eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-09-01
13:1
13:17
10.4230/LIPIcs.CONCUR.2017.13
article
The Robot Routing Problem for Collecting Aggregate Stochastic Rewards
Dimitrova, Rayna
Gavran, Ivan
Majumdar, Rupak
Prabhu, Vinayak S.
Soudjani, Sadegh Esmaeil Zadeh
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol085-concur2017/LIPIcs.CONCUR.2017.13/LIPIcs.CONCUR.2017.13.pdf
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