An Introduction to Variational Methods for Graphical Models
Machine Learning
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Fast particle smoothing: if I had a million particles
ICML '06 Proceedings of the 23rd international conference on Machine learning
Optimal on-line scheduling in stochastic multiagent systems in continuous space-time
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Robot trajectory optimization using approximate inference
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Graphical model inference in optimal control of stochastic multi-agent systems
Journal of Artificial Intelligence Research
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Path integral control by reproducing kernel Hilbert space embedding
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We address the problem of continuous stochastic optimal control in the presence of hard obstacles. Due to the non-smooth character of the obstacles, the traditional approach using dynamic programming in combination with function approximation tends to fail. We consider a recently introduced special class of control problems for which the optimal control computation is reformulated in terms of a path integral. The path integral is typically intractable, but amenable to techniques developed for approximate inference. We argue that the variational approach fails in this case due to the non-smooth cost function. Sampling techniques are simple to implement and converge to the exact results given enough samples. However, the infinite cost associated with hard obstacles renders the sampling procedures inefficient in practice. We suggest Expectation Propagation (EP) as a suitable approximation method, and compare the quality and efficiency of the resulting control with an MC sampler on a car steering task and a ball throwing task. We conclude that EP can solve these challenging problems much better than a sampling approach.