# Double Doubly Robust Thompson Sampling for Generalized Linear Contextual Bandits

arXiv: https://arxiv.org/abs/2209.06983 · HTML: https://mlsanity.com/paper/2209.06983/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 10 of 10)

- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Mostly Exploration-Free Algorithms for Contextual Bandits](https://mlsanity.com/paper/1704.09011/) (2017)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits](https://mlsanity.com/paper/1904.00242/) (2019)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits](https://mlsanity.com/paper/2011.11222/) (2020)
- [Balanced Linear Contextual Bandits](https://mlsanity.com/paper/1812.06227/) (2018)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [Doubly robust Thompson sampling for linear payoffs](https://mlsanity.com/paper/2102.01229/) (2021)

## Built on by (most cited first, 14 of 14)

- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Neural Logistic Bandits](https://mlsanity.com/paper/2505.02069/) (2025)
- [Learning the Pareto Front Using Bootstrapped Observation Samples](https://mlsanity.com/paper/2306.00096/) (2023)
- [RoME: A Robust Mixed-Effects Bandit Algorithm for Optimizing Mobile Health Interventions](https://mlsanity.com/paper/2312.06403/) (2023)
- [Linear Bandits with Partially Observable Features](https://mlsanity.com/paper/2502.06142/) (2025)
- [A Doubly Robust Approach to Sparse Reinforcement Learning](https://mlsanity.com/paper/2310.15286/) (2023)
- [Improved Algorithms for Multi-period Multi-class Packing Problems with Bandit Feedback](https://mlsanity.com/paper/2301.13791/) (2023)
- [Avoiding the Price of Adaptivity: Inference in Linear Contextual Bandits via Stability](https://mlsanity.com/paper/2512.20368/) (2025)
- [Logistic Bandits with tildeO(√dT) Regret without Context Diversity Assumptions](https://mlsanity.com/paper/2604.22161/) (2026)
- [Adaptive Data Augmentation for Thompson Sampling](https://mlsanity.com/paper/2506.14479/) (2025)
- [Combinatorial Allocation Bandits with Nonlinear Arm Utility](https://mlsanity.com/paper/2603.07005/) (2026)
- [Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling](https://mlsanity.com/paper/2609.01999/) (2026)

## Abstract (arXiv)

We propose a novel contextual bandit algorithm for generalized linear rewards with an tildeO(√kappa-1 φ T) regret over T rounds where φ is the minimum eigenvalue of the covariance of contexts and kappa is a lower bound of the variance of rewards. In several practical cases where φ=O(d), our result is the first regret bound for generalized linear model (GLM) bandits with the order √d without relying on the approach of Auer [2002]. We achieve this bound using a novel estimator called double doubly-robust (DDR) estimator, a subclass of doubly-robust (DR) estimator but with a tighter error bound. The approach of Auer [2002] achieves independence by discarding the observed rewards, whereas our algorithm achieves independence considering all contexts using our DDR estimator. We also provide an O(kappa-1 φ log (NT) log T) regret bound for N arms under a probabilistic margin condition. Regret bounds under the margin condition are given by Bastani and Bayati [2020] and Bastani et al. [2021] under the setting that contexts are common to all arms but coefficients are arm-specific. When contexts are different for all arms but coefficients are common, ours is the first regret bound under the margin condition for linear models or GLMs. We conduct empirical studies using synthetic data and real examples, demonstrating the effectiveness of our algorithm.