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arXiv · 1704.05303

The Robot Routing Problem for Collecting Aggregate Stochastic Rewards

Rayna Dimitrova·Ivan Gavran·Rupak Majumdar·Vinayak S. Prabhu·Sadegh Esmaeil Zadeh Soudjani
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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, Sadegh Esmaeil Zadeh Soudjani. 2017-04-18. The Robot Routing Problem for Collecting Aggregate Stochastic Rewards. https://arxiv.org/abs/1704.05303

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