arXiv subjects

Kamesh Munagala

Publications and source records attributed to Kamesh Munagala.

At least 19 recordsLinked to original sources

arXiv2026

Metric Distortion of Small-group Deliberation

We consider models for social choice where voters rank a set of choices (or alternatives) by deliberating in small groups of size at most $k$, and these outcomes are aggregated by a social choice rule to find the winning alternative. We ground these models in the metric distortion framework, where the voters and alternatives are embedded in a latent metric space, with closer alternative being more desirable for a voter. We posit that the outcome of a small-group interaction optimally uses the voters' collective knowledge of the metric, either deterministically or probabilistically. We characterize the distortion of our deliberation models for small $k$, showing that groups of size $k=3$ suffice to drive the distortion bound below the deterministic metric distortion lower bound of $3$, and groups of size $4$ suffice to break the randomized lower bound of $2.11$. We also show nearly tight asymptotic distortion bounds in the group size, showing that for any constant $ε> 0$, achieving a distortion of $1+ε$ needs group size that only depends on $1/ε$, and not the number of alternatives. We obtain these results via formulating a basic optimization problem in small deviations of the sum of $i.i.d.$ random variables, which we solve to global optimality via non-convex optimization. The resulting bounds may be of independent interest in probability theory.

cs.GT↗

arXiv2026

Efficient Online Conformal Selection with Limited Feedback

We address the problem of conformal selection, where an agent must select a low-cost subset of options to ensure that at least one "success" is identified at a pre-specified target rate $ϕ$. While traditional online conformal prediction focuses on maintaining validity for the observed sequence, minimizing the resource cost (efficiency) of such selections, especially under limited feedback, remains a significant challenge. In this work, we consider highly restricted "bandit" feedback, where the agent only observes feedback about the subset it selected, and not the true label, point, or outcomes of unchosen options. We demonstrate that the simple Adaptive Conformal Inference (ACI) update rule, when applied to the appropriate control parameter or dual variable and paired with explicit boundary actions, is both adversarially valid, ensuring the success target is met on average for any input sequence (and hence under distribution shifts), and stochastically efficient, achieving sublinear efficiency regret for i.i.d. inputs against an optimal stochastic benchmark. The key algorithmic idea is to avoid the projected updates standard in constrained bandits: projections break the exact telescoping identity behind ACI validity, whereas boundary actions stabilize the unprojected update through actual decisions. We show these guarantees under canonical models capturing bandit feedback via a unified algorithmic technique and Lyapunov-based analysis. Our approach handles more general settings than prior work, while requiring significantly less feedback, and provides a new theoretical bridge between efficient online learning with limited feedback and distribution-free uncertainty quantification.

cs.LG↗

arXiv2026

Sample-Efficient Optimization over Generative Priors via Coarse Learnability

We study zeroth-order optimization where solutions must minimize a cost $d(s)$ while maintaining high probability under a complex generative prior $L(s)$ (e.g., a parameterized model). This reduces to sampling from a target distribution proportional to $L(s) e^{-T \cdot d(s)}$. Since classical model-based optimization (MBO) lacks finite-sample guarantees for expressive approximate learners, we introduce "coarse learnability", a flexible statistical assumption requiring only that a learned model covers the target's probability mass within a polynomial factor. Leveraging this assumption, we design an iterative MBO algorithm called \alift with a sample correction step that provably approximates the target using only a polynomial number of samples. We apply this framework to globally optimizing non-convex objectives bounded by a quadratic envelope in $R^n$, where we show this assumption is naturally satisfied for a family of "optimistic" posterior distributions. To reach global $\varepsilon$-optimality, this implies a sample complexity of $\widetilde{O}(\log 1/\varepsilon)$, a rate characteristic of optimistic space-partitioning methods. We further justify coarse learnability as an assumption for generative priors theoretically, proving that in simple settings, parametric maximum likelihood estimation and over-smoothed kernel density estimators naturally satisfy it. Finally, one motivation for our framework comes from inference-time alignment. Though our primary contribution pertains to the theoretical foundations of MBO, we provide qualitative evidence that, in simple settings, even primitive LLMs can shift their distributions toward lower-cost regions when fine-tuned with zeroth-order feedback.

