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Pandora's Box Problem with Order Constraints [article]

Shant Boodaghians, Federico Fusco, Philip Lazos, Stefano Leonardi
2020 arXiv   pre-print
We study for the first time this problem when order - or precedence - constraints are imposed between the boxes.  ...  Weitzman showed that the Pandora's Box Problem admits an elegant, simple solution, where the options are considered in decreasing order of reservation value,i.e., the value that reduces to zero the expected  ...  Pandora's Box Problem with order constraints generalizing to any prefix-closed constraint.  ... 
arXiv:2002.06968v2 fatcat:erj35z7gljad3ojpvraapwxoem

Online Pandora's Boxes and Bandits

Hossein Esfandiari, MohammadTaghi HajiAghayi, Brendan Lucier, Michael Mitzenmacher
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Our problem generalizes both the classic Pandora's box problem and the prophet inequality framework.  ...  We consider online variations of the Pandora's box problem (Weitzman 1979), a standard model for understanding issues related to the cost of acquiring information for decision-making.  ...  The Pandora's box problem incorporates two key decision aspects: the ordering for opening boxes, and when to stop.  ... 
doi:10.1609/aaai.v33i01.33011885 fatcat:2xgwhubkcba6tbog5yfcvs47fu

Online Pandora's Boxes and Bandits [article]

Hossein Esfandiari, MohammadTaghi Hajiaghayi, Brendan Lucier, Michael Mitzenmacher
2019 arXiv   pre-print
Our problem generalizes both the classic Pandora's box problem and the prophet inequality framework.  ...  We consider online variations of the Pandora's box problem (Weitzman. 1979), a standard model for understanding issues related to the cost of acquiring information for decision-making.  ...  The Pandora's box problem incorporates two key decision aspects: the ordering for opening boxes, and when to stop.  ... 
arXiv:1901.10698v1 fatcat:bmcdbzvfavhjfhq42yujrumfby

Pandora's Problem with Nonobligatory Inspection [article]

Hedyeh Beyhaghi, Robert Kleinberg
2019 arXiv   pre-print
Unlike the original Pandora's problem, the version with nonobligatory inspection cannot be solved optimally by any simple ranking-based policy, and it is unknown whether there exists any polynomial-time  ...  Martin Weitzman's "Pandora's problem" furnishes the mathematical basis for optimal search theory in economics.  ...  To make the problem with paired boxes equivalent to the original problem instance, we must impose an additional constraint that search policies for the paired-box problem may open at most one of the two  ... 
arXiv:1905.01428v1 fatcat:sg6xcnh4fbcrdd5obxkemi5pti

Efficient Approximation Schemes for Stochastic Probing and Prophet Problems [article]

Danny Segev, Sahil Singla
2020 arXiv   pre-print
Turning our attention to selection-stopping settings, we further derive an EPTAS for the Free-Order Prophets problem [Agrawal et al., EC'20] and for its cost-driven generalization, Pandora's Box with Commitment  ...  Our main contribution is a general framework to design efficient polynomial time approximation schemes (EPTAS) for fundamental classes of stochastic combinatorial optimization problems.  ...  Equivalence of Pandora's Box with Commitment and Free-Order Prophets In what follows, we study the Pandora's Box with Commitment problem, showing how to obtain an EPTAS through a reduction to Free-Order  ... 
arXiv:2007.13121v1 fatcat:flwzg7nd6fal7grdgobje535pa

A more general Pandora's rule? [article]

Wojciech Olszewski, Richard Weber
2015 arXiv   pre-print
In a classic model analysed by Weitzman an agent is presented with boxes containing prizes. She may open boxes in any order, discover prizes within, and optimally stop.  ...  The problem is solved by a so-called Pandora's rule, and has applications to searching for a house or job.  ...  The so-called Pandora's rule, which is optimal for Weitzman's problem, is to first compute the reservation value of each box, as if each were the only box, and then open boxes in descending order of these  ... 
arXiv:1509.09095v1 fatcat:7ghj3yyynzejlhasu2jtbwpifu

The Price of Information in Combinatorial Optimization [chapter]

Sahil Singla
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
A classical example of the above setting is Weitzman's "Pandora's box" problem where we are given probability distributions on values of n independent random variables.  ...  Situations such as the above two often arise in practice where we wish to find a good solution to an optimization problem, but we start with only some partial knowledge about the parameters of the problem  ...  it to Pandora's box.  ... 
doi:10.1137/1.9781611975031.161 dblp:conf/soda/Singla18 fatcat:ffxlb43y4bdmrico7jzsvcb2fm

Pandora's Box with Correlations: Learning and Approximation [article]

Shuchi Chawla, Evangelia Gergatsouli, Yifeng Teng, Christos Tzamos, Ruimin Zhang
2020 arXiv   pre-print
In this paper, we provide the first approximation algorithms for Pandora's Box-type problems with correlations.  ...  The Pandora's Box problem and its extensions capture optimization problems with stochastic input where the algorithm can obtain instantiations of input random variables at some cost.  ...  to find it (as in the Pandora's Box problem).  ... 
arXiv:1911.01632v2 fatcat:jfdcn6ba4rcb3bjdvvrplsqqry

