arXiv subjects

Maria-Florina Balcan

Publications and source records attributed to Maria-Florina Balcan.

At least 19 recordsLinked to original sources

arXiv2026

Learning to Price with Persuasion

Motivated by modern marketplaces, where the platform or the seller routinely gathers detailed user profiles, we study a novel learning theoretic model that simultaneously involves information and mechanism design. Specifically, we consider the economic setting recently introduced by Bergemann et al. (2022), where in addition to the menu of quality-price pairs, the seller offers information on the value of the match between product quality and buyer's taste via a signaling scheme. We relax the assumption that the seller knows the buyers' belief about the distribution of tastes and study the sample requirements of designing a revenue maximizing scheme. We consider both the batch setting where we have access to data from a set of i.i.d. buyers and an online demand query model where we observe the buyers' behaviors to seller's schemes. Despite the apparent non-convexity of the problem, we also give the first FPTAS to compute a scheme that maximizes the revenue within an arbitrarily small additive loss, which was left open by Bergemann et al. (2022). Overall, this brings a new learning perspective in asymmetric economic settings where buyers and sellers know different types of information.

cs.GT↗

arXiv2026

Efficient Online Proportional Sampling with Applications to Smoothed Online Learning

We study the problem of efficient online proportional sampling from a high-dimensional domain under a $\sigma$-smoothed adversary, where the sampling distribution is induced by a dynamically evolving weight function defined over a sequence of piecewise-structured partitions. This setting captures a broad range of applications, including principal-agent games (e.g., pricing and contract design), and algorithm configuration and parameter tuning. The central challenge is maintaining an efficient data structure as the induced partition grows increasingly complex over time -- naively, the number of subregions can grow as $O(t^d)$ by round $t$ in $d$ dimensions. We design a data structure that supports efficient updates and proportional sampling while avoiding the cost of explicitly maintaining this exponential growth, where the discontinuities are structured from axis-parallel hyperplanes. Under a $\sigma$-smoothed adaptive adversary, we prove a tight $O(\sqrt{\sigma T})$ bound on the depth of our data structure, and an $O(\log T)$ bound under a random-order adversary -- to our knowledge, the first such results for this class of problems. We apply this framework to online learning with piecewise-structured rewards, obtaining efficient no-regret algorithms under both full-information and bandit feedback, with provable sublinear regret guarantees.

cs.LG↗

arXiv2026

Reward Learning from Best-of-$N$ Preference Data: Targets, Tradeoffs, and Design Principles

Best-of-$N$ sampling is widely used to construct pairwise preference data: $N$ candidates are drawn from a base distribution, and the best is paired with a rejected response. Despite its widespread use, what Bradley--Terry (BT) reward learning extracts from such data, and how to choose $N$ and the base distribution, remain unclear. We specialize a recent analysis of preference data via its induced conditional distribution to Best-of-$N$. For independent-reference variants, we derive closed-form reward targets as explicit functions of $N$ and the base distribution, and show that they preserve the latent reward ranking. For the practical Best-vs-Random and Best-vs-Worst variants, chosen and rejected responses are coupled through the same candidate set, so exact BT representability generally fails; nevertheless, bounded-class minimizers approach the reference targets as $N$ grows. Although margin and connectivity are known to govern sample efficiency in pairwise preference learning, Best-of-$N$ couples them through $N$ in opposing directions: larger $N$ widens pairwise margins but reduces connectivity. This trade-off yields two design principles: use larger $N$ when preference labels are the bottleneck, smaller $N$ when generation is the bottleneck; and shape the base distribution to place mass between the responses whose comparison matters most at test time. Experiments on synthetic and real preference data support the predicted dependence on sample size and base-distribution shape.

