Strong duality for the GROW criterion (opens in new tab)

This paper presents general strong duality results when testing hypotheses by betting against them. A bet is an e-variable for a composite null hypothesis $\mathcal{P}$: a nonnegative random variable $X$ whose expected value is at most one under every $\P \in \Pcal$. Following Kelly, Breiman, Cover, Shafer, Gr\"unwald and others, we study a natural minimax \emph{log-optimality} criterion: given a composite alternative $\Qcal$, we characterize th...