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The no-free-lunch theorems of supervised learning
The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification.
A Tight Excess Risk Bound via a Unified PAC-Bayesian-Rademacher-Shtarkov-MDL Complexity
Our first main result bounds excess risk in terms of the new complexity.
Fast Rates for General Unbounded Loss Functions: from ERM to Generalized Bayes
For general loss functions, our bounds rely on two separate conditions: the $v$-GRIP (generalized reversed information projection) conditions, which control the lower tail of the excess loss; and the newly introduced witness condition, which controls the upper tail.
Fast rates in statistical and online learning
For bounded losses, we show how the central condition enables a direct proof of fast rates and we prove its equivalence to the Bernstein condition, itself a generalization of the Tsybakov margin condition, both of which have played a central role in obtaining fast rates in statistical learning.
