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Journal Articles Entropy Year : 2021

PAC-Bayes unleashed: generalisation bounds with unbounded losses


We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learning problems where the loss function is bounded (typically assumed to take values in the interval [0;1]). In order to relax this assumption, we propose a new notion called the \emph{special boundedness condition}, which effectively allows the range of the loss to depend on each predictor. Based on this new notion we derive a novel PAC-Bayesian generalisation bound for unbounded loss functions, and we instantiate it on a linear regression problem. To make our theory usable by the largest audience possible, we include discussions on actual computation, practicality and limitations of our assumptions.
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hal-02872173 , version 1 (17-06-2020)



Maxime Haddouche, Benjamin Guedj, Omar Rivasplata, John Shawe-Taylor. PAC-Bayes unleashed: generalisation bounds with unbounded losses. Entropy, 2021, ⟨10.3390/e23101330⟩. ⟨hal-02872173⟩
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