stat.ML↗

arXiv2026

Verify to Amplify: Improving Reasoning via Learned Chain-of-Thought Verification

Large Language Models (LLMs) using chain-of-thought have demonstrated great potential for solving complex reasoning and planning tasks. Despite these advances, LLM-generated outputs remain susceptible to errors, making verification important for reliable reasoning systems. Learned verifiers can increase trust, enforce safety constraints, and ensure alignment with personal preferences, while also providing feedback to improve generation. This raises a central challenge: when learned verifiers are used to guide generation, the feedback loop between generator and verifier may induce a distribution shift. This is particularly salient for process reward models, a prominent class of learned verifiers that score or classify individual steps in a chain-of-thought reasoning trace. Motivated by this challenge, we propose a new online learning framework for chain-of-thought verifiers that, given a problem statement and a reasoning trace, check the correctness of each reasoning step given the preceding steps. Highlighting the asymmetric role of soundness errors (accepting an incorrect reasoning step) and completeness errors (flagging a correct step as wrong), we introduce novel notions of dimension that characterize their optimal tradeoff. We then show how our learned verifiers can boost the accuracy of a weak generator. Assuming that the generator can produce a correct next step with a small success probability, we show how to learn a strong generator with small error and abstention rates. Our results also allow learning from offline data when queries to an expert verifier can be simulated from a small set of correct reasoning traces. However, we establish a separation between our approach and learning from offline expert demonstrations: we show that learning from offline demonstrations cannot in general achieve the soundness-completeness guarantees produced by our interactive learning approach.

cs.LG↗

arXiv2026

The Complexity of Proper Equilibrium in Extensive-Form and Polytope Games

The proper equilibrium, introduced by Myerson (1978), is a classic refinement of the Nash equilibrium that has been referred to as the "mother of all refinements." For normal-form games, computing a proper equilibrium is known to be PPAD-complete for two-player games and FIXP$_a$-complete for games with at least three players. However, the complexity beyond normal-form games -- in particular, for extensive-form games (EFGs) -- was a long-standing open problem first highlighted by Miltersen and S{\o}rensen (SODA '08). In this paper, we resolve this problem by establishing PPAD- and FIXP$_a$-membership (and hence completeness) of normal-form proper equilibria in two-player and multi-player EFGs respectively. Our main ingredient is a technique for computing a perturbed (proper) best response that can be computed efficiently in EFGs. This is despite the fact that, as we show, computing a best response using the classic perturbation of Kohlberg and Mertens based on the permutahedron is #P-hard even in Bayesian games. In stark contrast, we show that computing a proper equilibrium in polytope games is NP-hard. This marks the first natural class in which the complexity of computing equilibrium refinements does not collapse to that of Nash equilibria, and the first problem in which equilibrium computation in polytope games is strictly harder -- unless there is a collapse in the complexity hierarchy -- relative to extensive-form games.

cs.GT↗

arXiv2026

What Does Preference Learning Recover from Pairwise Comparison Data?

Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets $(x, y^+, y^-)$, where response $y^+$ is preferred over response $y^-$ for context $x$. The Bradley--Terry (BT) model is the predominant approach, modeling preference probabilities as a function of latent score differences. Standard practice assumes data follows this model and learns the latent scores accordingly. However, real data may violate this assumption, and it remains unclear what BT learning recovers in such cases. Starting from triplet comparison data, we formalize the preference information it encodes through the conditional preference distribution (CPRD). We give precise conditions for when BT is appropriate for modeling the CPRD, and identify factors governing sample efficiency -- namely, margin and connectivity. Together, these results offer a data-centric foundation for understanding what preference learning actually recovers.

cs.LG↗

arXiv2025

The Active and Noise-Tolerant Strategic Perceptron

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 $\epsilon$ using only $\tilde{O}(d \ln \frac{1}{\epsilon})$ label queries and incurs at most $\tilde{O}(d \ln \frac{1}{\epsilon})$ additional mistakes relative to the optimal classifier, even in the nonrealizable case, when a $\tilde{\Omega}(\epsilon)$ 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].

cs.LG↗

arXiv2025

The Complexity of Equilibrium Refinements in Potential Games

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show that computing a pure(-strategy) perfect or proper equilibrium is $\mathsf{PLS}$-complete in concise potential games in normal form. For pure perfect equilibria, we extend this result to general polytope games, which includes extensive-form games. We next turn to more structured classes of games, namely symmetric network congestion and symmetric matroid congestion games. For both classes, we show that a pure perfect equilibrium can be computed in polynomial time, strengthening the existing results for pure Nash equilibria. More broadly, we make a connection between strongly polynomial-time algorithms and efficient perturbed optimization using fractional interpolation. On the other hand, we establish that, for a certain class of potential games, there is an exponential separation in the length of the best-response path between perfect and Nash equilibria. Finally, for mixed strategies, we prove that computing a point geometrically near a perfect equilibrium requires a doubly exponentially small perturbation even in $3$-player potential games in normal form. As a byproduct, this significantly strengthens and simplifies a seminal result of Etessami and Yannakakis (FOCS '07). On the flip side, in the special case of polymatrix potential games, we show that equilibrium refinements are amenable to perturbed gradient descent dynamics, thereby belonging to the complexity class $\mathsf{CLS}$. This provides a principled and practical way of refining the landscape of gradient descent in constrained optimization.

