2026

Pluralistic Leaderboards

Recent leaderboard-based evaluations of large language models aggregate user feedback by fitting a Bradley--Terry model to pairwise comparisons, producing a single global ranking based on a latent quality score. While appealing for its simplicity, this approach is incompatible with heterogeneous preferences: when LLMs are used across diverse tasks and use cases, users who favor fundamentally different model behaviors can be systematically misrepresented when collapsed into a single quality score. To address this issue, we study \emph{pluralistic leaderboards} that aim to remain \emph{stable} with respect to heterogeneous user populations. Drawing on ideas from social choice theory, we adapt the notion of \emph{local stability}, which requires that no model outside the top-$k$ positions is collectively preferred to the top-$k$ set by more than $O(1/k)$ fraction of users. Building on techniques from the social choice literature, we design an alternative leaderboard mechanism that satisfies local stability while eliciting only $\widetilde{O}(k)$ pairwise comparisons per user, where $k$ is the size of the prefix for which stability is guaranteed. Using data from LMArena, we show that standard Bradley--Terry aggregation can violate local stability in practice, whereas our method provides substantially stronger stability guarantees.

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arXiv2026

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale

We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-sensitive generalization of the fundamental theorem of PAC learning: for every bounded real-valued class and every $\gamma>0$, uniform convergence at scale $\gamma$, agnostic learnability at scale $\gamma/2$, and finiteness of the fat-shattering dimension at every scale $\gamma'>\gamma$ are equivalent. This resolves a question by Anthony and Bartlett (Cambridge Univ. Press 1999) on the precise scales governing learnability, refuting a conjecture attributed there to Phil Long that a multiplicative 2-factor gap is unavoidable, and improves the upper bounds of Bartlett and Long (JCSS 1998), which incur such a loss. The key technical ingredient is a direct bound on empirical $\ell_\infty$ covering numbers, avoiding the standard detour through packing numbers. As a consequence, we obtain sharp asymptotic metric-entropy bounds in terms of the fat-shattering scale $\gamma$: an $O(\log^2 n)$ bound holds already at scale $\gamma/2$, while an $O(\log n)$ bound holds at scale $2\gamma$. We further show that the $O(\log^2 n)$ bound is sometimes tight. These results resolve open questions by Alon et al. (JACM 1997) and Rudelson and Vershynin (Ann. of Math. 2006). As an application, we establish a sharp dichotomy for bounded integral probability metrics: every such IPM is either estimable or cannot be weakly evaluated within any multiplicative factor $c<3$, while $3$-weak evaluability always holds, resolving an open question from Aiyer et al. (ICML 2026). We also highlight several open questions on quantitative sample complexity and evaluability.

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arXiv2026

Online Set Learning from Precision and Recall Feedback

We consider the problem of learning an unknown subset $N_\text{target}$ of a domain in an online setting. In each round $t$, the learner predicts a set of items ${N}_t$ and receives one of two types of feedback, each with equal probability: precision feedback, in which a randomly chosen item from the predicted set $N_t$ is revealed and the learner is told whether it belongs to $N_\text{target}$ (incurring a reward if it does), or recall feedback, in which a randomly chosen item from the target set $N_\text{target}$ is revealed and the learner is told whether it belongs to $N_t$ (incurring a reward if it does). The goal is to maximize the cumulative reward over time. This simple online set learning problem abstracts a variety of learning scenarios with precision- and recall-type feedback. We show that a hypothesis class (a family of subsets of the domain) is learnable in this setting if and only if it has finite Vapnik-Chervonenkis (VC) dimension, mirroring the classical PAC characterization. However, the resulting algorithmic structure is markedly more intricate: in contrast to standard Probably Approximately Correct (PAC) learning -- where the algorithmic landscape is governed by the simple principle of Empirical Risk Minimization (ERM) -- our partial feedback model can invalidate ERM and even all proper learning rules. We develop algorithms to address the dependencies induced by the feedback, obtaining regret guarantees in both the realizable and agnostic settings. Our results provide a qualitative characterization of learnability in this model, addressing its most basic question, while pointing to a range of natural and intriguing open questions, including the determination of optimal regret rates.

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arXiv2026

A Theoretical Framework for Statistical Evaluability of Generative Models

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and R\'enyi divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, R\'enyi and KL divergences are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.

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arXiv2026

Equitable Evaluation via Elicitation

Individuals with similar qualifications and skills may vary in their demeanor, or outward manner: some tend toward self-promotion while others are modest to the point of omitting crucial information. Comparing the self-descriptions of equally qualified job-seekers with different self-presentation styles is therefore problematic. We build an interactive AI for skill elicitation that provides accurate determination of skills while simultaneously allowing individuals to speak in their own voice. Such a system can be deployed, for example, when a new user joins a professional networking platform, or when matching employees to needs during a company reorganization. To obtain sufficient training data, we train an LLM to act as synthetic humans. Elicitation mitigates endogenous bias arising from individuals' own self-reports. To address systematic model bias we enforce a mathematically rigorous notion of equitability ensuring that the covariance between self-presentation manner and skill evaluation error is small.

