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Interactive Value Iteration for Markov Decision Processes with Unknown Rewards

Paul Weng, Bruno Zanuttini

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Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence. Pages 2415-2420.

Abstract

To tackle the potentially hard task of defining the reward function in a Markov Decision Process, we propose a new approach, based on Value Iteration, which interweaves the elicitation and optimization phases. We assume that rewards whose numeric values are unknown can only be ordered, and that a tutor is present to help comparing sequences of re- wards. We first show how the set of possible reward functions for a given preference relation can be rep- resented as a polytope. Then our algorithm, called Interactive Value Iteration, searches for an optimal policy while refining its knowledge about the pos- sible reward functions, by querying a tutor when necessary. We prove that the number of queries needed before finding an optimal policy is upper- bounded by a polynomial in the size of the problem, and we present experimental results which demon- strate that our approach is efficient in practice.

Paul Weng, and Bruno Zanuttini. 2013. Interactive Value Iteration for Markov Decision Processes with Unknown Rewards. In Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI-13. IJCAI, 2415–2420. https://ijcai.org/proceedings/2013/355
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