# On the Complexity of Bandit Linear Optimization

arXiv: https://arxiv.org/abs/1408.2368 · HTML: https://mlsanity.com/paper/1408.2368/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2014.

## Built on by (most cited first, 8 of 8)

- [Nonstochastic Bandits with Composite Anonymous Feedback](https://mlsanity.com/paper/2112.02866/) (2021)
- [Safe Linear Bandits over Unknown Polytopes](https://mlsanity.com/paper/2209.13694/) (2022)
- [Linear bandits with polylogarithmic minimax regret](https://mlsanity.com/paper/2402.12042/) (2024)
- [On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization](https://mlsanity.com/paper/2605.02141/) (2026)
- [Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization](https://mlsanity.com/paper/2102.07387/) (2021)
- [Nearly-Optimal Algorithm for Adversarial Kernelized Bandits](https://mlsanity.com/paper/2605.10299/) (2026)
- [Stochastic Linear Bandits with Parameter Noise](https://mlsanity.com/paper/2601.23164/) (2026)
- [A Perturbation Approach to Unconstrained Linear Bandits](https://mlsanity.com/paper/2603.28201/) (2026)

## Abstract (arXiv)

We study the attainable regret for online linear optimization problems with bandit feedback, where unlike the full-information setting, the player can only observe its own loss rather than the full loss vector. We show that the price of bandit information in this setting can be as large as d, disproving the well-known conjecture that the regret for bandit linear optimization is at most √d times the full-information regret. Surprisingly, this is shown using "trivial" modifications of standard domains, which have no effect in the full-information setting. This and other results we present highlight some interesting differences between full-information and bandit learning, which were not considered in previous literature.