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arXiv2026

On Randomized Algorithms in Online Strategic Classification

Online strategic classification studies settings in which agents strategically modify their features to obtain favorable predictions. For example, given a classifier that determines loan approval based on credit scores, applicants may open or close credit cards and bank accounts to obtain a positive prediction. The learning goal is to achieve low mistake or regret bounds despite such behavior. While randomized algorithms have the potential to offer advantages to the learner in strategic settings, they have been largely underexplored. In the realizable setting, no lower bound is known for randomized algorithms, and existing lower bound constructions for deterministic learners can be circumvented by randomization. In the agnostic setting, the best known regret upper bound is $O(T^{3/4}\log^{1/4}T|\mathcal H|)$, which is far from the standard online learning rate of $O(\sqrt{T\log|\mathcal H|})$. In this work, we provide refined bounds for online strategic classification in both settings; our bounds depend on the Littlestone dimension $\mathrm{Ldim}(\mathcal H)$ of the hypothesis class $\mathcal H$ and the maximum degree $\Delta$ of the manipulation graph. In the realizable setting, we extend, for $T > \mathrm{Ldim}(\mathcal H) \Delta^2$, the existing lower bound $\Omega(\mathrm{Ldim}(\mathcal H) \Delta)$ for deterministic learners to all learners. This yields the first lower bound that applies to randomized learners. We then provide the first randomized learner that improves the known (deterministic) upper bound of $O(\mathrm{Ldim}(\mathcal H) \cdot \Delta \log \Delta)$. In the agnostic setting, we give an improper randomized learner that improves the regret upper bound to $O(\sqrt{T\log|\mathcal H|})$, matching the standard online learning rate. We also show a larger lower bound for all proper learning rules, demonstrating that improperness is necessary to achieve the optimal rate.

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arXiv2025

Incentives in Federated Learning with Heterogeneous Agents

Federated learning promises significant sample-efficiency gains by pooling data across multiple agents, yet incentive misalignment is an obstacle: each update is costly to the contributor but boosts every participant. We introduce a game-theoretic framework that captures heterogeneous data: an agent's utility depends on who supplies each sample, not just how many. Agents aim to meet a PAC-style accuracy threshold at minimal personal cost. We show that uncoordinated play yields pathologies: pure equilibria may not exist, and the best equilibrium can be arbitrarily more costly than cooperation. To steer collaboration, we analyze the cost-minimizing contribution vector, prove that computing it is NP-hard, and derive a polynomial-time linear program that achieves a logarithmic approximation. Finally, pairing the LP with a simple pay what you contribute rule, where each agent receives a payment equal to its sample cost, yields a mechanism that is strategy-proof and, within the class of contribution-based transfers, is unique.

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arXiv2025

How Many Domains Suffice for Domain Generalization? A Tight Characterization via the Domain Shattering Dimension

We study a fundamental question of domain generalization: given a family of domains (i.e., data distributions), how many randomly sampled domains do we need to collect data from in order to learn a model that performs reasonably well on every seen and unseen domain in the family? We model this problem in the PAC framework and introduce a new combinatorial measure, which we call the domain shattering dimension. We show that this dimension characterizes the domain sample complexity. Furthermore, we establish a tight quantitative relationship between the domain shattering dimension and the classic VC dimension, demonstrating that every hypothesis class that is learnable in the standard PAC setting is also learnable in our setting.

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arXiv2025

A Machine Learning Theory Perspective on Strategic Litigation

Strategic litigation involves bringing a case to court with the goal of having an impact beyond resolving the particular dispute at hand. In a common law system, one way a case may have far-reaching impact is by establishing new legal precedent that later courts must follow. In this paper, we explore strategic litigation from the perspective of machine learning theory. We consider an abstract model of a common law legal system where a lower court decides new cases by applying a decision rule learned from a higher court's past rulings. In this model, we explore the power of a strategic litigator, who strategically brings cases to the higher court to influence the decision rule applied by the lower court in future cases. We explore questions including: What impact can a strategic litigator have? Which cases should a strategic litigator bring to court? Does it ever make sense for a strategic litigator to bring a case when they are sure the court will rule against them? We show that this strategic case selection problem has interesting structure, with even simple settings exhibiting counterintuitive phenomena. When cases are represented by points in one dimension and the lower court's learning algorithm is nearest neighbor, or as points in d dimensions and the lower court's learning algorithm is a support vector machine, we characterize the set of inducible decision rules and develop algorithms for selecting an optimal set of cases to bring to the higher court given the strategic litigator's objectives.

