# Minimax optimal dual control -- The single input case

arXiv: https://arxiv.org/abs/2604.18550 · HTML: https://mlsanity.com/paper/2604.18550/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2026.

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

- [Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty](https://mlsanity.com/paper/2608.13651/) (2026)

## Abstract (arXiv)

An explicit solution is derived for the Bellman inequality corresponding to minimax optimal dual control. The minimizing player determines control action as a function of past state measurements and inputs. The maximizing player selects disturbances and model parameters for the underlying linear time-invariant dynamics. The optimal minimizing policy is a dual controller that optimizes the tradeoff between exploration and exploitation. Once sufficient data has been collected, the policy becomes a deterministic certainty equivalence controller. However, when data is insufficient, the policy introduces a randomized term to improve excitation.