Planning enables autonomous agents to solve complex decision-making problems by evaluating predictions of the future. However, classical planning algorithms often become infeasible in real-world settings where state spaces are high-dimensional and transition dynamics unknown. The idea behind latent planning is to simplify the decision-making task by mapping it to a lower-dimensional embedding space. Common latent planning strategies are based on trajectory optimization techniques such as shooting or collocation, which are prone to failure in long-horizon and highly non-convex settings. In this work, we study long-horizon goal-reaching scenarios from visual inputs and formulate latent planning as an explorative tree search. Inspired by classical sampling-based motion planning algorithms, we design a method which iteratively grows and optimizes a tree representation of visited areas of the latent space. To encourage fast exploration, the sampling of new states is biased towards sparsely represented regions within the estimated data support. Our method, called Expansive Latent Space Trees (ELAST), relies on self-supervised training via contrastive learning to obtain (a) a latent state representation and (b) a latent transition density model. We embed ELAST into a model-predictive control scheme and demonstrate significant performance improvements compared to existing baselines given challenging visual control tasks in simulation, including the navigation for a deformable object.

Planning enables autonomous agents to solve complex decision-making problems by evaluating predictions of the future. However, classical planning algorithms often become infeasible in real-world settings where state spaces are high-dimensional and transition dynamics unknown. The idea behind latent planning is to simplify the decision-making task by mapping it to a lower-dimensional embedding space. Common latent planning strategies are based on trajectory optimization techniques such as shooting or collocation, which are prone to failure in long-horizon and highly non-convex settings. In this work, we study long-horizon goal-reaching scenarios from visual inputs and formulate latent planning as an explorative tree search.

In the present paper, we propose an extension of the Deep Planning Network (PlaNet), also referred to as PlaNet of the Bayesians (PlaNet-Bayes). There has been a growing demand in model predictive control (MPC) in partially observable environments in which complete information is unavailable because of, for example, lack of expensive sensors. PlaNet is a promising solution to realize such latent MPC, as it is used to train state-space models via model-based reinforcement learning (MBRL) and to conduct planning in the latent space. However, recent state-of-the-art strategies mentioned in MBRR literature, such as involving uncertainty into training and planning, have not been considered, significantly suppressing the training performance. The proposed extension is to make PlaNet uncertainty-aware on the basis of Bayesian inference, in which both model and action uncertainty are incorporated. Uncertainty in latent models is represented using a neural network ensemble to approximately infer model posteriors. The ensemble of optimal action candidates is also employed to capture multimodal uncertainty in the optimality. The concept of the action ensemble relies on a general variational inference MPC (VI-MPC) framework and its instance, probabilistic action ensemble with trajectory sampling (PaETS). In this paper, we extend VI-MPC and PaETS, which have been originally introduced in previous literature, to address partially observable cases. We experimentally compare the performances on continuous control tasks, and conclude that our method can consistently improve the asymptotic performance compared with PlaNet.