@inproceedings{d16d046c60214f69a5c44fdee08fccb5,

title = "The Markovian Price of Information",

abstract = "Suppose there are n Markov chains and we need to pay a per-step price to advance them. The “destination” states of the Markov chains contain rewards; however, we can only get rewards for a subset of them that satisfy a combinatorial constraint, e.g., at most k of them, or they are acyclic in an underlying graph. What strategy should we choose to advance the Markov chains if our goal is to maximize the total reward minus the total price that we pay? In this paper we introduce a Markovian price of information model to capture settings such as the above, where the input parameters of a combinatorial optimization problem are given via Markov chains. We design optimal/approximation algorithms that jointly optimize the value of the combinatorial problem and the total paid price. We also study robustness of our algorithms to the distribution parameters and how to handle the commitment constraint. Our work brings together two classical lines of investigation: getting optimal strategies for Markovian multi-armed bandits, and getting exact and approximation algorithms for discrete optimization problems using combinatorial as well as linear-programming relaxation ideas.",

keywords = "Gittins index, Multi-armed bandits, Probing algorithms",

author = "Anupam Gupta and Haotian Jiang and Ziv Scully and Sahil Singla",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/978-3-030-17953-3_18",

language = "English (US)",

isbn = "9783030179526",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "233--246",

editor = "Andrea Lodi and Viswanath Nagarajan",

booktitle = "Integer Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings",

address = "Germany",

note = "20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019 ; Conference date: 22-05-2019 Through 24-05-2019",

}