# Geometric Exploration for Online Control

arXiv: https://arxiv.org/abs/2010.13178 · HTML: https://mlsanity.com/paper/2010.13178/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Uniform Last-Iterate Guarantee for Bandits and Reinforcement Learning](https://mlsanity.com/paper/2402.12711/) (2024)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)
- [Dynamical Linear Bandits](https://mlsanity.com/paper/2211.08997/) (2022)
- [Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noise](https://mlsanity.com/paper/2406.00234/) (2024)

## Abstract (arXiv)

We study the control of an unknown linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers, which encompasses all stabilizing linear-dynamical-controllers. In this work, we first consider the case of known cost functions, for which we design the first polynomial-time algorithm with n3√T-regret, where n is the dimension of the state plus the dimension of control input. The √T-horizon dependence is optimal, and improves upon the previous best known bound of T2/3. The main component of our algorithm is a novel geometric exploration strategy: we adaptively construct a sequence of barycentric spanners in the policy space. Second, we consider the case of bandit feedback, for which we give the first polynomial-time algorithm with poly(n)√T-regret, building on Stochastic Bandit Convex Optimization.