潜在世界模型中可预测性的控制理论
A Control Theory of Predictability in Latent World Models
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中文总结 AI 辅助
研究潜在世界模型中可预测性的控制理论，指出当前以预测误差为目标不可靠，重新定义目标为预测与真实计划成本的差异，证明规划器次优性受其限制，通过实验证实相关结论。
中文摘要 AI 辅助
潜在世界模型用于在学习表示中预测未来状态，并部署在通过模拟选择动作的规划器中。当前实践采用预测误差作为训练和模型选择目标，但作者表明该假设不可靠，因为规划器在候选动作到达的状态上查询模型，这些状态通常离开数据流形。因此作者将目标重新定义为预测计划成本与真实计划成本之间的差异，并证明规划器的次优性受此差异两倍的限制，而数据平均预测误差既不能限制也不能跟踪它。在线性控制前提下，差异分为两项，合成算子和潜在模型预测控制实验证实了相关结论。
英文摘要
Latent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single- or multi-step rollout loss on held-out data, as the training and model-selection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner's suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.
发表机构
- University of Science and Technology of China（中国科学技术大学）
- The Hong Kong University of Science and Technology（香港科技大学）
- Hong Kong Baptist University（香港浸会大学）
机构由 AI 辅助整理，请以论文原文为准。
