Breaking the Total Variance Barrier: Sharp Sample Complexity for Linear Heteroscedastic Bandits with Fixed Action Set

arXiv:2607.23679 · cs.LG, stat.ML · Submitted 2026-07-26 · Read on arXiv

Heyang Zhao, Tianyuan Jin, Weixin Wang, Vincent Y. F. Tan, Pan Xu, Quanquan Gu

cs.LG, stat.ML

Submitted: 2026-07-26

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regret — 103× in this paper · explained in 4 episodes
• Regret Bound — 39× in this paper · explained in 2 episodes
• Regret Bounds — 19× in this paper · explained in 2 episodes
• Reinforcement Learning — 11× in this paper · explained in 4 episodes
• Contextual Bandit — 7× in this paper · explained in 2 episodes
• Contextual Bandits — 7× in this paper · explained in 3 episodes
• Core — 6× in this paper · explained in 2 episodes
• Heavy-Tailed Noise — 6× in this paper · explained in 3 episodes
• Information Gain — 5× in this paper · explained in 2 episodes
• Variance-Aware Exploration with Elimination — 5× in this paper
• Sample Complexity — 3× in this paper · explained in 20 episodes
• Active Exploration — 2× in this paper · explained in 2 episodes
• EMMA — 2× in this paper · explained in 2 episodes
• Computational Efficiency — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Hamming Distance — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Variance Adaptive G-Optimal Design — 1× in this paper

Sources

• Variance-Dependent Regret Lower Bounds for Contextual Bandits
• Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPs
• Do we need to estimate the variance in robust mean estimation?
• Nearly Optimal Regret for Stochastic Linear Bandits with Heavy-Tailed Payoffs
• Instance-Dependent Continuous-Time Reinforcement Learning via Maximum Likelihood Estimation

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