PAC-Bayes-Chernoff bounds for unbounded losses
CoRR(2024)
Abstract
We present a new high-probability PAC-Bayes oracle bound for unbounded
losses. This result can be understood as a PAC-Bayes version of the Chernoff
bound. The proof technique relies on uniformly bounding the tail of certain
random variable based on the Cramér transform of the loss. We highlight two
applications of our main result. First, we show that our bound solves the open
problem of optimizing the free parameter on many PAC-Bayes bounds. Finally, we
show that our approach allows working with flexible assumptions on the loss
function, resulting in novel bounds that generalize previous ones and can be
minimized to obtain Gibbs-like posteriors.
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