Online Pandora’s Boxes and Bandits

Esfandiari, Hossein; Hajiaghayi, Mohammad Taghi; Lucier, Brendan; Mitzenmacher, Michael

doi:10.1609/aaai.v33i01.33011885

Cited by 10 publications

(5 citation statements)

References 8 publications

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“…The hardness result above, along with recent work on modified versions of the Pandora's Box Problem, such as Beyhaghi and Kleinberg [2019], Singla [2018b,a], Kleinberg and Kleinberg [2018], Esfandiari et al [2019], motivates the study of approximation algorithms for the more general case of order constraints. Of the above citations, the ones closest to our setting are Singla [2018b,a], where the author reduces the Pandora's Box Problem in the presence of downwards-closed constraints to adaptive maximization of non-negative submodular functions.…”

Section: Approximation Resultsmentioning

confidence: 99%

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Pandora's Box Problem with Order Constraints

Boodaghians¹,

Fusco²,

Lazos³

et al. 2020

Preprint

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The Pandora's Box Problem, originally formalized by Weitzman in 1979, models selection from set of random, alternative options, when evaluation is costly. This includes, for example, the problem of hiring a skilled worker, where only one hire can be made, but the evaluation of each candidate is an expensive procedure.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 marginal gain for opening the box. We study for the first time this problem when order -or precedence -constraints are imposed between the boxes. We show that, despite the difficulty of defining reservation values for the boxes which take into account both in-depth and in-breath exploration of the various options, greedy optimal strategies exist and can be efficiently computed for tree-like order constraints.We also prove that finding approximately optimal adaptive search strategies is NP-hard when certain matroid constraints are used to further restrict the set of boxes which may be opened, or when the order constraints are given as reachability constraints on a DAG. We complement the above result by giving approximate adaptive search strategies based on a connection between optimal adaptive strategies and non-adaptive strategies with bounded adaptivity gap for a carefully relaxed version of the problem.

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Section: Approximation Resultsmentioning

confidence: 99%

“…the ratio between the best adaptive solution and the best oblivious one as in Gupta et al [2017] and later Bradac et al [2019]. Recently Kleinberg and Kleinberg [2018] and Esfandiari et al [2019] studied a connection between the Pandora's Box Problem and another well known optimal stopping problem, termed the Prophet Inequalities.…”

Section: Related Workmentioning

confidence: 99%

Pandora's Box Problem with Order Constraints

Boodaghians¹,

Fusco²,

Lazos³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24) line of research studying PANDORA'S BOX and its variants e.g. where boxes can be selected without inspection (Doval 2018;Beyhaghi and Kleinberg 2019), there is correlation between the boxes (Chawla et al 2020(Chawla et al , 2023, the boxes have to be inspected in a specific order (Boodaghians et al 2020) or boxes are inspected in an online manner (Esfandiari et al 2019) or over T rounds (Gergatsouli and Tzamos 2022;Gatmiry et al 2022). Some work is also done in the generalized setting where more information can be obtained for a price (Charikar et al 2000;Gupta and Kumar 2001;Chen et al 2015b,a).…”

Section: Related Workmentioning

confidence: 99%

Contextual Pandora’s Box

Atsidakou,

Caramanis,

Gergatsouli

et al. 2024

AAAI

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Pandora’s Box is a fundamental stochastic optimization problem, where the decision-maker must find a good alternative, while minimizing the search cost of exploring the value of each alternative. In the original formulation, it is assumed that accurate distributions are given for the values of all the alternatives, while recent work studies the online variant of Pandora’s Box where the distributions are originally unknown. In this work, we study Pandora’s Box in the online setting, while incorporating context. At each round, we are presented with a number of alternatives each having a context, an exploration cost and an unknown value drawn from an unknown distribution that may change at every round. Our main result is a no-regret algorithm that performs comparably well against the optimal algorithm which knows all prior distributions exactly. Our algorithm works even in the bandit setting where the algorithm never learns the values of the alternatives that were not explored. The key technique that enables our result is a novel modification of the realizability condition in contextual bandits that connects a context to a sufficient statistic of each alternative’s distribution (its reservation value) rather than its mean.

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“…Since then, there has been a long line of research studying Pandora's Box and its variants e.g. where boxes can be selected without inspection [6,7], there is correlation between the boxes [8], the boxes have to be inspected in a specific order [9] or boxes are inspected in an online manner [10]. Some work is also done in the generalized setting where more information can be obtained for a price [11,12,13,14].…”

Section: Related Workmentioning

confidence: 99%

Contextual Pandora's Box

Atsidakou¹,

Caramanis²,

Gergatsouli³

et al. 2022

Preprint

View full text Add to dashboard Cite

Pandora's Box is a fundamental stochastic optimization problem, where the decisionmaker must find a good alternative while minimizing the search cost of exploring the value of each alternative. In the original formulation, it is assumed that accurate priors are given for the values of all the alternatives, while recent work studies the online variant of Pandora's Box where priors are originally unknown. In this work, we extend Pandora's Box to the online setting, while incorporating context. At every round, we are presented with a number of alternatives each having a context, an exploration cost and an unknown value drawn from an unknown prior distribution that may change at every round. Our main result is a noregret algorithm that performs comparably well to the optimal algorithm which knows all prior distributions exactly. Our algorithm works even in the bandit setting where the algorithm never learns the values of the alternatives that were not explored. The key technique that enables our result is novel a modification of the realizability condition in contextual bandits that connects a context to the reservation value of the corresponding distribution rather than its mean.

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Online Pandora’s Boxes and Bandits

Cited by 10 publications

References 8 publications

Pandora's Box Problem with Order Constraints

Pandora's Box Problem with Order Constraints

Contextual Pandora’s Box

Contextual Pandora's Box

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