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
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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
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References

SHOWING 1-10 OF 56 REFERENCES
Secretary Problems with Non-Uniform Arrival Order
TLDR
This work initiates an investigation into relaxations of the random-ordering hypothesis in online algorithms, by focusing on the secretary problem and asking what performance guarantees one can prove under relaxed assumptions, and proves that Θ(log log n) is the minimum entropy of any permutation distribution that permits constant probability of correct selection in the secretaries problem with $n$ elements. Expand
Online Facility Location against a t-Bounded Adversary
TLDR
This work presents a matching lower bound that any randomized algorithm has an expected competitive ratio of [EQUATION], and uses this result to construct an O(1)-approximate streaming algorithm for k-median clustering that stores O(k log t) points and has O(nk) worst-case update time. Expand
Stochastic bandits robust to adversarial corruptions
We introduce a new model of stochastic bandits with adversarial corruptions which aims to capture settings where most of the input follows a stochastic pattern but some fraction of it can beExpand
Matroids, secretary problems, and online mechanisms
TLDR
An O(log k)-competitive algorithm for general matroids (where k is the rank of the matroid), and constant-competitive algorithms for several special cases including graphicMatroids, truncated partition matroIDS, and bounded degree transversal matroid algorithms are presented. Expand
Online Matroid Intersection: Beating Half for Random Arrival
TLDR
This work presents the first randomized online algorithm that has a $\frac12 + \delta$ competitive ratio in expectation, where $\delta >0$ is a constant. Expand
Heuristics for Semirandom Graph Problems
TLDR
It is shown that when p<(1??)lnn /?n, an independent set of size |S| cannot be recovered, unless NP?BPP, and a heuristic is given that recovers this bisection with high probability when p?q?cplogn/n, for c a sufficiently large constant. Expand
Near optimal online algorithms and fast approximation algorithms for resource allocation problems
TLDR
A new distributional model called the adversarial stochastic input model, which is a generalization of the i.i.d model with unknown distributions, where the distributions can change over time is introduced, and a 1-O(ε) approximation algorithm is given for the resource allocation problem. Expand
Simultaneous approximations for adversarial and stochastic online budgeted allocation
TLDR
This paper designs algorithms that achieve a competitive ratio better than 1 -- 1/e on average, while preserving a nearly optimal worst case competitive ratio, and designs an algorithm with the optimal competitive ratio in both the adversarial and random arrival models. Expand
The adwords problem: online keyword matching with budgeted bidders under random permutations
TLDR
The problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit, is considered, and the current literature on this problem is extended by considering the setting where the keywords arrive in a random order. Expand
Stream Order and Order Statistics: Quantile Estimation in Random-Order Streams
TLDR
The first fully general lower bounds in the random-order model are proved: finding an element with rank n/2 ± n δ in the single-pass random- order model with probability at least 9/10 requires Ω( � n 1−3δ / logn) space. Expand
...
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4
5
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