MohammadTaghi Hajiaghayi

David P. Woodruff, Vincent Cohen-Addad, Lalit Jain et al.

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

Soheil Feizi, MohammadTaghi Hajiaghayi, Keivan Rezaei et al.

This paper explores the potential for leveraging Large Language Models (LLM) in the realm of online advertising systems. We introduce a general framework for LLM advertisement, consisting of modification, bidding, prediction, and auction modules. Different design considerations for each module are presented. These design choices are evaluated and discussed based on essential desiderata required to maintain a sustainable system. Further fundamental questions regarding practicality, efficiency, and implementation challenges are raised for future research. Finally, we exposit how recent approaches on mechanism design for LLM can be framed in our unified perspective.

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi et al.

Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the dynamic setting, where (1) we have oracle access to a monotone submodular function $f: 2^{V} \rightarrow \mathbb{R}^+$ and (2) we are given a sequence $\mathcal{S}$ of insertions and deletions of elements of an underlying ground set $V$. We develop the first fully dynamic $(4+ε)$-approximation algorithm for the submodular maximization problem under the matroid constraint using an expected worst-case $O(k\log(k)\log^3{(k/ε)})$ query complexity where $0 < ε\le 1$. This resolves an open problem of Chen and Peng (STOC'22) and Lattanzi et al. (NeurIPS'20). As a byproduct, for the submodular maximization under the cardinality constraint $k$, we propose a parameterized (by the cardinality constraint $k$) dynamic algorithm that maintains a $(2+ε)$-approximate solution of the sequence $\mathcal{S}$ at any time $t$ using an expected worst-case query complexity $O(kε^{-1}\log^2(k))$. This is the first dynamic algorithm for the problem that has a query complexity independent of the size of ground set $V$.

Marina Knittel, Max Springer, John P. Dickerson et al.

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous $O(n^{5/6}poly\log(n))$ fair approximation for cost to a near polylogarithmic $O(n^δpoly\log(n))$ fair approximation for any constant $δ\in(0,1)$. This result establishes a cost-fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

Kiarash Banihashem, MohammadTaghi Hajiaghayi, Suho Shin et al.

We study social learning dynamics motivated by reviews on online platforms. The agents collectively follow a simple multi-armed bandit protocol, but each agent acts myopically, without regards to exploration. We allow the greedy (exploitation-only) algorithm, as well as a wide range of behavioral biases. Specifically, we allow myopic behaviors that are consistent with (parameterized) confidence intervals for the arms' expected rewards. We derive stark learning failures for any such behavior, and provide matching positive results. The learning-failure results extend to Bayesian agents and Bayesian bandit environments. In particular, we obtain general, quantitatively strong results on failure of the greedy bandit algorithm, both for ``frequentist" and ``Bayesian" versions. Failure results known previously are quantitatively weak, and either trivial or very specialized. Thus, we provide a theoretical foundation for designing non-trivial bandit algorithms, \ie algorithms that intentionally explore, which has been missing from the literature. Our general behavioral model can be interpreted as agents' optimism or pessimism. The matching positive results entail a maximal allowed amount of optimism. Moreover, we find that no amount of pessimism helps against the learning failures, whereas even a small-but-constant fraction of extreme optimists avoids the failures and leads to near-optimal regret rates.

Kiarash Banihashem, MohammadTaghi Hajiaghayi, Max Springer

Decision trees are widely used for their low computational cost, good predictive performance, and ability to assess the importance of features. Though often used in practice for feature selection, the theoretical guarantees of these methods are not well understood. We here obtain a tight finite sample bound for the feature selection problem in linear regression using single-depth decision trees. We examine the statistical properties of these "decision stumps" for the recovery of the $s$ active features from $p$ total features, where $s \ll p$. Our analysis provides tight sample performance guarantees on high-dimensional sparse systems which align with the finite sample bound of $O(s \log p)$ as obtained by Lasso, improving upon previous bounds for both the median and optimal splitting criteria. Our results extend to the non-linear regime as well as arbitrary sub-Gaussian distributions, demonstrating that tree based methods attain strong feature selection properties under a wide variety of settings and further shedding light on the success of these methods in practice. As a byproduct of our analysis, we show that we can provably guarantee recovery even when the number of active features $s$ is unknown. We further validate our theoretical results and proof methodology using computational experiments.

