ערך של קדמונים מכניסטיים בהחלטות רצפיות

תקציר מקורי באנגליתarXiv:2605.10018v2 Announce Type: replace Abstract: Hybrid mechanistic models, physical priors with learned residuals, promise to reduce the data required for good decisions, but have no computable criterion to test this. We characterize the value of mechanistic priors in sequential decision-making within both asymptotic and burn-in regimes. To formalize this, we introduce the mechanistic information of a model: the mutual information between the model's recommended policy $\hat{\pi}$ and the true optimal policy $\pi^*$, bounded via a centered, occupancy-weighted bias. In the asymptotic regime (large $N$), matched bounds reveal that Bayesian regret scales with the residual entropy $H_{\mathrm{mech}}$, delivering a theoretical sample complexity reduction of $H(\mu)/H_{\mathrm{mech}}$ compar