Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization

Abstract: Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, and long-horizon planning, each posing distinct challenges for state-of-the-art optimization methods. To efficiently solve a wide range of tasks across varying scenarios, researchers either develop specialized algorithms for the task to achieve, or switch between different frameworks. Monte Carlo Tree Search (MCTS) is a general-purpose decision-making tool that enables strategic exploration across problem instances without relying on task-specific structures. However, MCTS suffers from combinatorial complexity, leading to slow convergence and high memory usage. To address this limitation, we propose \emph{Tensor Train Tree Search} (TTTS), which leverages tensor factorization to exploit the separable structure of decision trees. This yields a low-rank, linear-complexity representation that significantly reduces both computation time and storage requirements. We prove that TTTS can efficiently reach the bounded global optimum within a finite time. Experimental results across inverse kinematics, motion planning around obstacles, multi-stage motion planning, and bimanual whole-body manipulation demonstrate the efficiency of TTTS on a diverse set of robotic tasks.