Simple online learning with consistent oracle
This work addresses computational intractability in online learning for researchers in machine learning theory, offering a simpler algorithm and fundamental limits, though it is incremental over prior results.
The paper tackles the problem of online learning with a consistent oracle, improving the mistake bound from an unspecified exponential constant to O(256^d) and proving a lower bound of 3^d for classes of Littlestone dimension d.
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.