cs.LG↗

arXiv2026

Deliberation via Matching

We study deliberative social choice, where voters engage in small-group discussions to output collective preferences that are then aggregated by a social choice rule. We introduce a simple deliberation-via-matching protocol. In this protocol, for each pair of candidates, we form a maximum matching among voters who disagree on that pair, and have each matched pair deliberate. We then aggregate the resulting individual and deliberative preferences using the weighted uncovered set tournament rule. We show that this protocol has a tight distortion bound of $3$ within the metric distortion framework. In the absence of deliberation, general deterministic social choice rules can achieve this distortion, whereas deterministic tournament rules face a strictly larger lower bound of $3.11$. Our result closes this gap: Pairwise deliberation allows a tournament-based rule to attain distortion $3$. Conceptually, this shows that tournament rules can match the power of general deterministic social choice rules once they are given the minimal added power of pairwise deliberations. We prove this bound via a novel bilinear relaxation of the non-linear program capturing optimal distortion, whose vertices we can explicitly enumerate, leading to an analytic proof. Loosely speaking, our key technical insight is that the distortion objective, as a function of metric distances to any three alternatives, is both supermodular and convex. This characterization therefore provides a new analytical tool for studying the distortion of deliberative protocols, and may be of independent interest. Finally, although our analysis is for the full protocol, we show that this mechanism also admits a lightweight sampling-based implementation, yielding a high-probability approximation to the deterministic guarantee with arbitrary accuracy and low per-voter complexity.

cs.GT↗

arXiv2026

The Price of Competitive Information Disclosure

In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

cs.GT↗

arXiv2026

Compact Conformal Subgraphs

Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based conformal compression", a framework for constructing compact subgraphs that preserve statistical validity while reducing structural complexity. We formulate compression as selecting a smallest subgraph capturing a prescribed fraction of the probability mass, and reduce to a weighted version of densest $k$-subgraphs in hypergraphs, in the regime where the subgraph has a large fraction of edges. We design efficient approximation algorithms that achieve constant factor coverage and size trade-offs. Crucially, we prove that our relaxation satisfies a monotonicity property, derived from a connection to parametric minimum cuts, which guarantees the nestedness required for valid conformal guarantees. Our results on the one hand bridge efficient conformal prediction with combinatorial graph compression via monotonicity, to provide rigorous guarantees on both statistical validity, and compression or size. On the other hand, they also highlight an algorithmic regime, distinct from classical densest-$k$-subgraph hardness settings, where the problem can be approximated efficiently. We finally validate our algorithmic approach via simulations for trip planning and navigation, and compare to natural baselines.

cs.LG↗

arXiv2026

Beyond Polarization: Opinion Mixing and Social Influence in Deliberation

Deliberative processes are often discussed as increasing or decreasing polarization. This approach misses a different, and arguably more diagnostic, dimension of opinion change: whether deliberation reshuffles who agrees with whom, or simply moves everyone in parallel while preserving the pre-deliberation rank ordering. We introduce \opinion mixing, measured by Kendall's rank correlation (τ) between pre- and post-deliberation responses, as a complement to variance-based polarization metrics. Across two large online deliberative polls spanning 32 countries (MCF-2022: n=6,342; MCF-2023: n=1,529), deliberation increases opinion mixing relative to survey-only controls: treatment groups exhibit lower rank correlation on (97%) and (93%) of opinion questions, respectively. Polarization measures based on variance tell a more heterogeneous story: controls consistently converge, while treated groups sometimes converge and sometimes diverge depending on the issue. To probe mechanisms, we link transcripts and surveys in a third event (SOF: (n=617), 116 groups) and use LLM-assisted coding of 6,232 discussion statements. Expressed support in discussion statements strongly predicts subsequent group-level opinion shifts; this correlation is amplified by justification quality in the statements but not by argument novelty. To our knowledge, we are the first to observe how different notions of argument quality have different associations with the outcome of deliberation. This suggests that opinion change after deliberation is related to selective uptake of well-reasoned arguments, producing complex patterns of opinion reorganization that standard polarization metrics may miss.

