Efficient Online Learning for Optimizing Value of Information: Theory and Application to Interactive Troubleshooting 

Yuxin Chen, Jean-Michel Renders, Morteza Haghir Chehreghani, Andreas Krause
Conference on Uncertainty in Artificial Intelligence (UAI), Sydney, Australia, 11 - 15 August 2017

We consider the optimal value of information problem, where the goal is to sequentially select a set of tests with a minimal cost, so
that one can efficiently make the best decision based on the observed outcomes. Existing algorithms are either heuristics with no guarantees,
or scale poorly (with exponential run time in terms of the number of available tests). Moreover, these methods assume a known
distribution over the test outcomes, which is often not the case in practice. We propose a sampling-based online learning
framework to address the above issues. First, assuming the distribution over hypotheses is known, we propose a dynamic hypothesis enumeration strategy, which allows efficient information gathering with strong theoretical guarantees. We show that with
sufficient amount of samples, one can identify a near-optimal decision with high probability. Second, when the parameters of the hypotheses distribution are unknown, we propose an algorithm which learns the parameters progressively via posterior sampling in an online fashion. We further establish a rigorous bound on the expected regret. We
demonstrate the effectiveness of our approach on a real-world interactive troubleshooting application, and show that one can efficiently make high-quality decisions with low cost.

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