决策需要不确定性量化[讲义笔记]

中文摘要 AI 辅助

许多信号处理系统最终目的是行动。当决策者（或智能体）采取行动所依据的状态变量不确定时，不确定性的表示方式决定了智能体的表现及表现的可信度。本讲义笔记从基本原理出发，在单一决策理论框架内，阐述了智能体的目标、知识与足以实现最优行动的不确定性表示形式之间的联系。首先，在已知环境分布下，风险中性智能体需要状态的后验分布，风险厌恶智能体可依赖预测集和最坏情况决策规则且不失最优性。接着探讨环境未知的情况，确定了三种解决认知不确定性的互补方法：固定预测器的校准、基于分布鲁棒优化的可信（模糊）集以及对模型参数的贝叶斯推断。共同要点是可靠决策需要与决策目标和智能体知识概况相匹配的不确定性表示，以及对智能体实际获得效用的保证。

英文摘要

Many signal processing systems ultimately exist to act. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

发表机构

• Institute for Intelligent Networked Systems, Northeastern University London（智能网络系统研究所，伦敦大学东北学院）

机构由 AI 辅助整理，请以论文原文为准。