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arXiv2025

Should Decision-Makers Reveal Classifiers in Online Strategic Classification?

Strategic classification addresses a learning problem where a decision-maker implements a classifier over agents who may manipulate their features in order to receive favorable predictions. In the standard model of online strategic classification, in each round, the decision-maker implements and publicly reveals a classifier, after which agents perfectly best respond based on this knowledge. However, in practice, whether to disclose the classifier is often debated -- some decision-makers believe that hiding the classifier can prevent misclassification errors caused by manipulation. In this paper, we formally examine how limiting the agents' access to the current classifier affects the decision-maker's performance. Specifically, we consider an extended online strategic classification setting where agents lack direct knowledge about the current classifier and instead manipulate based on a weighted average of historically implemented classifiers. Our main result shows that in this setting, the decision-maker incurs $(1-\gamma)^{-1}$ or $k_{\text{in}}$ times more mistakes compared to the full-knowledge setting, where $k_{\text{in}}$ is the maximum in-degree of the manipulation graph (representing how many distinct feature vectors can be manipulated to appear as a single one), and $\gamma$ is the discount factor indicating agents' memory of past classifiers. Our results demonstrate how withholding access to the classifier can backfire and degrade the decision-maker's performance in online strategic classification.

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arXiv2024

Probably Approximately Precision and Recall Learning

Precision and Recall are fundamental metrics in machine learning tasks where both accurate predictions and comprehensive coverage are essential, such as in multi-label learning, language generation, medical studies, and recommender systems. A key challenge in these settings is the prevalence of one-sided feedback, where only positive examples are observed during training--e.g., in multi-label tasks like tagging people in Facebook photos, we may observe only a few tagged individuals, without knowing who else appears in the image. To address learning under such partial feedback, we introduce a Probably Approximately Correct (PAC) framework in which hypotheses are set functions that map each input to a set of labels, extending beyond single-label predictions and generalizing classical binary, multi-class, and multi-label models. Our results reveal sharp statistical and algorithmic separations from standard settings: classical methods such as Empirical Risk Minimization provably fail, even for simple hypothesis classes. We develop new algorithms that learn from positive data alone, achieving optimal sample complexity in the realizable case, and establishing multiplicative--rather than additive-approximation guarantees in the agnostic case, where achieving additive regret is impossible.

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arXiv2024

Transformation-Invariant Learning and Theoretical Guarantees for OOD Generalization

Learning with identical train and test distributions has been extensively investigated both practically and theoretically. Much remains to be understood, however, in statistical learning under distribution shifts. This paper focuses on a distribution shift setting where train and test distributions can be related by classes of (data) transformation maps. We initiate a theoretical study for this framework, investigating learning scenarios where the target class of transformations is either known or unknown. We establish learning rules and algorithmic reductions to Empirical Risk Minimization (ERM), accompanied with learning guarantees. We obtain upper bounds on the sample complexity in terms of the VC dimension of the class composing predictors with transformations, which we show in many cases is not much larger than the VC dimension of the class of predictors. We highlight that the learning rules we derive offer a game-theoretic viewpoint on distribution shift: a learner searching for predictors and an adversary searching for transformation maps to respectively minimize and maximize the worst-case loss.

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arXiv2024

Trustworthy Machine Learning under Social and Adversarial Data Sources

Machine learning has witnessed remarkable breakthroughs in recent years. As machine learning permeates various aspects of daily life, individuals and organizations increasingly interact with these systems, exhibiting a wide range of social and adversarial behaviors. These behaviors may have a notable impact on the behavior and performance of machine learning systems. Specifically, during these interactions, data may be generated by strategic individuals, collected by self-interested data collectors, possibly poisoned by adversarial attackers, and used to create predictors, models, and policies satisfying multiple objectives. As a result, the machine learning systems' outputs might degrade, such as the susceptibility of deep neural networks to adversarial examples (Shafahi et al., 2018; Szegedy et al., 2013) and the diminished performance of classic algorithms in the presence of strategic individuals (Ahmadi et al., 2021). Addressing these challenges is imperative for the success of machine learning in societal settings.

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arXiv2024

Learnability Gaps of Strategic Classification

In contrast with standard classification tasks, strategic classification involves agents strategically modifying their features in an effort to receive favorable predictions. For instance, given a classifier determining loan approval based on credit scores, applicants may open or close their credit cards to fool the classifier. The learning goal is to find a classifier robust against strategic manipulations. Various settings, based on what and when information is known, have been explored in strategic classification. In this work, we focus on addressing a fundamental question: the learnability gaps between strategic classification and standard learning. We essentially show that any learnable class is also strategically learnable: we first consider a fully informative setting, where the manipulation structure (which is modeled by a manipulation graph $G^\star$) is known and during training time the learner has access to both the pre-manipulation data and post-manipulation data. We provide nearly tight sample complexity and regret bounds, offering significant improvements over prior results. Then, we relax the fully informative setting by introducing two natural types of uncertainty. First, following Ahmadi et al. (2023), we consider the setting in which the learner only has access to the post-manipulation data. We improve the results of Ahmadi et al. (2023) and close the gap between mistake upper bound and lower bound raised by them. Our second relaxation of the fully informative setting introduces uncertainty to the manipulation structure. That is, we assume that the manipulation graph is unknown but belongs to a known class of graphs. We provide nearly tight bounds on the learning complexity in various unknown manipulation graph settings. Notably, our algorithm in this setting is of independent interest and can be applied to other problems such as multi-label learning.

