Master Thesis

Equivariant Function Approximators in applications to data-driven robot planning, perception, and control.

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  • If you are interested in the proposal, please contact with the supervisors.


This project aims at exploring the use of function approximators that have equivariance to certain symmetries (symmetry groups) in applications of robot perception, planning, and/or control. Robotic systems are inherently symmetric and therefore an exceptional testing case for machine learning techniques exploiting these symmetries as inductive biases, to improve overall performance, sample efficiency, and robustness. The theory of Equivariant function approximators, specially Equivariant Neural Networks has grown in the last 4 years, however, applications of these techniques have not been wildly adopted in practice mainly because there still are several implementations and theoretical developments required. In this project, you are expected to explore these practical and theoretical challenges focusing on data-driven applications to robotic systems (e.g., Perception, Legged Locomotion, Dexterous Manipulation, Motion Planning, State Estimation, Sensor Fusion) using any machine learning techniques (e.g., Neural Networks, Convex Optimization, Kernel Methods) that exploits the symmetries present in the robot morphology and exteroceptive and proprioceptive information.

Profile: The student is expected to have a background in machine learning and related fields, with a good background in either mathematics, physics, or robotics. Knowledge and experience in group theory, probability, and control are a plus.

Learning and Control:
Abdolhosseini, Farzad, et al. "On learning symmetric locomotion." Motion, Interaction and Games. 2019. 1-10.
Apraez, Daniel Felipe Ordoñez, et al. "An Adaptable Approach to Learn Realistic Legged Locomotion without Examples." arXiv preprint arXiv:2110.14998 (2021).
van der Pol, Elise, et al. "MDP homomorphic networks: Group symmetries in reinforcement learning." Advances in Neural Information Processing Systems 33 (2020): 4199-4210.
Equivariant Function Approximators:
Bronstein, Michael M., et al. "Geometric deep learning: going beyond euclidean data." IEEE Signal Processing Magazine 34.4 (2017): 18-42.
Finzi, Marc, Gregory Benton, and Andrew G. Wilson. "Residual Pathway Priors for Soft Equivariance Constraints." Advances in Neural Information Processing Systems 34 (2021).
Finzi, Marc, Max Welling, and Andrew Gordon Wilson. "A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups." International Conference on Machine Learning. PMLR, 2021.
Cao, Wenming, et al. "A comprehensive survey on geometric deep learning." IEEE Access 8 (2020): 35929-35949.