Structured Dynamics Optimization: Expert-Calibrated Energy Modulation of Multi-Motion Predictive Priors for Humanoid Imitation

<jats:p>Frame-wise imitation provides a clear reference but not a measure of whether a learned future deserves equal influence at every state. We present Structured Dynamics Optimization (SDO), a reward-level mechanism that converts internal discrepancies of a pretrained motion model into weak, state-dependent guidance for reinforcement learning. The high-level model is trained first on a multi-motion corpus containing dozens of expert trajectories, learning shared temporal structure before low-level policy optimization begins. From three past 67-dimensional states, a Transformer produces a 256-dimensional latent code and a 30-frame coarse future; a 20-step diffusion-inspired refiner produces the corrected future. SDO reads two quantities from this frozen model: expert-calibrated latent deviation and coarse-to-refined correction. Their calibrated sum forms an energy proxy that controls how strongly the predicted target is trusted, while a separate policy–prior agreement term checks its physical relevance to the current state. The auxiliary term enters only through the reward interface. In LocoMuJoCo, SDO energy is positively associated with future prediction error, and refinement energy reaches a Spearman correlation of about 0.55 at 15- and 30-step horizons. Across five paired 300-million-step runs, SDO raises deterministic imitation return from 16.4396 to 16.9191 (+2.92%) and episode length from 125.75 to 134.61; every paired seed improves on both measures. Evaluation disables the SDO bonus for both methods, so the gains reflect the policy learned during training rather than an altered test-time reward.</jats:p>