🤖 AI Summary
This paper addresses the non-uniform sequential hypothesis testing problem: minimizing the expected total cost of identifying the true hypothesis, where actions incur heterogeneous positive costs and the average error probability is constrained to be at most δ. Recognizing that the conventional “bit-per-unit-cost” criterion leads to suboptimal performance, we propose a new design principle that maximizes the ratio of expected information gain to expected action cost—thereby preserving the optimal log(1/δ) sample complexity. Building upon the Chernoff framework, we develop an adaptive policy that explicitly couples information acquisition efficiency with action cost-effectiveness. Simulation results demonstrate that our method reduces average cost by 50% compared to the classical Chernoff strategy and by up to 90% relative to a naive “bit-per-buck” heuristic, significantly improving decision efficiency and resource utilization in heterogeneous-cost settings.
📝 Abstract
We study the Non-Homogeneous Sequential Hypothesis Testing (NHSHT), where a single active Decision-Maker (DM) selects actions with heterogeneous positive costs to identify the true hypothesis under an average error constraint (δ), while minimizing expected total cost paid. Under standard arguments, we show that the objective decomposes into the product of the mean number of samples and the mean per-action cost induced by the policy. This leads to a key design principle: one should optimize the ratio of expectations (expected information gain per expected cost) rather than the expectation of per-step information-per-cost ("bit-per-buck"), which can be suboptimal. We adapt the Chernoff scheme to NHSHT, preserving its classical (log 1/δ) scaling. In simulations, the adapted scheme reduces mean cost by up to 50% relative to the classic Chernoff policy and by up to 90% relative to the naive bit-per-buck heuristic.