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi et al.

Maximizing submodular functions has been increasingly used in many applications of machine learning, such as data summarization, recommendation systems, and feature selection. Moreover, there has been a growing interest in both submodular maximization and dynamic algorithms. In 2020, Monemizadeh and Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, and Zadimoghaddam initiated developing dynamic algorithms for the monotone submodular maximization problem under the cardinality constraint $k$. Recently, there have been some improvements on the topic made by Banihashem, Biabani, Goudarzi, Hajiaghayi, Jabbarzade, and Monemizadeh. In 2022, Chen and Peng studied the complexity of this problem and raised an important open question: "Can we extend [fully dynamic] results (algorithm or hardness) to non-monotone submodular maximization?". We affirmatively answer their question by demonstrating a reduction from maximizing a non-monotone submodular function under the cardinality constraint $k$ to maximizing a monotone submodular function under the same constraint. Through this reduction, we obtain the first dynamic algorithms to solve the non-monotone submodular maximization problem under the cardinality constraint $k$. Our algorithms maintain an $(8+ε)$-approximate of the solution and use expected amortized $O(ε^{-3}k^3\log^3(n)\log(k))$ or $O(ε^{-1}k^2\log^3(k))$ oracle queries per update, respectively. Furthermore, we showcase the benefits of our dynamic algorithm for video summarization and max-cut problems on several real-world data sets.

Kiarash Banihashem, Samira Goudarzi, MohammadTaghi Hajiaghayi et al.

We initiate the study of the submodular cover problem in dynamic setting where the elements of the ground set are inserted and deleted. In the classical submodular cover problem, we are given a monotone submodular function $f : 2^{V} \to \mathbb{R}^{\ge 0}$ and the goal is to obtain a set $S \subseteq V$ that minimizes the cost subject to the constraint $f(S) = f(V)$. This is a classical problem in computer science and generalizes the Set Cover problem, 2-Set Cover, and dominating set problem among others. We consider this problem in a dynamic setting where there are updates to our set $V$, in the form of insertions and deletions of elements from a ground set $\mathcal{V}$, and the goal is to maintain an approximately optimal solution with low query complexity per update. For this problem, we propose a randomized algorithm that, in expectation, obtains a $(1-O(ε), O(ε^{-1}))$-bicriteria approximation using polylogarithmic query complexity per update.

MohammadTaghi Hajiaghayi, Mohammad Mahdavi, Keivan Rezaei et al.

We present a study on a repeated delegated choice problem, which is the first to consider an online learning variant of Kleinberg and Kleinberg, EC'18. In this model, a principal interacts repeatedly with an agent who possesses an exogenous set of solutions to search for efficient ones. Each solution can yield varying utility for both the principal and the agent, and the agent may propose a solution to maximize its own utility in a selfish manner. To mitigate this behavior, the principal announces an eligible set which screens out a certain set of solutions. The principal, however, does not have any information on the distribution of solutions in advance. Therefore, the principal dynamically announces various eligible sets to efficiently learn the distribution. The principal's objective is to minimize cumulative regret compared to the optimal eligible set in hindsight. We explore two dimensions of the problem setup, whether the agent behaves myopically or strategizes across the rounds, and whether the solutions yield deterministic or stochastic utility. Our analysis mainly characterizes some regimes under which the principal can recover the sublinear regret, thereby shedding light on the rise and fall of the repeated delegation procedure in various regimes.

Marina Knittel, Max Springer, John Dickerson et al.

Research in fair machine learning, and particularly clustering, has been crucial in recent years given the many ethical controversies that modern intelligent systems have posed. Ahmadian et al. [2020] established the study of fairness in \textit{hierarchical} clustering, a stronger, more structured variant of its well-known flat counterpart, though their proposed algorithm that optimizes for Dasgupta's [2016] famous cost function was highly theoretical. Knittel et al. [2023] then proposed the first practical fair approximation for cost, however they were unable to break the polynomial-approximate barrier they posed as a hurdle of interest. We break this barrier, proposing the first truly polylogarithmic-approximate low-cost fair hierarchical clustering, thus greatly bridging the gap between the best fair and vanilla hierarchical clustering approximations.

