提出可信度新概念，统一学习速率、卡尔曼滤波等机制。
Learning with Confidence
- 用公理化方法定义学习中的可信度，区别于概率
- 证明可信度可连续测量，且在特定条件下可用向量场表示
- 适用于理解自适应学习系统，如强化学习与贝叶斯更新
我们刻画了一种在学习或信念更新中出现的可信度概念：对新信息的信任程度及其对信念状态的影响。这种学习者的可信度常被误认为概率或似然，但本质不同——它涵盖了文献中多个常见概念，包括学习速率、训练轮次、Shafer的证据权重和卡尔曼增益。我们形式化地给出了学习可信度的公理体系，提出了两种在连续尺度上衡量可信度的典型方式，并证明可信度总能以这种方式表示。在额外假设下，我们导出了基于向量场和损失函数的更紧凑的可信度学习表示。这些表示引入了复合“并行”观测的扩展语言。我们还指出，贝叶斯规则是损失表示为线性期望时的特例。
原文摘要 · Abstract (English)
We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily mistaken for) probability or likelihood, but it is fundamentally a different concept -- one that captures many familiar concepts in the literature, including learning rates and number of training epochs, Shafer's weight of evidence, and Kalman gain. We formally axiomatize what it means to learn with confidence, give two canonical ways of measuring confidence on a continuum, and prove that confidence can always be represented in this way. Under additional assumptions, we derive more compact representations of confidence-based learning in terms of vector fields and loss functions. These representations induce an extended language of compound "parallel" observations. We characterize Bayes Rule as the special case of an optimizing learner whose loss representation is a linear expectation.
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