  Logistic Bandits have recently undergone careful scrutiny by virtue of their
combined theoretical and practical relevance. This research effort delivered
statistically efficient algorithms, improving the regret of previous strategies
by exponentially large factors. Such algorithms are however strikingly costly
as they require $\Omega(t)$ operations at each round. On the other hand, a
different line of research focused on computational efficiency
($\mathcal{O}(1)$ per-round cost), but at the cost of letting go of the
aforementioned exponential improvements. Obtaining the best of both world is
unfortunately not a matter of marrying both approaches. Instead we introduce a
new learning procedure for Logistic Bandits. It yields confidence sets which
sufficient statistics can be easily maintained online without sacrificing
statistical tightness. Combined with efficient planning mechanisms we design
fast algorithms which regret performance still match the problem-dependent
lower-bound of Abeille et al. (2021). To the best of our knowledge, those are
the first Logistic Bandit algorithms that simultaneously enjoy statistical and
computational efficiency.
