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DOI: 10.4230/LIPIcs.CONCUR.2017.13

The Robot Routing Problem for Collecting Aggregate Stochastic Rewards

Authors: Rayna Dimitrova, Ivan Gavran, Rupak Majumdar, Vinayak S. Prabhu, and Sadegh Esmaeil Zadeh Soudjani

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract

We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The robot routing problem is modeled as a graph whose nodes are stochastic processes generating potential rewards over discrete time. The rewards are generated according to the stochastic process, but at each step, an existing reward disappears with a given probability. The edges in the graph encode the (unit-distance) paths between the rewards' locations. On visiting a node, the robot collects the accumulated reward at the node at that time, but traveling between the nodes takes time. The optimization question asks to compute an optimal (or epsilon-optimal) path that maximizes the expected collected rewards. We consider the finite and infinite-horizon robot routing problems. For finite-horizon, the goal is to maximize the total expected reward, while for infinite horizon we consider limit-average objectives. We study the computational and strategy complexity of these problems, establish NP-lower bounds and show that optimal strategies require memory in general. We also provide an algorithm for computing epsilon-optimal infinite paths for arbitrary epsilon > 0.

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Rayna Dimitrova, Ivan Gavran, Rupak Majumdar, Vinayak S. Prabhu, and Sadegh Esmaeil Zadeh Soudjani. The Robot Routing Problem for Collecting Aggregate Stochastic Rewards. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dimitrova_et_al:LIPIcs.CONCUR.2017.13,
  author =	{Dimitrova, Rayna and Gavran, Ivan and Majumdar, Rupak and Prabhu, Vinayak S. and Soudjani, Sadegh Esmaeil Zadeh},
  title =	{{The Robot Routing Problem for Collecting Aggregate Stochastic Rewards}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.13},
  URN =		{urn:nbn:de:0030-drops-77920},
  doi =		{10.4230/LIPIcs.CONCUR.2017.13},
  annote =	{Keywords: Path Planning, Graph Games, Quantitative Objectives, Discounting}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2015.483

Rely/Guarantee Reasoning for Asynchronous Programs

Authors: Ivan Gavran, Filip Niksic, Aditya Kanade, Rupak Majumdar, and Viktor Vafeiadis

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract

Asynchronous programming has become ubiquitous in smartphone and web application development, as well as in the development of server-side and system applications. Many of the uses of asynchrony can be modeled by extending programming languages with asynchronous procedure calls - procedures not executed immediately, but stored and selected for execution at a later point by a non-deterministic scheduler. Asynchronous calls induce a flow of control that is difficult to reason about, which in turn makes formal verification of asynchronous programs challenging. In response, we take a rely/guarantee approach: Each asynchronous procedure is verified separately with respect to its rely and guarantee predicates; the correctness of the whole program then follows from the natural conditions the rely/guarantee predicates have to satisfy. In this way, the verification of asynchronous programs is modularly decomposed into the more usual verification of sequential programs with synchronous calls. For the sequential program verification we use Hoare-style deductive reasoning, which we demonstrate on several simplified examples. These examples were inspired from programs written in C using the popular Libevent library; they are manually annotated and verified within the state-of-the-art Frama-C platform.

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Ivan Gavran, Filip Niksic, Aditya Kanade, Rupak Majumdar, and Viktor Vafeiadis. Rely/Guarantee Reasoning for Asynchronous Programs. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 483-496, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{gavran_et_al:LIPIcs.CONCUR.2015.483,
  author =	{Gavran, Ivan and Niksic, Filip and Kanade, Aditya and Majumdar, Rupak and Vafeiadis, Viktor},
  title =	{{Rely/Guarantee Reasoning for Asynchronous Programs}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{483--496},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.483},
  URN =		{urn:nbn:de:0030-drops-53902},
  doi =		{10.4230/LIPIcs.CONCUR.2015.483},
  annote =	{Keywords: Asynchronous programs, rely/guarantee reasoning}
}

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Documents authored by Gavran, Ivan

The Robot Routing Problem for Collecting Aggregate Stochastic Rewards

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Rely/Guarantee Reasoning for Asynchronous Programs

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