On the Complexity of Bayesian Signal Processing

2026-08-30

AI Summary

本文探讨了贝叶斯信号处理的复杂性问题，通过构建计算框架分析最优决策的难解性，并讨论了近似概念下的可处理条件。

Abstract

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.

Problem

• Bayesian decision-making
• computational complexity
• signal processing
• tractability

Innovation

• Bayesian decision-making
• tractability
• signal support
• sample-based Bayesian learning
• bounded rationality