We study the stochastic linear bandits with heavy-tailed noise. Two principled strategies for handling heavy-tailed noise, truncation and median-of-means, have been introduced to heavy-tailed bandits. Nonetheless, these methods rely on specific noise assumptions or bandit structures, limiting their applicability to general settings. The recent work Huang et al. 2024 develops a soft truncation method via the adaptive Huber regression to address these limitations. However, their method suffers undesired computational costs: it requires storing all historical data and performing a full pass over these data at each round. In this paper, we propose a one-pass algorithm based on the online mirror descent framework. Our method updates using only current data at each round, reducing the per-round computational cost from O (t T) to O (1) with respect to current round t and the time horizon T, and achieves a near-optimal and variance-aware regret of order O (d T^1-{2 (1+) } ₓ=₁ₓ 䂻ℂ + d T^1-{2 (1+) }) where d is the dimension and ₜ^1+ is the (1+) -th central moment of reward at round t.
Wang et al. (Sat,) studied this question.