cs.SI↗

arXiv2026

Balanced Spanning Tree Distributions Have Separation Fairness

Sampling-based methods such as ReCom are widely used to audit redistricting plans for fairness, with the balanced spanning tree distribution playing a central role since it favors compact, contiguous, and population-balanced districts. However, whether such samples are truly representative or exhibit hidden biases remains an open question. In this work, we introduce the notion of separation fairness, which asks whether adjacent geographic units are separated with at most a constant probability (bounded away from one) in sampled redistricting plans. Focusing on grid graphs and two-district partitions, we prove that a smooth variant of the balanced spanning tree distribution satisfies separation fairness. Our results also provide theoretical support for popular MCMC methods like ReCom, suggesting that they maintain fairness at a granular level in the sampling process. Along the way, we develop tools for analyzing loop-erased random walks and partitions that may be of independent interest.

cs.DS↗

arXiv2026

Auditing for Core Stability in Participatory Budgeting

We consider the participatory budgeting problem where each of $n$ voters specifies additive utilities over $m$ candidate projects with given sizes, and the goal is to choose a subset of projects (i.e., a committee) with total size at most $k$. Participatory budgeting mathematically generalizes multiwinner elections, and both have received great attention in computational social choice recently. A well-studied notion of group fairness in this setting is core stability: Each voter is assigned an "entitlement" of $\frac{k}{n}$, so that a subset $S$ of voters can pay for a committee of size at most $|S| \cdot \frac{k}{n}$. A given committee is in the core if no subset of voters can pay for another committee that provides each of them strictly larger utility. This provides proportional representation to all voters in a strong sense. In this paper, we study the following auditing question: Given a committee computed by some preference aggregation method, how close is it to the core? Concretely, how much does the entitlement of each voter need to be scaled down by, so that the core property subsequently holds? As our main contribution, we present computational hardness results for this problem, as well as a logarithmic approximation algorithm via linear program rounding. We show that our analysis is tight against the linear programming bound. Additionally, we consider two related notions of group fairness that have similar audit properties. The first is Lindahl priceability, which audits the closeness of a committee to a market clearing solution. We show that this is related to the linear programming relaxation of auditing the core, leading to efficient exact and approximation algorithms for auditing. The second is a novel weakening of the core that we term the sub-core, and we present computational results for auditing this notion as well.

cs.GT↗

arXiv2025

Fair Multi-agent Persuasion with Submodular Constraints

We study the problem of selection in the context of Bayesian persuasion. We are given multiple agents with hidden values (or quality scores), to whom resources must be allocated by a welfare-maximizing decision-maker. An intermediary with knowledge of the agents' values seeks to influence the outcome of the selection by designing informative signals and providing tie-breaking policies, so that when the receiver maximizes welfare over the resulting posteriors, the expected utilities of the agents (where utility is defined as allocation times value) achieve certain fairness properties. The fairness measure we will use is majorization, which simultaneously approximately maximizes all symmetric, monotone, concave functions of the utilities. We consider the general setting where the allocation to the agents needs to respect arbitrary submodular constraints, as given by the corresponding polymatroid. We present a signaling policy that, under a mild bounded rationality assumption on the receiver, achieves a logarithmically approximate majorized policy in this setting. The approximation ratio is almost best possible, and that significantly outperforms generic results that only yield linear approximations. A key component of our result is a structural characterization showing that the vector of agent utilities for a given signaling policy defines the base polytope of a different polymatroid, a result that may be of independent interest. In addition, we show that an arbitrarily good additive approximation to this vector can be produced in (weakly) polynomial time via the multiplicative weights update method.

cs.GT↗

arXiv2025

The Limits of Interval-Regulated Price Discrimination

In this paper, we study third-degree price discrimination in a model first presented by Bergemann, Brooks, and Morris [2015]. Since such price discrimination might create market segments with vastly different posted prices, we consider regulating these prices, specifically, by restricting them to lie within an interval. Given a price interval, we consider segmentations of the market where a seller, who is oblivious to the existence of such regulation, still posts prices within the price interval. We show the following surprising result: For any market and price interval where such segmentation is feasible, there is always a different segmentation that optimally transfers all excess surplus to the consumers. In addition, we characterize the entire space of buyer and seller surplus that is achievable by such segmentation, including maximizing seller surplus, and simultaneously minimizing buyer and seller surplus. A key technical challenge is that the classical segmentation method of Bergemann, Brooks, and Morris [2015] fails under price constraints. To address this, we develop three intuitive but fundamentally distinct segmentation constructions, each tailored to a different surplus objective. These constructions maintain different invariants, reflect different economic intuitions, and collectively form the core of our regulated surplus characterization.

