AI Insight
This paper introduces Cost-Aware Sequential Hypothesis Testing (CASHT), a framework where decision-makers select sensing actions with varying costs to identify the correct hypothesis while minimizing total expected cost rather than just sample count. The authors prove that optimal expected cost scales logarithmically with the inverse of the error constraint and demonstrate that the key design principle is maximizing the ratio of expected information gain to expected cost. They analyze two cost revelation models (ex-post and ex-ante) and show that in the ex-ante case, allowing action cancellation mid-operation can reduce total costs under certain conditions.
Why it matters
This framework has practical applications in resource-constrained decision-making scenarios such as medical diagnosis, quality control, and sensor network design, where different tests or measurements have different costs and decision-makers must balance accuracy against resource expenditure. The ability to cancel costly actions before completion could lead to significant cost savings in real-world sequential testing applications.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with differing, random costs to identify the true hypothesis under an average-error constraint $delta$ while minimizing the expected total cost rather than the number of samples. For fixed costs, we prove that the optimal expected total cost scales as $Theta(log(1/delta))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classical counterparts, and when action cancellation helps or hurts.
Source: On Cost-Aware Designs for Sequential Hypothesis Testing