# Input Perturbations for Adaptive Control and Learning

arXiv: https://arxiv.org/abs/1811.04258 · HTML: https://mlsanity.com/paper/1811.04258/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2018.

## Built on by (most cited first, 18 of 18)

- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Joint Learning of Linear Time-Invariant Dynamical Systems](https://mlsanity.com/paper/2112.10955/) (2021)
- [Minimal Expected Regret in Linear Quadratic Control](https://mlsanity.com/paper/2109.14429/) (2021)
- [Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems](https://mlsanity.com/paper/2201.01680/) (2022)
- [Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systems](https://mlsanity.com/paper/2112.10753/) (2021)
- [Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systems](https://mlsanity.com/paper/2201.10542/) (2022)
- [Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems](https://mlsanity.com/paper/2111.03772/) (2021)
- [Joint Learning-Based Stabilization of Multiple Unknown Linear Systems](https://mlsanity.com/paper/2201.01387/) (2022)
- [Efficient Algorithms for Learning to Control Bandits with Unobserved Contexts](https://mlsanity.com/paper/2202.00867/) (2022)
- [Scalable regret for learning to control network-coupled subsystems with unknown dynamics](https://mlsanity.com/paper/2108.07970/) (2021)
- [Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systems](https://mlsanity.com/paper/2112.15094/) (2021)
- [Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observations](https://mlsanity.com/paper/2204.04773/) (2022)
- [A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems](https://mlsanity.com/paper/2108.08502/) (2021)
- [Safe Linear-Quadratic Dual Control with Almost Sure Performance Guarantee](https://mlsanity.com/paper/2103.13278/) (2021)
- [Reinforcement Learning Policies in Continuous-Time Linear Systems](https://mlsanity.com/paper/2109.07630/) (2021)
- [Regret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systems](https://mlsanity.com/paper/2206.04434/) (2022)
- [Almost Surely √T Regret for Adaptive LQR](https://mlsanity.com/paper/2301.05537/) (2023)
- [Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs](https://mlsanity.com/paper/2305.16974/) (2023)

## Abstract (arXiv)

This paper studies adaptive algorithms for simultaneous regulation (i.e., control) and estimation (i.e., learning) of Multiple Input Multiple Output (MIMO) linear dynamical systems. It proposes practical, easy to implement control policies based on perturbations of input signals. Such policies are shown to achieve a worst-case regret that scales as the square-root of the time horizon, and holds uniformly over time. Further, it discusses specific settings where such greedy policies attain the information theoretic lower bound of logarithmic regret. To establish the results, recent advances on self-normalized martingales together with a novel method of policy decomposition are leveraged.