Kiarash Banihashem, MohammadTaghi Hajiaghayi, Suho Shin et al.

We present an oracle-efficient relaxation for the adversarial contextual bandits problem, where the contexts are sequentially drawn i.i.d from a known distribution and the cost sequence is chosen by an online adversary. Our algorithm has a regret bound of $O(T^{\frac{2}{3}}(K\log(|Π|))^{\frac{1}{3}})$ and makes at most $O(K)$ calls per round to an offline optimization oracle, where $K$ denotes the number of actions, $T$ denotes the number of rounds and $Π$ denotes the set of policies. This is the first result to improve the prior best bound of $O((TK)^{\frac{2}{3}}(\log(|Π|))^{\frac{1}{3}})$ as obtained by Syrgkanis et al. at NeurIPS 2016, and the first to match the original bound of Langford and Zhang at NeurIPS 2007 which was obtained for the stochastic case.

Simina Brânzei, MohammadTaghi Hajiaghayi, Reed Phillips et al.

We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at a point of her choice, while Bob chooses the left piece or the right piece, leaving the remainder for Alice. We consider two versions: sequential, where Bob observes Alice's cut point before choosing left/right, and simultaneous, where he only observes her cut point after making his choice. The simultaneous version was first considered by Aumann and Maschler (1995). We observe that if Bob is almost myopic and chooses his favorite piece too often, then he can be systematically exploited by Alice through a strategy akin to a binary search. This strategy allows Alice to approximate Bob's preferences with increasing precision, thereby securing a disproportionate share of the resource over time. We analyze the limits of how much a player can exploit the other one and show that fair utility profiles are in fact achievable. Specifically, the players can enforce the equitable utility profile of $(1/2, 1/2)$ in the limit on every trajectory of play, by keeping the other player's utility to approximately $1/2$ on average while guaranteeing they themselves get at least approximately $1/2$ on average. We show this theorem using a connection with Blackwell approachability. Finally, we analyze a natural dynamic known as fictitious play, where players best respond to the empirical distribution of the other player. We show that fictitious play converges to the equitable utility profile of $(1/2, 1/2)$ at a rate of $O(1/\sqrt{T})$.

Suho Shin, Seyed A. Esmaeili, MohammadTaghi Hajiaghayi

We study the problem of designing replication-proof bandit mechanisms when agents strategically register or replicate their own arms to maximize their payoff. Specifically, we consider Bayesian agents who only know the distribution from which their own arms' mean rewards are sampled, unlike the original setting of by Shin et al. 2022. Interestingly, with Bayesian agents in stark contrast to the previous work, analyzing the replication-proofness of an algorithm becomes significantly complicated even in a single-agent setting. We provide sufficient and necessary conditions for an algorithm to be replication-proof in the single-agent setting, and present an algorithm that satisfies these properties. These results center around several analytical theorems that focus on \emph{comparing the expected regret of multiple bandit instances}, and therefore might be of independent interest since they have not been studied before to the best of our knowledge. We expand this result to the multi-agent setting, and provide a replication-proof algorithm for any problem instance. We finalize our result by proving its sublinear regret upper bound which matches that of Shin et al. 2022.

