# Almost Optimal Agnostic Control of Unknown Linear Dynamics

arXiv: https://arxiv.org/abs/2403.06320 · HTML: https://mlsanity.com/paper/2403.06320/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Adaptive Symmetry Discovery for Dynamical System Identification](https://mlsanity.com/paper/2608.08091/) (2026)

## Abstract (arXiv)

We consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. We study three variants of the control problem: Bayesian control, in which we have a prior belief about a; bounded agnostic control, in which we have no prior belief about a but we assume that a belongs to a bounded set; and fully agnostic control, in which a is allowed to be an arbitrary real number about which we have no prior belief. In the Bayesian variant, a control strategy is optimal if it minimizes a certain expected cost. In the agnostic variants, a control strategy is optimal if it minimizes a quantity called the worst-case regret. For the Bayesian and bounded agnostic variants above, we produce optimal control strategies. For the fully agnostic variant, we produce almost optimal control strategies, i.e., for any varepsilon>0 we produce a strategy that minimizes the worst-case regret to within a multiplicative factor of (1+varepsilon).