Robot Learning using Tensor Networks

In various robotics applications, the selection of function approximation methods greatly influences the feasibility and computational efficiency of algorithms. Tensor Networks (TNs), also referred to as tensor decomposition techniques, present a versatile approach for approximating functions involving continuous variables, discrete variables, or combinations of these variable types. Apart from their approximation capabilities, TNs offer efficient methods for conducting algebraic operations, calculus, probability modeling, and optimization, which are particularly essential in robotics applications. This thesis highlights the importance of a specific TN known as Tensor Train (TT) for function approximation in robotics by addressing a diverse range of previously challenging problems. Initially, utilizing TT, the thesis enhances the scalability and deployability of an ergodic exploration algorithm commonly employed in robotic exploration. Subsequently, the thesis introduces a novel numerical optimization algorithm named Tensor Train for Global Optimization (TTGO) to determine the optima of functions represented in TT format. Given that numerous robotics tasks are framed as numerical optimization problems, TTGO provides efficient solutions to several optimization-based problems in robotics, including inverse kinematics with obstacles, motion planning, and policy learning, as demonstrated in the thesis. In summary, this thesis underscores the promising potential of TNs as valuable tools in the field of robotics.