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Daisee: Adaptive importance sampling by balancing exploration and exploitation

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  • Xiaoyu Lu
  • Tom Rainforth
  • Yee Whye Teh

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 online learning literature, we propose Daisee, a partition‐based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has 𝒪(T(logT)34) cumulative pseudo‐regret, where T$$ T $$ 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.

Suggested Citation

  • Xiaoyu Lu & Tom Rainforth & Yee Whye Teh, 2023. "Daisee: Adaptive importance sampling by balancing exploration and exploitation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1298-1324, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1298-1324
    DOI: 10.1111/sjos.12637
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    References listed on IDEAS

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    1. Jean-Marie Cornuet & Jean-Michel Marin & Antonietta Mira & Christian P. Robert, 2012. "Adaptive Multiple Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 798-812, December.
    2. repec:dau:papers:123456789/6072 is not listed on IDEAS
    3. repec:dau:papers:123456789/10690 is not listed on IDEAS
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