We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution 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 problem. The proposed methodology can be seen as a computationally friendly reformulation of the classical sequential testing.
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