# Robust Algorithms for the Secretary Problem

@inproceedings{Bradac2020RobustAF,
title={Robust Algorithms for the Secretary Problem},
author={Domagoj Bradac and Anupam Gupta and Sahil Singla and Goran Zuzic},
booktitle={ITCS},
year={2020}
}
In classical secretary problems, a sequence of $n$ elements arrive in a uniformly random order, and we want to choose a single item, or a set of size $K$. The random order model allows us to escape from the strong lower bounds for the adversarial order setting, and excellent algorithms are known in this setting. However, one worrying aspect of these results is that the algorithms overfit to the model: they are not very robust. Indeed, if a few "outlier" arrivals are adversarially placed in the… Expand
12 Citations
The Secretary Problem with Independent Sampling
• Computer Science
• SODA
• 2021
In this paper it is proved that the best possible algorithm is characterized by a fixed sequence of time thresholds, dictating at which point in time the authors should start accepting a value that is both a maximum of the online sequence and has a given ranking within the sampled elements. Expand
• Mathematics, Computer Science
• ICALP
• 2020
An algorithm is designed that gives an approximation of $1 - \tilde{O}(\Gamma/k)$ when the adversarial time steps can be covered by $\Gamma \ge \sqrt{k}$ intervals of size $\tilde{\Omega}(\frac{n}{k})$. Expand
• Computer Science
• ICALP
• 2020
This paper proposes a new \emph{adversarial injections} model, in which the input is ordered randomly, but an adversary may inject misleading elements at arbitrary positions, and investigates two classical combinatorial-optimization problems in this model: Maximum matching and cardinality constrained monotone submodular function maximization. Expand
Random-Order Models
• Computer Science
• Beyond the Worst-Case Analysis of Algorithms
• 2020
Improvements in the random-order model are shown for two broad classes of problems: packing problems where the authors must pick a constrained set of items to maximize total value, and covering problems where they must satisfy given requirements at minimum total cost. Expand
Robust Algorithms for Online Convex Problems via Primal-Dual
A more unified analysis of primal-dual algorithms to better understand the mechanisms behind this important method and obtains robust online algorithm for fairly general online convex problems on the MIXED model. Expand
Revenue Monotonicity Under Misspecified Bidders
• Mathematics, Computer Science
• WINE
• 2020
This work investigates revenue guarantees for auction mechanisms in a model where a distribution is specified for each bidder, but only some of the distributions are correct, and finds that the answer depends on the feasibility constraint. Expand
Learning Product Rankings Robust to Fake Users
• Computer Science, Mathematics
• ArXiv
• 2020
This work shows that existing learning algorithms---that are optimal in the absence of fake users---may converge to highly sub-optimal rankings under manipulation by fake users, and develops efficient learning algorithms that significantly outperform existing algorithms. Expand
This paper formalizes the online adversarial attack problem, emphasizing two key elements found in realworld use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. Expand
Motivation : Picking a Large Element 2 2 The Secretary Problem 4 3 Multiple-Secretary and Other Maximization Problems 5 4 Minimization Problems 14 5 Related Models and Extensions
• 2020
Prophet Inequalities with Linear Correlations and Augmentations
• Computer Science, Mathematics
• EC
• 2020
A natural "linear" correlation structure is considered as a generalization of the common-base value model of Chawla et al. as a way to prove bounds (matching up to constant factors) that decay gracefully with the amount of correlation of the arriving items. Expand

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