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About this paper
Francesco Orabona
A technical note by Francesco Orabona at KAUST demonstrates how to remove the ln ln T factor from the data-independent regret bound of the Squint algorithm, achieving an O(√T) bound. This is accomplished by leveraging a modified prior distribution, specifically a truncated Gaussian, which reinterprets previously developed "shifted Krichevsky-Trofimov potentials".
Key insights
- The mechanism for eliminating the ln ln T term, previously described as "shifted Krichevsky-Trofimov potentials", is mathematically equivalent to selecting a specific prior distribution.
- A truncated Gaussian prior can effectively serve as this optimized prior, simplifying the analysis and enabling the removal of polylogarithmic factors from regret bounds.
- Careful engineering of prior distributions in Bayesian online learning frameworks is a powerful technique for achieving tighter and more optimal theoretical regret guarantees.
Summary by alphaXiv.
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