  We consider online learning in the model where a learning algorithm can
access the class only via the \emph{consistent oracle} -- an oracle, that, at
any moment, can give a function from the class that agrees with all examples
seen so far. This model was recently considered by Assos et al.~(COLT'23). It
is motivated by the fact that standard methods of online learning rely on
computing the Littlestone dimension of subclasses, a computationally
intractable problem.
  Assos et al.~gave an online learning algorithm in this model that makes at
most $C^d$ mistakes on classes of Littlestone dimension $d$, for some absolute
unspecified constant $C > 0$. We give a novel algorithm that makes at most
$O(256^d)$ mistakes. Our proof is significantly simpler and uses only very
basic properties of the Littlestone dimension. We also show that there exists
no algorithm in this model that makes less than $3^d$ mistakes.
