PILCO, PETS, Ensembles, and MBPO › Summary

This chapter compared three decision-centric methods (PILCO, PETS, and MBPO) and deep ensembles, an uncertainty-estimation method used by PETS.

• PILCO. Gaussian-process dynamics, analytic moment integrals, repeated Gaussian approximation, and analytic gradients make data-efficient feedback-policy search possible. Modeling uncertainty can mitigate exploitation, but neither the GP assumptions nor expected-cost optimization guarantees it away.
• Deep ensembles and PETS. Ensemble disagreement is an empirical epistemic proxy. PETS evaluates each CEM candidate by averaging returns over state particles, with TS1 or TS$\infty$ controlling bootstrap assignments. That arithmetic mean is risk-neutral; explicit pessimism, variance penalties, lower-confidence scores, or CVaR are separate choices.
• Receding-horizon control. PETS executes one planned action and replans from the next observation. This limits commitment and the uncorrected forecast span, but it does not place a numerical bound on model error or guarantee global competence.
• MBPO. Short branches from real replay states generate data for an off-policy learner. The expression printed in Theorem 4.3 favors positive truncated rollouts when current-policy model error is sufficiently low, but a later reproduction disputes pre/post-branch indexing in its proof. Treat that expression as the paper's motivation, not a verified performance guarantee; actual return and the practical schedule still require empirical validation.

Uncertainty representations and trust controls should not be conflated. A GP posterior and an ensemble predictive distribution represent uncertainty under different assumptions. A short rollout does not represent uncertainty; it limits consecutive reliance on the model. Predictive fidelity, uncertainty quality, and decision usefulness are the main lenses developed here. Representation quality is introduced but deferred to the later latent-model chapters. These methods supplied influential mechanisms that recur in learned control, but they are not a single lineage or the foundation of every later world-model system.