Lipschitz Lifelong Monte Carlo Tree Search for Mastering Non-Stationary Tasks

2025-02-02

AI Summary

To address the low planning efficiency and poor adaptability of traditional Monte Carlo Tree Search (MCTS) in non-stationary environments—where transition and reward functions evolve dynamically—this paper proposes LiZero. First, it introduces Lipschitz continuity to model inter-task relationships, enabling cross-task knowledge transfer. Second, it designs an adaptive Upper Confidence Bound for Trees (aUCT) mechanism that jointly incorporates task similarity and sampling confidence to dynamically balance exploration and exploitation. Third, it establishes a theoretical framework for sampling-efficiency acceleration in Lipschitz lifelong MCTS and provides an online-executable algorithm. Experiments demonstrate that LiZero achieves 3–4× faster convergence on non-stationary task sequences compared to classical MCTS and state-of-the-art lifelong learning baselines, validating its effectiveness and generalization capability in dynamic real-world decision-making.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

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

Abstract

Monte Carlo Tree Search (MCTS) has proven highly effective in solving complex planning tasks by balancing exploration and exploitation using Upper Confidence Bound for Trees (UCT). However, existing work have not considered MCTS-based lifelong planning, where an agent faces a non-stationary series of tasks -- e.g., with varying transition probabilities and rewards -- that are drawn sequentially throughout the operational lifetime. This paper presents LiZero for Lipschitz lifelong planning using MCTS. We propose a novel concept of adaptive UCT (aUCT) to transfer knowledge from a source task to the exploration/exploitation of a new task, depending on both the Lipschitz continuity between tasks and the confidence of knowledge in in Monte Carlo action sampling. We analyze LiZero's acceleration factor in terms of improved sampling efficiency and also develop efficient algorithms to compute aUCT in an online fashion by both data-driven and model-based approaches, whose sampling complexity and error bounds are also characterized. Experiment results show that LiZero significantly outperforms existing MCTS and lifelong learning baselines in terms of much faster convergence (3$sim$4x) to optimal rewards. Our results highlight the potential of LiZero to advance decision-making and planning in dynamic real-world environments.

Problem

• Adaptive decision-making
• Monte Carlo Tree Search (MCTS)
• Time-varying tasks

Innovation

• LiZero
• Adaptive Upper Confidence Bound
• Lipschitz MCTS