Reinforcement learning (RL) algorithms have become indispensable tools in artificial intelligence, empowering agents to acquire optimal decision-making policies through interactions with their environment and feedback mechanisms. This study explores the performance of RL agents in both two-dimensional (2D) and three-dimensional (3D) environments, aiming to research the dynamics of learning across different spatial dimensions. A key aspect of this investigation is the absence of pre-made libraries for learning, with the algorithm developed exclusively through computational mathematics. The methodological framework centers on RL principles, employing a Q-learning agent class and distinct environment classes tailored to each spatial dimension. The research aims to address the question: How do reinforcement learning agents adapt and perform in environments of varying spatial dimensions, particularly in 2D and 3D settings? Through empirical analysis, the study evaluates agents' learning trajectories and adaptation processes, revealing insights into the efficacy of RL algorithms in navigating complex, multi-dimensional spaces. Reflections on the findings prompt considerations for future research, particularly in understanding the dynamics of learning in higher-dimensional environments.

翻译：强化学习算法已成为人工智能领域不可或缺的工具，通过智能体与环境交互及反馈机制，使其能够习得最优决策策略。本研究探索了强化学习智能体在二维（2D）与三维（3D）环境中的表现，旨在研究不同空间维度下的学习动态。该研究的关键特征在于不使用预置学习库，算法完全通过计算数学方法开发。方法论框架以强化学习原理为核心，采用Q学习智能体类以及针对各空间维度定制的环境类。研究旨在探讨以下问题：强化学习智能体如何在二维与三维等不同空间维度环境中实现适应与表现？通过实证分析，研究评估了智能体的学习轨迹与适应过程，揭示了强化学习算法在复杂多维空间导航中的效能。研究结论启示未来研究需深入理解高维环境中的学习动态机制。