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The Robot Routing Problem for Collecting Aggregate Stochastic Rewards

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

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Rayna Dimitrova
Ivan Gavran
Rupak Majumdar
Vinayak S. Prabhu
Sadegh Esmaeil Zadeh Soudjani

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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) https://doi.org/10.4230/LIPIcs.CONCUR.2017.13

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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Keywords
  • Path Planning
  • Graph Games
  • Quantitative Objectives
  • Discounting

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