PETS (probabilistic ensembles with trajectory sampling)

PETS is a clean, influential answer to the question "how do I plan with a deep model without it lying to me?" Its trick is to train not one dynamics network but a small ensemble of them, each probabilistic, and to treat their disagreement as a measure of doubt. Where the ensemble members agree, the model is trusted; where they diverge, the planner knows it is on thin ice.

Each network outputs a Gaussian over the next state, capturing aleatoric noise, while the spread across the several networks captures epistemic uncertainty from limited data. To evaluate a candidate action sequence, PETS samples many trajectories, propagating each through a randomly chosen ensemble member at every step so that model uncertainty is folded into the predicted returns. A sampling-based MPC controller then picks actions by optimising these uncertainty-aware predictions, replanning each step.

PETS showed that careful uncertainty handling lets a model-based agent reach the asymptotic performance of model-free methods with dramatically fewer samples on continuous-control benchmarks. Its limitation is computational weight at decision time — many models, many sampled trajectories, fresh optimisation every step.