Hedyeh Beyhaghi

Maria-Florina Balcan, Hedyeh Beyhaghi

We advance a recently flourishing line of work at the intersection of learning theory and computational economics by studying the learnability of two classes of mechanisms prominent in economics, namely menus of lotteries and two-part tariffs. The former is a family of randomized mechanisms designed for selling multiple items, known to achieve revenue beyond deterministic mechanisms, while the latter is designed for selling multiple units (copies) of a single item with applications in real-world scenarios such as car or bike-sharing services. We focus on learning high-revenue mechanisms of this form from buyer valuation data in both distributional settings, where we have access to buyers' valuation samples up-front, and the more challenging and less-studied online settings, where buyers arrive one-at-a-time and no distributional assumption is made about their values. We provide a suite of results with regard to these two families of mechanisms. We provide the first online learning algorithms for menus of lotteries and two-part tariffs with strong regret-bound guarantees. Since the space of parameters is infinite and the revenue functions have discontinuities, the known techniques do not readily apply. However, we are able to provide a reduction to online learning over a finite number of experts, in our case, a finite number of parameters. Furthermore, in the limited buyers type case, we show a reduction to online linear optimization, which allows us to obtain no-regret guarantees by presenting buyers with menus that correspond to a barycentric spanner. In addition, we provide algorithms with improved running times over prior work for the distributional settings. Finally, we demonstrate how techniques from the recent literature in data-driven algorithm design are insufficient for our studied problems.

Maria-Florina Balcan, Hedyeh Beyhaghi

We initiate the study of active learning algorithms for classifying strategic agents. Active learning is a well-established framework in machine learning in which the learner selectively queries labels, often achieving substantially higher accuracy and efficiency than classical supervised methods-especially in settings where labeling is costly or time-consuming, such as hiring, admissions, and loan decisions. Strategic classification, however, addresses scenarios where agents modify their features to obtain more favorable outcomes, resulting in observed data that is not truthful. Such manipulation introduces challenges beyond those in learning from clean data. Our goal is to design active and noise-tolerant algorithms that remain effective in strategic environments-algorithms that classify strategic agents accurately while issuing as few label requests as possible. The central difficulty is to simultaneously account for strategic manipulation and preserve the efficiency gains of active learning. Our main result is an algorithm for actively learning linear separators in the strategic setting that preserves the exponential improvement in label complexity over passive learning previously obtained only in the non-strategic case. Specifically, for data drawn uniformly from the unit sphere, we show that a modified version of the Active Perceptron algorithm [DKM05,YZ17] achieves excess error $ε$ using only $\tilde{O}(d \ln \frac{1}ε)$ label queries and incurs at most $\tilde{O}(d \ln \frac{1}ε)$ additional mistakes relative to the optimal classifier, even in the nonrealizable case, when a $\tildeΩ(ε)$ fraction of inputs have inconsistent labels with the optimal classifier. The algorithm is computationally efficient and, under these distributional assumptions, requires substantially fewer label queries than prior work on strategic Perceptron [ABBN21].

Amirmahdi Mirfakhar, Xuchuang Wang, Mengfan Xu et al.

Two-sided matching markets rely on preferences from both sides, yet it is often impractical to evaluate preferences. Participants, therefore, conduct a limited number of interviews, which provide early, noisy impressions and shape final decisions. We study bandit learning in matching markets with interviews, modeling interviews as \textit{low-cost hints} that reveal partial preference information to both sides. Our framework departs from existing work by allowing firm-side uncertainty: firms, like agents, may be unsure of their own preferences and can make early hiring mistakes by hiring less preferred agents. To handle this, we extend the firm's action space to allow \emph{strategic deferral} (choosing not to hire in a round), enabling recovery from suboptimal hires and supporting decentralized learning without coordination. We design novel algorithms for (i) a centralized setting with an omniscient interview allocator and (ii) decentralized settings with two types of firm-side feedback. Across all settings, our algorithms achieve time-independent regret, a substantial improvement over the $O(\log T)$ regret bounds known for learning stable matchings without interviews. Also, under mild structured markets, decentralized performance matches the centralized counterpart up to polynomial factors in the number of agents and firms.

Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi et al.

We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023), in which the decision-maker has access to machine-learned predictions of candidate values. The central challenge is to balance consistency and robustness: when predictions are accurate, the algorithm should select a near-optimal secretary, while under inaccurate predictions it should still guarantee a bounded competitive ratio. We consider both the classical Random Order Secretary Problem (ROSP), where candidates arrive in a uniformly random order, and a more natural learning-augmented model in which the decision-maker may choose the arrival order based on predicted values. We call this model the Chosen Order Secretary Problem (COSP), capturing scenarios such as interview schedules set in advance. We propose a new randomized algorithm applicable to both ROSP and COSP. Our method switches from fully trusting predictions to a threshold-based rule once a large prediction deviation is detected. Let $ε\in [0,1]$ denote the maximum multiplicative prediction error. For ROSP, our algorithm achieves a competitive ratio of $\max\{0.221, (1-ε)/(1+ε)\}$, improving upon the prior bound of $\max\{0.215, (1-ε)/(1+ε)\}$. For COSP, we achieve $\max\{0.262, (1-ε)/(1+ε)\}$, surpassing the $0.25$ worst-case bound for prior approaches and moving closer to the classical secretary benchmark of $1/e \approx 0.368$. These results highlight the benefit of combining predictions with arrival-order control in online decision-making.