On optimal ordering in the optimal stopping problem [article]

Shipra Agrawal, Jay Sethuraman, Xingyu Zhang
2020 arXiv   pre-print
In the classical optimal stopping problem, a player is given a sequence of random variables X_1... X_n with known distributions.  ...  To demonstrate the benefits of order selection, we prove a novel prophet inequality showing that, when the support of each random variable has size at most 2, the optimal ordering can achieve an expected  ...  In fact the optimal ordering problem is a special case of what they refer to as the committed Pandora's box problem, a variant of the Pandora's box problem Weitzman (1979) .  ... 
arXiv:1911.05096v2 fatcat:ld6lydhdxbh7fpwgkepf3uzf2y

Knowledge Discovery in Real Databases: A Report on the IJCAI-89 Workshop

Gregory Piatetsky-Shapiro
1991 The AI Magazine  
General Motors is automatically constructing diagnostic expert systems from a database of car trouble symptoms and problems found. The IRS is looking for patterns of tax cheating in its databases.  ...  This is the goal of the recently started MACHINE LEARNING TOOLBOX project at the University of Aberdeen in Scotland, UK, run in cooperation with Esprit.  ...  Pandora's Box? An important issue that was only touched at the workshop is the appropriateness of discovery. A careless approach to discovery may open a Pandora's Box of unpleasant surprises.  ... 
doi:10.1609/aimag.v11i4.873 dblp:journals/aim/Piatetsky-Shapiro91 fatcat:7hinxwf6prhpvdnbjsa4peun54

Reverse engineering for mobile systems forensics with Ares

John Tuttle, Robert J. Walls, Erik Learned-Miller, Brian Neil Levine
2010 Proceedings of the 2010 ACM workshop on Insider threats - Insider Threats '10  
Without modification to that grammar, Ares parsed most phones' data with 90% of the accuracy of a commercial forensics tool based on manual reverse engineering, and all phones with at least 50% accuracy  ...  In preliminary tests, Ares was able to parse data on Motorola phones with minimal modification to the Nokia-based grammar.  ...  The programmers of Pandora's Box confirmed with us that they manually reverse engineered the format of each of the tested phones.  ... 
doi:10.1145/1866886.1866892 fatcat:wedk4alz4rg3ppf7vr5rogztp4

Handling audio and video streams in a distributed environment

Alan Jones, Andrew Hopper
1993 ACM SIGOPS Operating Systems Review  
They attempt to give the user the best possible service while dealing with error and overload conditions. Pandora uses a sub-system to handle the multi-media peripherals.  ...  Clawback buffers are used to resynchronise streams at their destinations with minimum latency. The system has proved robust in normal use, under overload, and in the presence of errors.  ...  While we will use Pandora's boxes and special purpose video tablets for display, the majority of video will be displayed on standard workstations equipped with ATM network cards.  ... 
doi:10.1145/173668.168638 fatcat:w4si3gspqfglddwsont42v744m

Handling audio and video streams in a distributed environment

Alan Jones, Andrew Hopper
1993 Proceedings of the fourteenth ACM symposium on Operating systems principles - SOSP '93  
They attempt to give the user the best possible service while dealing with error and overload conditions. Pandora uses a sub-system to handle the multi-media peripherals.  ...  Clawback buffers are used to resynchronise streams at their destinations with minimum latency. The system has proved robust in normal use, under overload, and in the presence of errors.  ...  While we will use Pandora's boxes and special purpose video tablets for display, the majority of video will be displayed on standard workstations equipped with ATM network cards.  ... 
doi:10.1145/168619.168638 dblp:conf/sosp/JonesH93 fatcat:fpumg5hj7zahrjljbuucmcnprm

A PTAS for a Class of Stochastic Dynamic Programs [article]

Hao Fu, Jian Li, Pan Xu
2018 arXiv   pre-print
random variable with a known (discrete) distribution π_i.  ...  We also obtain PTAS for some generalizations and variants of the problem and some other problems.  ...  Hao Fu would like to thank Sahil Singla for useful discussions about Pandora's Box problem. Pan Xu would like to thank Aravind Srinivasan for his many useful comments.  ... 
arXiv:1805.07742v1 fatcat:smtddqvovfenvhjsy5nep5dfmq

ROC++: Robust Optimization in C++ [article]

Phebe Vayanos, Qing Jin, George Elissaios
2020 arXiv   pre-print
Many of these techniques apply to problems with either robust (worst-case) or stochastic (expectation) objectives and can thus be tailored to the risk preferences of the decision-maker.  ...  Robust optimization techniques rely on duality theory (potentially augmented with approximations) to transform a semi-infinite optimization problem to a finite program of benign complexity (the "robust  ...  Stochastic Best Box Problem with Uncertain Observation Costs We consider a variant of Pandora's Box problem, known as Best Box (BB), in which observation costs are uncertain and subject to a budget constraint  ... 
arXiv:2006.08741v1 fatcat:pkqlls3yf5gzdg6w7pwpzg6kfm
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