On Limited-Memory Subsampling Strategies for Bandits
This work addresses efficiency and adaptability problems for researchers and practitioners in bandit algorithms, though it is incremental as it builds on prior subsampling methods.
The paper tackles the complexity and storage issues of nonparametric bandit algorithms by showing that a deterministic subsampling rule called 'last-block subsampling' is asymptotically optimal in one-parameter exponential families, and it achieves optimal regret with polylogarithmic memory and in non-stationary scenarios with abrupt changes.
There has been a recent surge of interest in nonparametric bandit algorithms based on subsampling. One drawback however of these approaches is the additional complexity required by random subsampling and the storage of the full history of rewards. Our first contribution is to show that a simple deterministic subsampling rule, proposed in the recent work of Baudry et al. (2020) under the name of ''last-block subsampling'', is asymptotically optimal in one-parameter exponential families. In addition, we prove that these guarantees also hold when limiting the algorithm memory to a polylogarithmic function of the time horizon. These findings open up new perspectives, in particular for non-stationary scenarios in which the arm distributions evolve over time. We propose a variant of the algorithm in which only the most recent observations are used for subsampling, achieving optimal regret guarantees under the assumption of a known number of abrupt changes. Extensive numerical simulations highlight the merits of this approach, particularly when the changes are not only affecting the means of the rewards.