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Stochastic Matching with Few Queries: (1-ε) Approximation [article]

Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi
2020 arXiv   pre-print
In this work, we analyze a natural sampling-based algorithm and show that it can obtain all the way up to (1-ϵ) approximation, for any constant ϵ > 0.  ...  This allows us to bypass a previously known barrier towards achieving (1-ϵ) approximation based on existence of dense Ruzsa-Szemerédi graphs.  ...  Acknowledgements We thank Noga Alon for referring us to his paper [1] on construction of Ruzsa-Szemerédi graphs and discussing its implications which were extremely insightful.  ... 
arXiv:2002.11880v1 fatcat:oiq5zkm5yzcyhlhvm2n4edgdcy

Almost Optimal Stochastic Weighted Matching With Few Queries [article]

Soheil Behnezhad, Nima Reyhani
2018 arXiv   pre-print
We consider the stochastic matching problem.  ...  Our main result is an adaptive algorithm that for any arbitrarily small ϵ > 0, finds a (1-ϵ)-approximation in expectation, by querying only O(1) edges per vertex.  ...  To ensure that with probability at least 1 − one of the queried edges is realized, one needs to query at least Ω(log (1/ )/p) edges of v. 2 Stochastic matching settings have been studied extensively  ... 
arXiv:1710.10592v3 fatcat:zqcozarlvjd4ph2pdfmwe6qybu

The Stochastic Matching Problem with (Very) Few Queries

Sepehr Assadi, Sanjeev Khanna, Yang Li
2016 Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16  
We further present a non-adaptive algorithm that makes O log (1/εp) εp queries per vertex and computes a ( 1 2 − ε)-approximate maximum matching in Gp with high probability.  ...  We design an adaptive algorithm for this problem that, for any graph G, computes a (1ε)-approximate maximum matching in the realized graph Gp with high probability, while making O log (1/εp) εp queries  ...  ACKNOWLEDGMENTS We would like to thank Nika Haghtalab for introducing us to the stochastic matching problem.  ... 
doi:10.1145/2940716.2940769 dblp:conf/sigecom/AssadiKL16 fatcat:6qfwjd5psfejndegs77qshf76i

Ignorance is Almost Bliss

Avrim Blum, John P. Dickerson, Nika Haghtalab, Ariel D. Procaccia, Tuomas Sandholm, Ankit Sharma
2015 Proceedings of the Sixteenth ACM Conference on Economics and Computation - EC '15  
The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries.  ...  Our main theoretical result for the stochastic matching (i.e., 2-set packing) problem is the design of an adaptive algorithm that queries only a constant number of edges per vertex and achieves a (1-ϵ)  ...  Algorithm 1 ADAPTIVE ALGORITHM FOR STOCHASTIC MATCHING: (1 − ) APPROXIMATION Input: A graph G = (V, E).  ... 
doi:10.1145/2764468.2764479 dblp:conf/sigecom/BlumDHPSS15 fatcat:loefmact5rgbveyafmesg6zf64

Stochastic Weighted Matching: (1-ϵ) Approximation [article]

Soheil Behnezhad, Mahsa Derakhshan
2020 arXiv   pre-print
In this paper, we prove that for any desirably small ϵ∈ (0, 1), every graph G has a subgraph Q that guarantees a (1-ϵ)-approximation and has maximum degree only O_ϵ, p(1).  ...  The stochastic matching problem has been studied extensively on both weighted and unweighted graphs.  ...  The stochastic matching problem has been studied extensively on both weighted and unweighted graphs.  ... 
arXiv:2004.08703v1 fatcat:e7nr2fljbvcibdvxllrui6ybti

Low-Rank Approximation with 1/ϵ^1/3 Matrix-Vector Products [article]

