arXiv subjects

Juan Luque

Publications and source records attributed to Juan Luque.

5 recordsLinked to original sources

arXiv2024

Proportionally Fair Matching via Randomized Rounding

Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond to demographic groups or other protected traits where we seek to ensure roughly equal representation from each group. It is known that, assuming ETH, it is impossible to approximate the problem with $\ell$ colors in time $2^{o(\ell)} n^{\mathcal{O}(1)}$ (i.e., subexponential in $\ell$) even on \emph{unweighted path graphs}. Further, even determining the existence of a non-empty matching satisfying proportionality is NP-Hard. To overcome this hardness, we relax the stringent proportional fairness constraints to a probabilistic notion. We introduce a notion we call $\delta$-\textsc{ProbablyAlmostFair}, where we ensure proportionality up to a factor of at most $(1 \pm \delta)$ for some small $\delta >0$ with high probability. The violation $\delta$ can be brought arbitrarily close to $0$ for some \emph{good} instances with large values of matching size. We propose and analyze simple and fast algorithms for bipartite graphs that achieve constant-factor approximation guarantees, and return a $\delta$-\textsc{ProbablyAlmostFair} matching.

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arXiv2024

Barter Exchange with Shared Item Valuations

In barter exchanges agents enter seeking to swap their items for other items on their wishlist. We consider a centralized barter exchange with a set of agents and items where each item has a positive value. The goal is to compute a (re)allocation of items maximizing the agents' collective utility subject to each agent's total received value being comparable to their total given value. Many such centralized barter exchanges exist and serve crucial roles; e.g., kidney exchange programs, which are often formulated as variants of directed cycle packing. We show finding a reallocation where each agent's total given and total received values are equal is NP-hard. On the other hand, we develop a randomized algorithm that achieves optimal utility in expectation and where, i) for any agent, with probability 1 their received value is at least their given value minus $v^*$ where $v^*$ is said agent's most valuable owned and wished-for item, and ii) each agent's given and received values are equal in expectation.

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arXiv2024

Robust Fair Clustering with Group Membership Uncertainty Sets

We study the canonical fair clustering problem where each cluster is constrained to have close to population-level representation of each group. Despite significant attention, the salient issue of having incomplete knowledge about the group membership of each point has been superficially addressed. In this paper, we consider a setting where the assigned group memberships are noisy. We introduce a simple noise model that requires a small number of parameters to be given by the decision maker. We then present an algorithm for fair clustering with provable \emph{robustness} guarantees. Our framework enables the decision maker to trade off between the robustness and the clustering quality. Unlike previous work, our algorithms are backed by worst-case theoretical guarantees. Finally, we empirically verify the performance of our algorithm on real world datasets and show its superior performance over existing baselines.

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arXiv2023

Concentration of Submodular Functions and Read-k Families Under Negative Dependence

We study the question of whether submodular functions of random variables satisfying various notions of negative dependence satisfy Chernoff-like concentration inequalities. We prove such a concentration inequality for the lower tail when the random variables satisfy negative association or negative regression, partially resolving an open problem raised in (Qiu and Singla [QS22]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms (Chekuri, Vondrak, and Zenklusen [CVZ10] and Harvey and Olver [HO14]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read-k families [Gav+15] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [Gav+15].

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arXiv2021

Insta-RS: Instance-wise Randomized Smoothing for Improved Robustness and Accuracy

Randomized smoothing (RS) is an effective and scalable technique for constructing neural network classifiers that are certifiably robust to adversarial perturbations. Most RS works focus on training a good base model that boosts the certified robustness of the smoothed model. However, existing RS techniques treat every data point the same, i.e., the variance of the Gaussian noise used to form the smoothed model is preset and universal for all training and test data. This preset and universal Gaussian noise variance is suboptimal since different data points have different margins and the local properties of the base model vary across the input examples. In this paper, we examine the impact of customized handling of examples and propose Instance-wise Randomized Smoothing (Insta-RS) -- a multiple-start search algorithm that assigns customized Gaussian variances to test examples. We also design Insta-RS Train -- a novel two-stage training algorithm that adaptively adjusts and customizes the noise level of each training example for training a base model that boosts the certified robustness of the instance-wise Gaussian smoothed model. Through extensive experiments on CIFAR-10 and ImageNet, we show that our method significantly enhances the average certified radius (ACR) as well as the clean data accuracy compared to existing state-of-the-art provably robust classifiers.

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