Year: 2026
Type: preprint
Abstract: Witsenhausen's counterexample has resisted a closed form solution for decades. However, it has remained unknown whether a mathematically tractable representation exists or not. In this paper, we solve this open problem, showing that the optimal policies are either linear or not tame and characterizing the exact regions where the two properties hold. Moreover, in the linear optimal region, we give an essentially unique closed form solution for the optimal policy, and show that no optimal first-stage policy is definable in any $o$-minimal expansion of the ordered real field in the nonlinear optimal region.
Source: arXiv (Cornell University)
Authors: Lu, Yikai, Li, Tongxin
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222993060