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arXiv2023

On the Effect of Defections in Federated Learning and How to Prevent Them

Federated learning is a machine learning protocol that enables a large population of agents to collaborate over multiple rounds to produce a single consensus model. There are several federated learning applications where agents may choose to defect permanently$-$essentially withdrawing from the collaboration$-$if they are content with their instantaneous model in that round. This work demonstrates the detrimental impact of such defections on the final model's robustness and ability to generalize. We also show that current federated optimization algorithms fail to disincentivize these harmful defections. We introduce a novel optimization algorithm with theoretical guarantees to prevent defections while ensuring asymptotic convergence to an effective solution for all participating agents. We also provide numerical experiments to corroborate our findings and demonstrate the effectiveness of our algorithm.

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arXiv2023

Efficient Prior-Free Mechanisms for No-Regret Agents

We study a repeated Principal Agent problem between a long lived Principal and Agent pair in a prior free setting. In our setting, the sequence of realized states of nature may be adversarially chosen, the Agent is non-myopic, and the Principal aims for a strong form of policy regret. Following Camara, Hartline, and Johnson, we model the Agent's long-run behavior with behavioral assumptions that relax the common prior assumption (for example, that the Agent has no swap regret). Within this framework, we revisit the mechanism proposed by Camara et al., which informally uses calibrated forecasts of the unknown states of nature in place of a common prior. We give two main improvements. First, we give a mechanism that has an exponentially improved dependence (in terms of both running time and regret bounds) on the number of distinct states of nature. To do this, we show that our mechanism does not require truly calibrated forecasts, but rather forecasts that are unbiased subject to only a polynomially sized collection of events -- which can be produced with polynomial overhead. Second, in several important special cases -- including the focal linear contracting setting -- we show how to remove strong ``Alignment'' assumptions (which informally require that near-ties are always broken in favor of the Principal) by specifically deploying ``stable'' policies that do not have any near ties that are payoff relevant to the Principal. Taken together, our new mechanism makes the compelling framework proposed by Camara et al. much more powerful, now able to be realized over polynomially sized state spaces, and while requiring only mild assumptions on Agent behavior.

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arXiv2023

Incentivized Collaboration in Active Learning

In collaborative active learning, where multiple agents try to learn labels from a common hypothesis, we introduce an innovative framework for incentivized collaboration. Here, rational agents aim to obtain labels for their data sets while keeping label complexity at a minimum. We focus on designing (strict) individually rational (IR) collaboration protocols, ensuring that agents cannot reduce their expected label complexity by acting individually. We first show that given any optimal active learning algorithm, the collaboration protocol that runs the algorithm as is over the entire data is already IR. However, computing the optimal algorithm is NP-hard. We therefore provide collaboration protocols that achieve (strict) IR and are comparable with the best known tractable approximation algorithm in terms of label complexity.

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arXiv2023

Strategic Classification under Unknown Personalized Manipulation

We study the fundamental mistake bound and sample complexity in the strategic classification, where agents can strategically manipulate their feature vector up to an extent in order to be predicted as positive. For example, given a classifier determining college admission, student candidates may try to take easier classes to improve their GPA, retake SAT and change schools in an effort to fool the classifier. Ball manipulations are a widely studied class of manipulations in the literature, where agents can modify their feature vector within a bounded radius ball. Unlike most prior work, our work considers manipulations to be personalized, meaning that agents can have different levels of manipulation abilities (e.g., varying radii for ball manipulations), and unknown to the learner. We formalize the learning problem in an interaction model where the learner first deploys a classifier and the agent manipulates the feature vector within their manipulation set to game the deployed classifier. We investigate various scenarios in terms of the information available to the learner during the interaction, such as observing the original feature vector before or after deployment, observing the manipulated feature vector, or not seeing either the original or the manipulated feature vector. We begin by providing online mistake bounds and PAC sample complexity in these scenarios for ball manipulations. We also explore non-ball manipulations and show that, even in the simplest scenario where both the original and the manipulated feature vectors are revealed, the mistake bounds and sample complexity are lower bounded by $\Omega(|H|)$ when the target function belongs to a known class $H$.

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