用强化学习思路优化采样，大幅减少昂贵密度评估次数。
Sampling as Bandits: Evaluation-Efficient Design for Black-Box Densities
- 基于多臂老虎机框架，逐个选择最优样本。
- 在多重模式和重尾分布上显著减少评估次数。
- 适合高成本密度评估的贝叶斯推断场景。
我们提出带状重要性采样（BIS），一种针对目标密度计算代价高昂场景的重要性采样框架。BIS通过多臂老虎机驱动的序列选择过程，直接优化样本集合，而非调整提案分布，从而在保证采样精度的同时最小化目标密度评估次数。理论证明，无论采用何种策略，加权样本均弱收敛，蒙特卡洛估计具有一致性。本文还提出一种实用策略，利用高斯过程代理模型指导采样，借鉴贝叶斯优化思想。大量数值实验表明，BIS在多重模式、重尾分布及涉及马尔可夫随机场的真实贝叶斯推断任务中表现优异。
原文摘要 · Abstract (English)
We propose bandit importance sampling (BIS), a powerful importance sampling framework tailored for settings in which evaluating the target density is computationally expensive. BIS facilitates accurate sampling while minimizing the required number of target-density evaluations. In contrast to adaptive importance sampling, which optimizes a proposal distribution, BIS directly optimizes the set of samples through a sequential selection process driven by multi-armed bandits. BIS serves as a general framework that accommodates user-defined bandit strategies. Theoretically, the weak convergence of the weighted samples, and thus the consistency of the Monte Carlo estimator, is established regardless of the specific strategy employed. In this paper, we present a practical strategy that leverages Gaussian process surrogates to guide sample selection, adapting the principles of Bayesian optimization for sampling. Comprehensive numerical studies demonstrate the superior performance of BIS across multimodal, heavy-tailed distributions, and real-world Bayesian inference tasks involving Markov random fields.
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