On sequential hypotheses testing via convex optimization

TL;DR

This paper introduces an adaptive sequential hypothesis testing method based on convex optimization, allowing for efficient, on-line testing of parameter sets within convex regions, extending classical approaches.

Contribution

It presents a novel convex optimization-based framework for adaptive sequential testing of convex hypotheses, improving computational efficiency and flexibility.

Findings

Provides a nearly optimal test under certain conditions

Formulates the testing problem as a convex optimization task

Offers a computationally efficient approach for sequential testing

Abstract

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the dis- tribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solution to an efficiently solvable convex optimization prob- lem. The proposed methodology can be seen as a computationally friendly reformulation of the classical sequential testing.