Optimal Stopping and Loading Rules Considering Multiple Attempts and Task Success Criteria

Optimal Stopping Rules for Directionally Reinforced Processes

Optimal Stopping Rules for Sequential Hypothesis Testing

Suppose that we are given sample access to an unknown distribution p over n elements and an explicit distribution q over the same n elements. We would like to reject the null hypothesis “p = q” after seeing as few samples as possible, when p 6= q, while we never want to reject the null, when p = q. Well-known results show that Θ( √ n/ 2) samples are necessary and sufficient for distinguishing w...

Optimal stopping rules for active learning

Active learning algorithms aim to minimise the amount of labelled data used to learn a target concept. However, there is no formal framework for expressing the trade-off between needed accuracy and the cost of label acquisition, rendering the objective evaluation of algorithms problematic and the development of criteria for deciding when to terminate data acquisition impossible. This paper aims...

Optimal Stopping with Multiple Priors

We develop a theory of optimal stopping under Knightian uncertainty. A suitable martingale theory for multiple priors is derived in order to extend the classical dynamic programming or Snell envelope approach to multiple priors. We relate the multiple prior theory to the classical setup via a minimax theorem. In a multiple prior version of the classical i.i.d. model we discuss several examples ...

Optimal stopping in a natural sampling task

Sampling biases are often assumed to arise from the type of information that learners sample (Fiedler, 2008), the possibility of negative payoffs (Denrell, 2001), or the prevalence of small samples (Kareev et al., 2002). Here, we show that even in a natural sampling situation (repeated Bernoulli trials), in which a learner’s only decision is when to stop sampling, different sampling goals can h...