cs.GT↗

arXiv2025

Distribution-dependent Generalization Bounds for Tuning Linear Regression Across Tasks

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties like effective variable selection. We study the recently introduced direction of tuning regularization hyperparameters in linear regression across multiple related tasks. We obtain distribution-dependent bounds on the generalization error for the validation loss when tuning the L1 and L2 coefficients, including ridge, lasso and the elastic net. In contrast, prior work develops bounds that apply uniformly to all distributions, but such bounds necessarily degrade with feature dimension, d. While these bounds are shown to be tight for worst-case distributions, our bounds improve with the "niceness" of the data distribution. Concretely, we show that under additional assumptions that instances within each task are i.i.d. draws from broad well-studied classes of distributions including sub-Gaussians, our generalization bounds do not get worse with increasing d, and are much sharper than prior work for very large d. We also extend our results to a generalization of ridge regression, where we achieve tighter bounds that take into account an estimate of the mean of the ground truth distribution.

cs.LG↗

arXiv2025

On Learning Verifiers and Implications to Chain-of-Thought Reasoning

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which can be checked with a formal verifier, is one approach to addressing this issue. However, currently LLMs are simply not good enough to solve complex problems in a formal way, and even just formalizing an informal problem statement can be challenging. Motivated by this fact, in this work we consider the problem of learning reliable verifiers for natural language Chain-of-Thought reasoning. That is, given a problem statement and step-by-step solution in natural language, the aim of the verifier is to output [Yes] if the reasoning steps in the solution are all valid, and [No] otherwise. In this work we give a formal PAC-learning framework for studying this problem. We propose and analyze several natural verification goals, at different levels of strength, in this framework. We provide sample complexity upper-bounds for learning verifiers satisfying these goals, as well as lower-bound and impossibility results for learning other natural verification objectives without additional assumptions.

cs.LG↗

arXiv2025

Weakest Bidder Types and New Core-Selecting Combinatorial Auctions

Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders -- with the seller -- to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders -- these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques -- and build upon existing quadratic programming techniques -- to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.

cs.GT↗

arXiv2025

Revenue-Optimal Efficient Mechanism Design with General Type Spaces

We derive the revenue-optimal efficient (welfare-maximizing) mechanism in a general multidimensional mechanism design setting when type spaces -- that is, the underlying domains from which agents' values come from -- can capture arbitrarily complex informational constraints about the agents. Type spaces can encode information about agents representing, for example, machine learning predictions of agent behavior, institutional knowledge about feasible market outcomes (such as item substitutability or complementarity in auctions), and correlations between multiple agents. Prior work has only dealt with connected type spaces, which are not expressive enough to capture many natural kinds of constraints such as disjunctive constraints. We provide two characterizations of the optimal mechanism based on allocations and connected components; both make use of an underlying network flow structure to the mechanism design. Our results significantly generalize and improve the prior state of the art in revenue-optimal efficient mechanism design. They also considerably expand the scope of what forms of agent information can be expressed and used to improve revenue.

cs.GT↗

arXiv2025

Learning in Structured Stackelberg Games

We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. Notably, we find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that tightly characterizes the leader's instance-optimal regret. We term this the Stackelberg-Littlestone dimension, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

cs.GT↗

arXiv2025

Nearly-Optimal Bandit Learning in Stackelberg Games with Side Information

We study the problem of online learning in Stackelberg games with side information between a leader and a sequence of followers. In every round the leader observes contextual information and commits to a mixed strategy, after which the follower best-responds. We provide learning algorithms for the leader which achieve $O(T^{1/2})$ regret under bandit feedback, an improvement from the previously best-known rates of $O(T^{2/3})$. Our algorithms rely on a reduction to linear contextual bandits in the utility space: In each round, a linear contextual bandit algorithm recommends a utility vector, which our algorithm inverts to determine the leader's mixed strategy. We extend our algorithms to the setting in which the leader's utility function is unknown, and also apply it to the problems of bidding in second-price auctions with side information and online Bayesian persuasion with public and private states. Finally, we observe that our algorithms empirically outperform previous results on numerical simulations.

