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Why It Matters
Accounting for information flow on the path space of trajectories of a nonnegative martingale yields exact variational identities for it, even at arbitrary random times.
Provenance
Discovered via ArXiv and published by ArXiv.
Key Claims
Original description
Accounting for information flow on the path space of trajectories of a nonnegative martingale yields exact variational identities for it, even at arbitrary random times. This recovers the widely used classical concentration inequalities, from Ville to PAC-Bayes, and measures what each one discards. The tail a bound controls is itself a relative entropy, resolved by the chain rule into per-step conditional divergences. The discarded slack has an exact form in each of three geometries: a Gibbs tilt for the Azuma-Hoeffding and PAC-Bayes bounds, the crossing itself for Ville's and for pooled tests...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2608.20337v1 · Indexed 8 days ago