# Bandit Linear Control

arXiv: https://arxiv.org/abs/2007.00759 · HTML: https://mlsanity.com/paper/2007.00759/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)
- [Online Nonstochastic Model-Free Reinforcement Learning](https://mlsanity.com/paper/2305.17552/) (2023)
- [Tight Rates for Bandit Control Beyond Quadratics](https://mlsanity.com/paper/2410.00993/) (2024)
- [SCaLE: Switching Cost aware Learning and Exploration](https://mlsanity.com/paper/2601.09042/) (2026)

## Abstract (arXiv)

We consider the problem of controlling a known linear dynamical system under stochastic noise, adversarially chosen costs, and bandit feedback. Unlike the full feedback setting where the entire cost function is revealed after each decision, here only the cost incurred by the learner is observed. We present a new and efficient algorithm that, for strongly convex and smooth costs, obtains regret that grows with the square root of the time horizon T. We also give extensions of this result to general convex, possibly non-smooth costs, and to non-stochastic system noise. A key component of our algorithm is a new technique for addressing bandit optimization of loss functions with memory.