Translate, then decide: asymptotic optimality of latent-space control in bistable systems
Abstract
This paper asks whether an optimal decision can be separated from the physical dynamics on which it acts. It studies this question through minimum-energy barrier crossing in scalar bistable systems. It characterizes the finite-horizon optimal feedback and shows that, as the horizon grows, it converges to a law that doubles and reverses the drift while it opposes crossing, and switches off once the barrier is passed. In physical coordinates, this law inherits the plant's nonlinearity, entangling decision and dynamics. We show that a plant-specific translation of state, input, and time maps every double well in the considered class to the same unit-rate linear world model, allowing a downstream decision stage to use a single plant-independent control primitive. This separation generally loses optimality at finite horizons because the translation does not preserve the physical control energy. Nevertheless, we prove that the excess physical energy of the layered controller vanishes as the horizon grows and that its limiting feedback reproduces the asymptotic optimum exactly. Thus, translation and optimization generally do not commute at a finite horizon, but commute in the asymptotic limit.
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BibTeX
@misc{oliveira2026translate,
title = {{Translate, then decide: asymptotic optimality of latent-space control in bistable systems}},
author = {Arthur Castello B. de Oliveira},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05736},
eprint = {2611.05736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05736},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Translate, then decide: asymptotic optimality of latent-space control in bistable systems
AU - Arthur Castello B. de Oliveira
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05736
UR - https://arxiv.org/abs/2611.05736
AB - This paper asks whether an optimal decision can be separated from the physical dynamics on which it acts. It studies this question through minimum-energy barrier crossing in scalar bistable systems. It characterizes the finite-horizon optimal feedback and shows that, as the horizon grows, it converges to a law that doubles and reverses the drift while it opposes crossing, and switches off once the barrier is passed. In physical coordinates, this law inherits the plant's nonlinearity, entangling decision and dynamics. We show that a plant-specific translation of state, input, and time maps every double well in the considered class to the same unit-rate linear world model, allowing a downstream decision stage to use a single plant-independent control primitive. This separation generally loses optimality at finite horizons because the translation does not preserve the physical control energy. Nevertheless, we prove that the excess physical energy of the layered controller vanishes as the horizon grows and that its limiting feedback reproduces the asymptotic optimum exactly. Thus, translation and optimization generally do not commute at a finite horizon, but commute in the asymptotic limit.
ER -