[Paper Review] Approximate Bayesian inference in spatial environments

Atanas Mirchev, Baris Kayalibay+3 more|arXiv (Cornell University)|May 18, 2018

Time Series Analysis and Forecasting4 citations

TL;DR

This paper proposes a deep variational Bayes filter with a latent map (DVBF-LM) that unifies SLAM, autonomous exploration, and navigation in spatial environments using variational inference and neural networks. It achieves competitive performance to specialized state-of-the-art methods in simulated LiDAR and maze environments by enabling end-to-end learning and approximate Bayesian inference over complex, non-Gaussian posteriors.

ABSTRACT

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous exploration are typically adressed with specialised methods, often relying on detailed knowledge of the system at hand. We express these tasks as probabilistic inference and planning under the umbrella of deep sequential generative models. Using the frameworks of variational inference and neural networks, our method inherits favourable properties such as flexibility, scalability and the ability to learn from data. The method performs comparably to specialised state-of-the-art methodology in two distinct simulated environments.

Motivation & Objective

• To unify multiple spatial reasoning tasks—SLAM, autonomous exploration, and navigation—under a single probabilistic deep learning framework.
• To enable end-to-end training of stochastic recurrent models on long, sequential time series without supervision.
• To model complex, non-Gaussian posterior distributions in SLAM using a variational posterior that captures multi-modal uncertainty.
• To perform active exploration by optimizing expected information gain without assuming Gaussian or grid-based state space discretizations.
• To demonstrate competitive performance against specialized baselines in simulated environments without architectural or inductive bias for specific tasks.

Proposed method

• Uses a deep non-linear state space model augmented with a global latent map variable representing the environment, enabling joint inference of agent pose and map.
• Employs variational inference with a structured posterior to approximate the complex, multi-modal joint posterior over maps and trajectories in SLAM.
• Applies a pose-based attention mechanism to conditionally attend to relevant map regions for observation reconstruction and belief updating.
• Optimizes control sequences for exploration by maximizing mutual information between observations and map uncertainty, using a heuristic obstacle penalty to improve sample efficiency.
• Trains the model end-to-end via stochastic backpropagation on long sequential data using a variational lower bound on the marginal likelihood.
• Uses a differentiable, differentiable map representation that supports planning and information gain estimation in continuous spatial states.

Experimental results

Research questions

• RQ1 Can a single deep generative model effectively unify SLAM, autonomous exploration, and navigation in spatial environments?
• RQ2 How can complex, non-Gaussian posterior distributions in SLAM be effectively approximated using deep neural networks and variational inference?
• RQ3 Can information-theoretic exploration be performed efficiently in continuous spatial states without relying on occupancy grids or Gaussian assumptions?
• RQ4 To what extent can a single end-to-end trained model outperform task-specific baselines in simulated spatial environments?
• RQ5 How does the proposed method handle long sequential dependencies in real-world-like spatial sequences?

Key findings

• The DVBF-LM model achieves competitive localisation accuracy compared to a state-of-the-art 2D LiDAR SLAM system in simulated environments.
• The proposed exploration method significantly outperforms a strong LSTM-based baseline (PEMA) in both information gain and exploration ratio, even though PEMA is directly trained on the latter metric.
• The model exhibits nearly uniform coverage in mazes, actively targeting unexplored and uncertain regions, demonstrating effective curiosity-driven exploration.
• The method maintains high performance in planning tasks, with minimal loss in accuracy when used as a simulator for trajectory optimization.
• The use of an obstacle penalty during control sequence generation improves sample efficiency, reducing the number of invalid trajectories in exploration.
• The model generalizes across maze complexities and corridor widths, showing robustness to environmental variations in the experiments.