Ainesh Bakshi, Kenneth L. Clarkson, David P. Woodruff
2022 arXiv   pre-print
Further, we prove a matrix-vector query lower bound of Ω(1/ϵ^1/3) for any fixed constant p ≥ 1, showing that surprisingly Θ̃(1/ϵ^1/3) is the optimal complexity for constant k.  ...  Our main result is an algorithm that uses only Õ(kp^1/6/ϵ^1/3) matrix-vector products, and works for all p ≥ 1. For p = 2 our bound improves the previous Õ(k/ϵ^1/2) bound to Õ(k/ϵ^1/3).  ...  CCF-1815840, Office of Naval Research (ONR) grant N00014-18-1-2562, and a Simons Investigator Award. Part of this work was done while A. Bakshi was an intern at IBM Almaden.  ... 
arXiv:2202.05120v4 fatcat:rdsx4fa3rvglhoxr2lj4yqpsfy

Vector-Matrix-Vector Queries for Solving Linear Algebra, Statistics, and Graph Problems

Cyrus Rashtchian, David P. Woodruff, Hanlin Zhu, Raghu Meka, Jarosław Byrka
2020 International Workshop on Approximation Algorithms for Combinatorial Optimization  
To motivate these queries, we observe that they generalize many previously studied models, such as independent set queries, cut queries, and standard graph queries.  ...  They also specialize the recently studied matrix-vector query model.  ...  Then with O(log( 1 ε )) queries, one can test whether M is a symmetric matrix with probability at least 1ε.  ... 
doi:10.4230/lipics.approx/random.2020.26 dblp:conf/approx/RashtchianWZ20 fatcat:lnwrpizapnhwxicklk5kbrailu

Stochastic Vertex Cover with Few Queries [article]

Soheil Behnezhad, Avrim Blum, Mahsa Derakhshan
2021 arXiv   pre-print
Our techniques also lead to improved bounds for bipartite stochastic matching. We obtain a 0.731-approximation with nearly-linear in 1/p per-vertex queries.  ...  In this work, we present a: * (2+ϵ)-approximation for general graphs which queries O(1/ϵ^3 p) edges per vertex, and a * 1.367-approximation for bipartite graphs which queries poly(1/p) edges per vertex  ...  Can we find an approximate MVC of G p by querying few, preferrably poly(1/p), edges of each vertex in the base graph G?  ... 
arXiv:2112.05415v1 fatcat:sf7lax56ane6zavpjkegeqmkhu

A Few Expert Queries Suffices for Sample-Efficient RL with Resets and Linear Value Approximation [article]

Philip Amortila, Nan Jiang, Dhruv Madeka, Dean P. Foster
2022 arXiv   pre-print
In particular, Delphi requires 𝒪̃(d) expert queries and a (d,H,|𝒜|,1/ε) amount of exploratory samples to provably recover an ε-suboptimal policy.  ...  expert queries.  ...  with poly (d, H, A, 1 ε ) queries [WAS21; WSG21].  ... 
arXiv:2207.08342v1 fatcat:5wulm3egt5ek5bgior6fhfnzjm

Ignorance is Almost Bliss: Near-Optimal Stochastic Matching With Few Queries

Avrim Blum, John Dickerson, Nika Haghtalab, Ariel D. Procaccia, Tuomas W Sandholm, Ankit Sharma
2018
The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries.  ...  Our main theoretical result for the stochastic matching (i.e., 2-set packing) problem is the design of an adaptive algorithm that queries only a constant number of edges per vertex and achieves a (1-ε)  ...  Matching With Few Queries we get M (E) ≤ M (E 1 ) + M (E 2 ).  ... 
doi:10.1184/r1/6606266.v1 fatcat:o53ui4uxjbb7fd6qzyj67jaxmi

Practical Route Planning Under Delay Uncertainty: Stochastic Shortest Path Queries

