Connects stochastic optimal control to the Schrödinger equation, enabling analytic solutions for long-horizon problems that previously scaled exponentially with difficulty.
March 25, 2026
Original Paper
A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control
arXiv · 2603.23173
The Takeaway
This mathematical bridge allows for an order-of-magnitude improvement in control accuracy for complex dynamical systems. It moves beyond traditional iterative solvers to a spectral method that is significantly more stable for high-dimensional, long-duration planning.
From the abstract
High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a subclass of linearly-solvable SOC problems-those whose uncontrolled drift is the gradient of a potential. In this setting, the Hamilton-Jacobi-Bellman equation reduces to a linear PDE governed by an operator $\mathcal{L}$. We prove that, under the gradient drift a