Alireza Farhadi, MohammadTaghi Hajiaghayi, Elaine Shi

Given a graph, the densest subgraph problem asks for a set of vertices such that the average degree among these vertices is maximized. Densest subgraph has numerous applications in learning, e.g., community detection in social networks, link spam detection, correlation mining, bioinformatics, and so on. Although there are efficient algorithms that output either exact or approximate solutions to the densest subgraph problem, existing algorithms may violate the privacy of the individuals in the network, e.g., leaking the existence/non-existence of edges. In this paper, we study the densest subgraph problem in the framework of the differential privacy, and we derive the first upper and lower bounds for this problem. We show that there exists a linear-time $ε$-differentially private algorithm that finds a $2$-approximation of the densest subgraph with an extra poly-logarithmic additive error. Our algorithm not only reports the approximate density of the densest subgraph, but also reports the vertices that form the dense subgraph. Our upper bound almost matches the famous $2$-approximation by Charikar both in performance and in approximation ratio, but we additionally achieve differential privacy. In comparison with Charikar's algorithm, our algorithm has an extra poly-logarithmic additive error. We partly justify the additive error with a new lower bound, showing that for any differentially private algorithm that provides a constant-factor approximation, a sub-logarithmic additive error is inherent. We also practically study our differentially private algorithm on real-world graphs, and we show that in practice the algorithm finds a solution which is very close to the optimal

Behzad Ghazanfari, Fatemeh Afghah, MohammadTaghi Hajiaghayi

This paper proposes inverse feature learning as a novel supervised feature learning technique that learns a set of high-level features for classification based on an error representation approach. The key contribution of this method is to learn the representation of error as high-level features, while current representation learning methods interpret error by loss functions which are obtained as a function of differences between the true labels and the predicted ones. One advantage of such learning method is that the learned features for each class are independent of learned features for other classes; therefore, this method can learn simultaneously meaning that it can learn new classes without retraining. Error representation learning can also help with generalization and reduce the chance of over-fitting by adding a set of impactful features to the original data set which capture the relationships between each instance and different classes through an error generation and analysis process. This method can be particularly effective in data sets, where the instances of each class have diverse feature representations or the ones with imbalanced classes. The experimental results show that the proposed method results in significantly better performance compared to the state-of-the-art classification techniques for several popular data sets. We hope this paper can open a new path to utilize the proposed perspective of error representation learning in different feature learning domains.

Hossein Esfandiari, MohammadTaghi Hajiaghayi, Brendan Lucier et al.

We consider online variations of the Pandora's box problem (Weitzman. 1979), a standard model for understanding issues related to the cost of acquiring information for decision-making. Our problem generalizes both the classic Pandora's box problem and the prophet inequality framework. Boxes are presented online, each with a random value and cost drew jointly from some known distribution. Pandora chooses online whether to open each box given its cost, and then chooses irrevocably whether to keep the revealed prize or pass on it. We aim for approximation algorithms against adversaries that can choose the largest prize over any opened box, and use optimal offline policies to decide which boxes to open (without knowledge of the value inside). We consider variations where Pandora can collect multiple prizes subject to feasibility constraints, such as cardinality, matroid, or knapsack constraints. We also consider variations related to classic multi-armed bandit problems from reinforcement learning. Our results use a reduction-based framework where we separate the issues of the cost of acquiring information from the online decision process of which prizes to keep. Our work shows that in many scenarios, Pandora can achieve a good approximation to the best possible performance.

Rajesh Chitnis, MohammadTaghi Hajiaghayi, Jonathan Katz et al.

In this paper we propose a game-theoretic model to analyze events similar to the 2009 \emph{DARPA Network Challenge}, which was organized by the Defense Advanced Research Projects Agency (DARPA) for exploring the roles that the Internet and social networks play in incentivizing wide-area collaborations. The challenge was to form a group that would be the first to find the locations of ten moored weather balloons across the United States. We consider a model in which $N$ people (who can form groups) are located in some topology with a fixed coverage volume around each person's geographical location. We consider various topologies where the players can be located such as the Euclidean $d$-dimension space and the vertices of a graph. A balloon is placed in the space and a group wins if it is the first one to report the location of the balloon. A larger team has a higher probability of finding the balloon, but we assume that the prize money is divided equally among the team members. Hence there is a competing tension to keep teams as small as possible. \emph{Risk aversion} is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. In our model we consider the \emph{isoelastic} utility function derived from the Arrow-Pratt measure of relative risk aversion. The main aim is to analyze the structures of the groups in Nash equilibria for our model. For the $d$-dimensional Euclidean space ($d\geq 1$) and the class of bounded degree regular graphs we show that in any Nash Equilibrium the \emph{richest} group (having maximum expected utility per person) covers a constant fraction of the total volume.