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arXiv · 2603.10329

Combining e-values using demi-supermartingales

Jiahao Ming·Aaditya Ramdas·Yi Shen·Ruodu Wang·Ian Waudby-Smith
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Abstract

We present a new method for combining e-variables through demi-supermartingales, which settles an old conjecture in the literature on nonparametric mean testing. It also provides an explicit concentration bound for a certain Kullback--Leibler-type statistic arising in the stochastic multi-armed bandit literature. All of these combination results hold for independent e-variables as well as for the class of co-valid e-variables, whose dependence structure lies somewhere between independence and sequential validity. The results are further generalized to compound e-variables. The proofs proceed by analyzing elementary symmetric polynomials and their behavior as nonnegative demi-supermartingales.

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Jiahao Ming, Aaditya Ramdas, Yi Shen, Ruodu Wang, Ian Waudby-Smith. 2026-03-11. Combining e-values using demi-supermartingales. https://arxiv.org/abs/2603.10329

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