Model posterior updates and subsequent control decisions

Develop an explicit model of how posterior updates alter subsequent control decisions in task-oriented information acquisition for model predictive path integral control, extending the computationally tractable surrogate toward Bayesian value-of-information planning.

Background

The proposed Task-Oriented Information Acquisition (ToIA) method estimates predictive variance reduction for prospective observations along existing model predictive path integral (MPPI) rollouts. This provides a computationally tractable approximation to Bayesian value-of-information planning because it avoids sampling future observations and re-optimizing control under hypothetical posterior updates.

The paper acknowledges that the current formulation does not explicitly represent the effect of posterior model updates on later control decisions. Incorporating this coupling would move the method closer to dual-control or belief-space planning, although it would introduce additional computational complexity for online operation.