mlsanityData to 14 Oct 2026

Stochastic Linear Bandits with Parameter Noise

arXiv 2601.23164 ↗First posted 30 Jan 2026cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

We study the stochastic linear bandits with parameter noise model, in which the reward of action a is a^top θ where θ is sampled i.i.d. We show a regret upper bound of widetildeO (√d T log (K/δ) σ2max) for a horizon T, general action set of size K of dimension d, and where σ2max is the maximal variance of the reward for any action. We further provide a lower bound of widetildeOmega (d √T σ2max) which is tight (up to logarithmic factors) whenever log (K) ≈ d. For more specific action sets, ℓp unit balls with p ≤ 2 and dual norm q, we show that the minimax regret is widetildeTheta (√dT σ2q), where σ2q is a variance-dependent quantity that is always at most 4. This is in contrast to the minimax regret attainable for such sets in the classic additive noise model, where the regret is of order d √T. Surprisingly, we show that this optimal (up to logarithmic factors) regret bound is attainable using a very simple explore-exploit algorithm.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 13 of its 33 references that are in the map. First posted on arXiv 30 Jan 2026.

Builds on

13 of 33 references.

References · 13

  1. 2020Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processescited by 200
  2. 2014Learning to Optimize via Information-Directed Samplingcited by 168
  3. 2019Mean estimation and regression under heavy-tailed distributions--a surveycited by 136
  4. 2019Learning with Good Feature Representations in Bandits and in RL with a Generative Modelcited by 127
  5. 2022Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPscited by 52
  6. 2021Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDPcited by 45
  7. 2021Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPscited by 44
  8. 2023Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiencycited by 40
  9. 2017Sparsity, variance and curvature in multi-armed banditscited by 24
  10. 2014On the Complexity of Bandit Linear Optimizationcited by 8
  11. 2025Variance-Dependent Regret Lower Bounds for Contextual Banditscited by 4
  12. 2019Rarely-switching linear bandits: optimization of causal effects for the real worldcited by 3
1 more
  1. 2022Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routingcited by 1

Built on by

Not cited yet.