econ.TH↗

arXiv2025

Online Distributed Queue Length Estimation

Queue length monitoring is a commonly arising problem in numerous applications such as queue management systems, scheduling, and traffic monitoring. Motivated by such applications, we formulate a queue monitoring problem, where there is a FIFO queue with arbitrary arrivals and departures, and a server needs to monitor the length of a queue by using decentralized pings from packets in the queue. Packets can send pings informing the server about the number of packets ahead of them in the queue. Via novel online policies and lower bounds, we tightly characterize the trade-off between the number of pings sent and the accuracy of the server's real time estimates. Our work studies the trade-off under various arrival and departure processes, including constant-rate, Poisson, and adversarial processes.

cs.DS↗

arXiv2025

Group Fairness and Multi-criteria Optimization in School Assignment

We consider the problem of assigning students to schools, when students have different utilities for schools and schools have capacity. There are additional group fairness considerations over students that can be captured either by concave objectives, or additional constraints on the groups. We present approximation algorithms for this problem via convex program rounding that achieve various trade-offs between utility violation, capacity violation, and running time. We also show that our techniques easily extend to the setting where there are arbitrary covering constraints on the feasible assignment, capturing multi-criteria and ranking optimization.

cs.DS↗

arXiv2025

Multi-Selection for Recommendation Systems

We present the construction of a multi-selection model to answer differentially private queries in the context of recommendation systems. The server sends back multiple recommendations and a ``local model'' to the user, which the user can run locally on its device to select the item that best fits its private features. We study a setup where the server uses a deep neural network (trained on the Movielens 25M dataset as the ground truth for movie recommendation. In the multi-selection paradigm, the average recommendation utility is approximately 97\% of the optimal utility (as determined by the ground truth neural network) while maintaining a local differential privacy guarantee with $ε$ ranging around 1 with respect to feature vectors of neighboring users. This is in comparison to an average recommendation utility of 91\% in the non-multi-selection regime under the same constraints.

cs.LG↗

arXiv2024

Fair Division via the Cake-Cutting Share

In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of $n$ and $m$. In particular, we show a tight approximation bound of $Θ(\sqrt{n})$ for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of $O(m^{2/3})$ for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

cs.GT↗

arXiv2024

Majorized Bayesian Persuasion and Fair Selection

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multi-dimensional information sets.

cs.GT↗

arXiv2024

Differential Privacy with Multiple Selections

We consider the setting where a user with sensitive features wishes to obtain a recommendation from a server in a differentially private fashion. We propose a ``multi-selection'' architecture where the server can send back multiple recommendations and the user chooses one from these that matches best with their private features. When the user feature is one-dimensional -- on an infinite line -- and the accuracy measure is defined w.r.t some increasing function $\mathfrak{h}(.)$ of the distance on the line, we precisely characterize the optimal mechanism that satisfies differential privacy. The specification of the optimal mechanism includes both the distribution of the noise that the user adds to its private value, and the algorithm used by the server to determine the set of results to send back as a response and further show that Laplace is an optimal noise distribution. We further show that this optimal mechanism results in an error that is inversely proportional to the number of results returned when the function $\mathfrak{h}(.)$ is the identity function.

cs.DS↗

arXiv2024

Individual Fairness in Graph Decomposition

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability. We require the additional aspect of individual fairness - pairs of nodes at comparable distances should be separated with comparable probability. We show that classic decomposition procedures do not satisfy this property. We present novel algorithms that achieve various trade-offs between this property and additional desiderata of connectivity of the clusters and optimality in the number of clusters. We show that our individual fairness bounds may be difficult to improve by tying the improvement to resolving a major open question in metric embeddings. We finally show the efficacy of our algorithms on real planar networks modeling congressional redistricting.

cs.DS↗