cs.LG↗

arXiv2025

Sample complexity of data-driven tuning of model hyperparameters in neural networks with structured parameter-dependent dual function

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

cs.LG↗

arXiv2024

Algorithm Configuration for Structured Pfaffian Settings

Data-driven algorithm design automatically adapts algorithms to specific application domains, achieving better performance. In the context of parameterized algorithms, this approach involves tuning the algorithm's hyperparameters using problem instances drawn from the problem distribution of the target application domain. This can be achieved by maximizing empirical utilities that measure the algorithms' performance as a function of their hyperparameters, using problem instances. While empirical evidence supports the effectiveness of data-driven algorithm design, providing theoretical guarantees for several parameterized families remains challenging. This is due to the intricate behaviors of their corresponding utility functions, which typically admit piecewise discontinuous structures. In this work, we present refined frameworks for providing learning guarantees for parameterized data-driven algorithm design problems in both distributional and online learning settings. For the distributional learning setting, we introduce the \textit{Pfaffian GJ framework}, an extension of the classical \textit{GJ framework}, that is capable of providing learning guarantees for function classes for which the computation involves Pfaffian functions. Unlike the GJ framework, which is limited to function classes with computation characterized by rational functions, our proposed framework can deal with function classes involving Pfaffian functions, which are much more general and widely applicable. We then show that for many parameterized algorithms of interest, their utility function possesses a \textit{refined piecewise structure}, which automatically translates to learning guarantees using our proposed framework.

cs.LG↗

arXiv2024

Subsidy design for better social outcomes

Overcoming the impact of selfish behavior of rational players in multiagent systems is a fundamental problem in game theory. Without any intervention from a central agent, strategic users take actions in order to maximize their personal utility, which can lead to extremely inefficient overall system performance, often indicated by a high Price of Anarchy. Recent work (Lin et al. 2021) investigated and formalized yet another undesirable behavior of rational agents, that of avoiding freely available information about the game for selfish reasons, leading to worse social outcomes. A central planner can significantly mitigate these issues by injecting a subsidy to reduce certain costs associated with the system and obtain net gains in the system performance. Crucially, the planner needs to determine how to allocate this subsidy effectively. We formally show that designing subsidies that perfectly optimize the social good, in terms of minimizing the Price of Anarchy or preventing the information avoidance behavior, is computationally hard under standard complexity theoretic assumptions. On the positive side, we show that we can learn provably good values of subsidy in repeated games coming from the same domain. This data-driven subsidy design approach avoids solving computationally hard problems for unseen games by learning over polynomially many games. We also show that optimal subsidy can be learned with no-regret given an online sequence of games, under mild assumptions on the cost matrix. Our study focuses on two distinct games: a Bayesian extension of the well-studied fair cost-sharing game, and a component maintenance game with engineering applications.

cs.GT↗

arXiv2024

Learning accurate and interpretable tree-based models

Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data from different domains. In this work, we develop approaches to design tree-based learning algorithms given repeated access to data from the same domain. We study multiple formulations covering different aspects and popular techniques for learning decision tree based approaches. We propose novel parameterized classes of node splitting criteria in top-down algorithms, which interpolate between popularly used entropy and Gini impurity based criteria, and provide theoretical bounds on the number of samples needed to learn the splitting function appropriate for the data at hand. We also study the sample complexity of tuning prior parameters in Bayesian decision tree learning, and extend our results to decision tree regression. We further consider the problem of tuning hyperparameters in pruning the decision tree for classical pruning algorithms including min-cost complexity pruning. In addition, our techniques can be used to optimize the explainability versus accuracy trade-off when using decision trees. We extend our results to tuning popular tree-based ensembles, including random forests and gradient-boosted trees. We demonstrate the significance of our approach on real world datasets by learning data-specific decision trees which are simultaneously more accurate and interpretable.

cs.LG↗