Small steps no more: Global convergence of stochastic gradient bandits for arbitrary learning rates
This provides theoretical guarantees for stochastic gradient methods in bandit problems, addressing convergence issues in non-ideal scenarios.
The paper proves that stochastic gradient bandit algorithms converge to globally optimal policies almost surely with any constant learning rate, even when standard smoothness and noise assumptions fail, demonstrating robust exploration-exploitation balance.
We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic gradient algorithm continues to balance exploration and exploitation appropriately even in scenarios where standard smoothness and noise control assumptions break down. The proofs are based on novel findings about action sampling rates and the relationship between cumulative progress and noise, and extend the current understanding of how simple stochastic gradient methods behave in bandit settings.