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Abstract:
We present a set of high-probability inequalities
that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. We also present a comparison inequality that bounds expectation of a convex function of martingale difference type variables by expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma inequality.