Ehsan Aghazadeh, Ahmad Ghasemi, Hedyeh Beyhaghi et al.

Large language models (LLMs) are often queried multiple times at test time, with predictions aggregated by majority vote. While effective, this self-consistency strategy (arXiv:2203.11171) requires a fixed number of calls and can fail when the correct answer is rare. We introduce Confidence-Guided Early Stopping (CGES), a Bayesian framework that forms posteriors over candidate answers using scalar confidence signals derived from token probabilities or reward models. CGES adaptively halts sampling once the posterior mass of a candidate exceeds a threshold. We provide theoretical guarantees for both perfectly calibrated confidences and realistic noisy confidence signals. Across five reasoning benchmarks, CGES reduces the average number of model calls by about 69 percent (for example, from 16.0 to 4.9) while matching the accuracy of self-consistency within 0.06 percentage points.

Xuchuang Wang, Bo Sun, Hedyeh Beyhaghi et al.

This paper introduces a novel multi-agent ski-rental problem that generalizes the classical ski-rental dilemma to a group setting where agents incur individual and shared costs. In our model, each agent can either rent at a fixed daily cost, or purchase a pass at an individual cost, with an additional third option of a discounted group pass available to all. We consider scenarios in which agents' active days differ, leading to dynamic states as agents drop out of the decision process. To address this problem from different perspectives, we define three distinct competitive ratios: overall, state-dependent, and individual rational. For each objective, we design and analyze optimal deterministic and randomized policies. Our deterministic policies employ state-aware threshold functions that adapt to the dynamic states, while our randomized policies sample and resample thresholds from tailored state-aware distributions. The analysis reveals that symmetric policies, in which all agents use the same threshold, outperform asymmetric ones. Our results provide competitive ratio upper and lower bounds and extend classical ski-rental insights to multi-agent settings, highlighting both theoretical and practical implications for group decision-making under uncertainty.

Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum et al.

We consider the problem of helping agents improve by setting short-term goals. Given a set of target skill levels, we assume each agent will try to improve from their initial skill level to the closest target level within reach or do nothing if no target level is within reach. We consider two models: the common improvement capacity model, where agents have the same limit on how much they can improve, and the individualized improvement capacity model, where agents have individualized limits. Our goal is to optimize the target levels for social welfare and fairness objectives, where social welfare is defined as the total amount of improvement, and fairness objectives are considered where the agents belong to different underlying populations. A key technical challenge of this problem is the non-monotonicity of social welfare in the set of target levels, i.e., adding a new target level may decrease the total amount of improvement as it may get easier for some agents to improve. This is especially challenging when considering multiple groups because optimizing target levels in isolation for each group and outputting the union may result in arbitrarily low improvement for a group, failing the fairness objective. Considering these properties, we provide algorithms for optimal and near-optimal improvement for both social welfare and fairness objectives. These algorithmic results work for both the common and individualized improvement capacity models. Furthermore, we show a placement of target levels exists that is approximately optimal for the social welfare of each group. Unlike the algorithmic results, this structural statement only holds in the common improvement capacity model, and we show counterexamples in the individualized improvement capacity model. Finally, we extend our algorithms to learning settings where we have only sample access to the initial skill levels of agents.

Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum et al.

In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum et al.

The classical Perceptron algorithm provides a simple and elegant procedure for learning a linear classifier. In each step, the algorithm observes the sample's position and label and updates the current predictor accordingly if it makes a mistake. However, in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, the classifier may not be able to observe the true position of agents but rather a position where the agent pretends to be. Unlike the original setting with perfect knowledge of positions, in this situation the Perceptron algorithm fails to achieve its guarantees, and we illustrate examples with the predictor oscillating between two solutions forever, making an unbounded number of mistakes even though a perfect large-margin linear classifier exists. Our main contribution is providing a modified Perceptron-style algorithm which makes a bounded number of mistakes in presence of strategic agents with both $\ell_2$ and weighted $\ell_1$ manipulation costs. In our baseline model, knowledge of the manipulation costs (i.e., the extent to which an agent may manipulate) is assumed. In our most general model, we relax this assumption and provide an algorithm which learns and refines both the classifier and its cost estimates to achieve good mistake bounds even when manipulation costs are unknown.