Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization

2025-07-07

AI Summary

Nonlinear, high-dimensional, and long-horizon optimization problems—such as robotic inverse kinematics, obstacle-avoidance planning, and multi-stage optimal control—suffer from poor generalizability and excessive computational overhead in existing approaches. This paper proposes Tensor-Train Monte Carlo Tree Search (TT-MCTS), the first method to integrate tensor decomposition—specifically the tensor-train (TT) format—into the MCTS framework. Leveraging the low-rank separability of decision structures, TT-MCTS achieves linear-complexity compression of the state-action space. We provide theoretical guarantees proving finite-step convergence to a bounded global optimum. Experiments on single-arm and dual-arm manipulation, whole-body obstacle avoidance, and multi-task coordination demonstrate that TT-MCTS reduces memory consumption by over 70% and computation time by over 50% compared to standard MCTS, while maintaining strong generalizability, scalability, and robustness.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Addressing nonlinear kinematics and complex dynamics in robotics
• Reducing combinatorial complexity in Monte Carlo Tree Search
• Improving efficiency in diverse robotic optimization tasks

Innovation

• Monte Carlo Tree Search for general decision-making
• Tensor factorization to reduce complexity
• Low-rank representation for efficient computation