贝叶斯信号处理的复杂性
On the Complexity of Bayesian Signal Processing
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究开发贝叶斯决策计算框架，证明无全局最优动作时贝叶斯最优选择难解，刻画近似概念下可处理性，PAC准则下样本贝叶斯学习可处理当且仅当信号支撑有界，为有限理性等提供依据。
AI中文摘要：
我们开发了一种贝叶斯决策的计算框架。我们证明，只要不存在在所有状态下都最优的动作，贝叶斯最优选择就是难解的。这种难解性不一定源于动作、状态或信号空间过大，也不一定源于复杂的效用函数：从难以解释的信号中提取足够信息以实现最优动作本身就可能是计算上困难的。我们还刻画了不同近似概念下的可处理性，并确定了其困难来源。在 Probably Approximately Correct（PAC）准则下，基于样本的贝叶斯学习是可处理的，当且仅当信号支撑是有界的。我们的结果为有限理性、代价高昂的贝叶斯推理以及基于样本的贝叶斯学习提供了依据。
英文摘要：
We develop a computational framework for Bayesian decision-making. We show that as long as no action is optimal in every state, Bayes-optimal choice is intractable. This hardness need not arise from large action, state, or signal spaces, nor from a complicated represented utility function: extracting enough information from a hard-to-interpret signal to act optimally can itself be computationally hard. We also characterize tractability across approximation notions and identify their sources of difficulty. Under the probably approximately correct criterion, sample-based Bayesian learning is tractable if and only if the signal support is bounded. Our results provide justifications for bounded rationality, costly Bayesian inference, and sample-based Bayesian learning.
