# Online Learning with Automata-based Expert Sequences

## TL;DR

This paper introduces a versatile framework for online learning with expert advice using automata, offering new algorithms that improve efficiency and extend to sleeping experts, with applications to k-shifting experts and n-gram models.

## Contribution

It presents novel automata-based algorithms for online learning with expert sequences, including efficient methods using failure transitions and automaton approximation techniques.

## Key findings

- Automata-based algorithms outperform previous methods in certain settings.
- Approximation of automata with n-gram models maintains competitive regret bounds.
- Extended algorithms effectively handle sleeping experts scenarios.

## Abstract

We consider a general framework of online learning with expert advice where regret is defined with respect to sequences of experts accepted by a weighted automaton. Our framework covers several problems previously studied, including competing against k-shifting experts. We give a series of algorithms for this problem, including an automata-based algorithm extending weighted-majority and more efficient algorithms based on the notion of failure transitions. We further present efficient algorithms based on an approximation of the competitor automaton, in particular n-gram models obtained by minimizing the \infty-R\'{e}nyi divergence, and present an extensive study of the approximation properties of such models. Finally, we also extend our algorithms and results to the framework of sleeping experts.