Sejoon Lim, Christian Sommer, Evdokia Nikolova, Daniela Rus
2012 Robotics: Science and Systems VIII  
such that approximate stochastic shortestpath queries can be answered in poly-logarithmic time (actual worst-case bounds depend on the probabilistic model).  ...  We improve on the prior state of the art by designing, analyzing, implementing, and evaluating data structures that answer approximate stochastic shortest-path queries.  ...  We improve upon the state of the art in stochastic path planning, providing a method that can answer stochastic shortestpath queries in poly-logarithmic time using a data structure that occupies space  ... 
doi:10.15607/rss.2012.viii.032 dblp:conf/rss/LimSNR12 fatcat:rg4z57d5jracff7uxyjcqupwky

Learning Approximate Stochastic Transition Models [article]

Yuhang Song, Christopher Grimm, Xianming Wang, Michael L. Littman
2017 arXiv   pre-print
We examine the problem of learning mappings from state to state, suitable for use in a model-based reinforcement-learning setting, that simultaneously generalize to novel states and can capture stochastic  ...  We show that currently popular generative adversarial networks struggle to learn these stochastic transition models but a modification to their loss functions results in a powerful learning algorithm for  ...  To connect back to Equation (14) , we consider following limit, lim δ=zε,ε→0 (11 d/ε ) d/δ = lim δ=zε,ε→0 e d/δ ln(11 d/ε ) = lim δ=zε,ε→0 e ln( d−ε d ) δ/d = lim ε→0 e d d−ε1 d z/d = e −1/z (16  ... 
arXiv:1710.09718v1 fatcat:da6rr6m7mrgg3bin343tzj3pru

Constructive derandomization of query algorithms [article]

Guy Blanc, Jane Lange, Li-Yang Tan
2019 arXiv   pre-print
algorithm that ε-approximates R. ∘ Online: Deterministically approximate the acceptance probability of R for a specific input x in time poly(N,q,1/ε), without constructing D in its entirety.  ...  We first give an algorithm that takes as input a randomized q-query algorithm R with description length N and a parameter ε, runs in time poly(N) · 2^O(q/ε), and returns a deterministic O(q/ε)-query algorithm  ...  a deterministic O(q/ε)-query algorithm D : {0, 1} n → [0, 1] satisfying E x D(x) − E r [R(x, r)] 2 ≤ ε. (3) The query complexity of D matches the guarantee of Fact 1.1, and is optimal by Fact 1.2.  ... 
arXiv:1912.03042v1 fatcat:jp7spyafu5csxoj3bui4hyus34

Query-focused multi-document summarization based on query-sensitive feature space

Wenpeng Yin, Yulong Pei, Fan Zhang, Lian'en Huang
2012 Proceedings of the 21st ACM international conference on Information and knowledge management - CIKM '12  
Query-oriented relevance, information richness and novelty are important requirements in query-focused summarization, which, to a considerable extent, determine the summary quality.  ...  Previous work either rarely took into account all above demands simultaneously or dealt with part of them in the dynamic process of choosing sentences to generate a summary.  ...  We report three common ROUGE scores in this paper, namely ROUGE-1, ROUGE-2 and ROUGE-SU4 which base on Uni-gram match, Bi-gram match, and unigram plus skip-bigram match with maximum skip distance of 4,  ... 
doi:10.1145/2396761.2398491 dblp:conf/cikm/YinPZH12 fatcat:itfqauwz4nf6la5moe6qk7jn7q

Memory, Communication, and Statistical Queries

Jacob Steinhardt, Gregory Valiant, Stefan Wager
2016 Annual Conference Computational Learning Theory  
Research Fellowship. ‡ Supported in part by a BC and EJ Eaves Stanford Graduate Fellowship. 1.  ...  What concepts can be efficiently learned by algorithms that extract only a few bits of information from each example?  ...  In our situation, we want to estimate z * = ∇f (w) as defined in Lemma 21 with as few statistical queries as possible.  ... 
dblp:conf/colt/SteinhardtVW16 fatcat:gviwx634pfaw7a4a4v3egwt5ny
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