用鞅后验神经网络实现快速在线决策，推理速度比传统方法快10-100倍。
Martingale Posterior Neural Networks for Fast Sequential Decision Making
- 直接建模未来一步预测分布，用神经网络参数化并实时更新
- 在非平稳上下文随机赌局和贝叶斯优化中表现优异，推理提速10-100倍
- 无需重放数据，适合需要快速响应的在线决策场景
我们提出可扩展的在线学习算法，用于神经网络参数与贝叶斯序贯决策。不同于传统贝叶斯神经网络通过参数后验生成预测不确定性，我们的方法采用以预测为核心的视角，基于鞅后验。具体而言，我们直接对一步前向后验预测进行参数化，使用神经网络表示，并通过随观测数据到来而顺序更新。该方法将贝叶斯决策与参数空间推断解耦：决策时从后验预测中采样，参数更新则通过快速的类似卡尔曼滤波的频率主义递推完成。算法在完全在线、无重放的设置下运行，提供有原则的不确定性量化，且无需代价高昂的后验采样。实验表明，其在非平稳上下文随机赌局和贝叶斯优化任务中表现出色，推理速度比经典汤普森采样快10-100倍，同时保持相当或更优的决策性能。
原文摘要 · Abstract (English)
We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model parameters, our methods adopt a predictive-first perspective based on martingale posteriors. In particular, we work directly with the one-step-ahead posterior predictive, which we parameterize with a neural network and update sequentially with incoming observations. This decouples Bayesian decision-making from parameter-space inference: we sample from the posterior predictive for decision making, and update the parameters of the posterior predictive via fast, frequentist Kalman-filter-like recursions. Our algorithms operate in a fully online, replay-free setting, providing principled uncertainty quantification without costly posterior sampling. Empirically, they achieve competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization, offering 10-100 times faster inference than classical Thompson sampling while maintaining comparable or superior decision performance.
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