Model Explanation

The new trajectory-based models (T ) focuses model capacity on how trajectories act over time rather than discrete steps. This is captured by training the model to predict the evolution from a starting state, s_n, subject to control parameters, θ_π, and a future-time index, t, as in Eq. (1) and Fig. 1b. The trajectory-based formulation conveys substantial benefits in stable, uncertainty-aware estimates of trajectories and data-efficiency of model learning. The labelled dataset in D grows by re-labelling every sub-sequence from state s in a trajectory τ = {s }^L to the final state s . By training on below .

For prediction propagation, by only passing in a time index t from a current state, a planner can evaluate the future with one forward pass, alleviating the computational burden and compounding, all sub-trajectories, the model gains two strengths: 1) it can predict into the future from any state, not just those given as initial states from a environment, and 2) the number of training points grows proportional to the square of trajectory length: n_trajL² points from n trajectories of length L, shown multiplicative error associated with evaluating many steps of one-step models. By propagating time directly, the uncertainty of a probabilistic, trajectory-based model is proportional to the variation in dynamics in the training set (i.e., the model is more uncertain in areas of rapid movement and can shrink when motion converges). The uncertainty propagation is drawn in Fig. 2a and in experiment in Fig. 2b, and compared to one-step models that have diverging uncertainty as the states encountered leave the training distribution.