On Cost-Aware Sequential Hypothesis Testing with Random Costs and Action Cancellation

TL;DR

This paper investigates cost-aware sequential hypothesis testing with random action costs and the option to cancel actions, analyzing how deadlines influence total costs under different cost-revelation models.

Contribution

It introduces a framework for incorporating action cancellation with deadlines in cost-aware hypothesis testing and characterizes their effects under ex-post and ex-ante cost models.

Findings

Per-action deadlines do not affect expected cost in ex-post model.

In ex-ante model, deadlines can reduce total expected cost by inflating action counts.

The paper provides conditions when deadlines are beneficial and analyzes specific families.

Abstract

We study a variant of cost-aware sequential hypothesis testing in which a single active Decision Maker (DM) selects actions with positive, random costs to identify the true hypothesis under an average error constraint, while minimizing the expected total cost. The DM may abort an in-progress action, yielding no sample, by truncating its realized cost at a smaller, tunable deterministic limit, which we term a per-action deadline. We analyze how this cancellation option can be exploited under two cost-revelation models: ex-post, where the cost is revealed only after the sample is obtained, and ex-ante, where the cost accrues before sample acquisition. In the ex-post model, per-action deadlines do not affect the expected total cost, and the cost-error tradeoffs coincide with the baseline obtained by replacing deterministic costs with cost means. In the ex-ante model, we show how per-action deadlines inflate the expected number of times actions are applied, and that the resulting expected total cost can be reduced to the constant-cost setting by introducing an effective per-action cost. We characterize when deadlines are beneficial and study several families in detail.