Constraint-Enhanced Physical Search through Correlation Matching
This work provides a general organizing principle for efficient exploration in physical systems with constraints, relevant to fields like robotics or active matter.
The paper proposes a principle of constraint-enhanced physical search where temporal correlations in exploration are matched to spatial correlations from physical constraints. Using a tug-of-war bandit model, they show that matching temporal correlation to the update scale improves search efficiency, with the update-noise-to-contrast ratio limiting anti-correlation strength.
Physical systems do not merely add noise to search processes; they impose constraints that generate structured correlations. We propose a principle of constraint-enhanced physical search in which temporal correlations in exploration are matched to constraint-induced spatial correlations in the update dynamics. Using a minimal tug-of-war bandit model (TOW), we show that a conservation law converts local observations into differential evidence across alternatives, while a temporally correlated drive controls the order of exploration. Search efficiency is improved not by stronger randomness or by maximal anti-correlation, but by matching the temporal correlation to the physical update scale that converts feedback into evidence. A scaling estimate identifies the update-noise-to-contrast ratio as the leading parameter that limits how strongly temporal anti-correlation can be used. The results suggest a general organizing principle for physical search: constraints and fluctuations can generate structured spatiotemporal correlations, and efficient exploration emerges when these correlations are matched to the update dynamics.