🤖 AI Summary
This paper studies cost-aware sequential hypothesis testing: a decision-maker selects actions with random positive costs to identify the true hypothesis while minimizing the expected total cost, subject to an average error-rate constraint. We innovatively introduce an adjustable per-action deadline mechanism that allows action termination to cap unbounded costs. Under the ex-post cost revelation model, we prove that deadlines do not alter the optimal expected cost. In the ex-ante model—where costs are unknown at selection time—we first quantify the deadline-induced inflation in action frequency and propose the “effective equivalent cost” concept, enabling performance under stochastic costs to approach that of the constant-cost benchmark. Our methodology integrates sequential decision-making, optimal stopping, Bayesian hypothesis testing, and cost-sensitive optimization.
📝 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.