A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control
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 assumption, $\mathcal{L}$ is unitarily equivalent to a Schrödinger operator $\mathcal{S} = -Δ+ \mathcal{V}$ with purely discrete spectrum, allowing the long-horizon control to be efficiently describ...
| Authors | Louis Claeys, Artur Goldman, Zebang Shen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 24 March 2026 |
| Last updated at source | 24 March 2026 |
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