On Exploration, Exploitation and Learning in Adaptive Importance Sampling

Xiaoyu Lu; Tom Rainforth; Yuan Zhou; Jan-Willem van de Meent; Yee Whye Teh

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arXiv · 1810.13296

On Exploration, Exploitation and Learning in Adaptive Importance Sampling

Xiaoyu Lu·Tom Rainforth·Yuan Zhou·Jan-Willem van de Meent·Yee Whye Teh

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Abstract

We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade-off between exploration and exploitation in this adaptation. Borrowing ideas from the bandits literature, we propose Daisee, a partition-based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has $\mathcal{O}(\sqrt{T}(\log T)^{\frac{3}{4}})$ cumulative pseudo-regret, where $T$ is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.

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Xiaoyu Lu, Tom Rainforth, Yuan Zhou, Jan-Willem van de Meent, Yee Whye Teh. 2018-10-31. On Exploration, Exploitation and Learning in Adaptive Importance Sampling. https://arxiv.org/abs/1810.13296

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