The Minesweeper game is modeled as a sequential decision-making task, for which a neural network architecture, state encoding, and reward function were herein designed. Both a Deep Q-Network (DQN) and supervised learning methods were successfully applied to optimize the training of the game. The experiments were conducted on the AutoDL platform using an NVIDIA RTX 3090 GPU for efficient computation. The results showed that in a 6 × 6 grid with four mines, the DQN model achieved an average win rate of 93.3% (standard deviation: 0.77%), while the supervised learning method achieved 91.2% (standard deviation: 0.9%), both outperforming human players and baseline algorithms and demonstrating high intelligence. The mechanisms of the two methods in the Minesweeper task were analyzed, with the reasons for the faster training speed and more stable performance of supervised learning explained from the perspectives of means–ends analysis and feedback control. Although there is room for improvement in sample efficiency and training stability in the DQN model, its greater generalization ability makes it highly promising for application in more complex decision-making tasks.

Minesweeper is both an intellectual challenge for human players and an effective testbed for intelligent algorithms. For the standard Minesweeper task on a 9 × 9 grid with 10 mines, a convolutional neural network (CNN)-based supervised learning approach, together with optimized network architecture, state encoding, and dynamic learning rate scheduling, achieves a test win rate of 85.16% (SD = 0.36 percentage points), exceeding the baseline Single-Point (SP) algorithm by more than 10 percentage points. The combined use of dropout and data augmentation achieves a higher test win rate than either technique alone under the evaluated settings. Building on this model, we propose an easy-to-hard staged curriculum learning (SCL) strategy to address the increasing task difficulty caused by higher mine density and the difficulty of training models from scratch. By progressively increasing the number of mines and transferring model parameters from the preceding training stage, the model can inherit previously acquired knowledge and gradually adapt to more complex tasks. Representative SCL models achieved test win rates of 55.85%, 20.38%, and 4.00% on the 14-, 18-, and 22-mine tasks, respectively. In the three-seed ablation study on the 18-mine task using validation-based checkpoint selection, SCL achieved the highest mean test win rate of 21.65%, compared with 20.85% for mixed-density adaptation, 17.08% for direct transfer, and 15.59% for training from scratch. SCL achieved numerically higher test win rates than mixed-density adaptation across all three seeds, although the difference was not statistically significant. However, a constraint satisfaction problem (CSP) solver achieves a higher win rate of 47.17% on the same task, highlighting the advantage of explicit constraint-based reasoning in absolute solving performance. Further analysis of clue-value distributions shows that the frequencies of local patterns change with mine density, providing a structural motivation for the easy-to-hard curriculum. These findings indicate that staged curriculum learning can facilitate knowledge transfer across increasingly difficult Minesweeper tasks, although reliable solving of high-density configurations remains challenging.

This paper introduces and proves a novel proposition on the structural closure property of Linear Time-Invariant (LTI) invertible systems. Specifically, it demonstrates that systems composed by arbitrarily combining LTI invertible systems through cascade, parallel, and feedback configurations remain LTI invertible systems. Furthermore, a constructive approach is proposed to reinterpret systems governed by linear constant-coefficient differential equations, proving that under the assumption of causality, such systems are invertible. The theoretical contribution of this work enriches the understanding of invertibility in signal and system theory, while its practical value lies in providing structural support for the design and analysis of complex systems.

Improving sample efficiency and achieving balanced multi-task performance across different tasks remain important research challenges in reinforcement learning. Yie Ar Kung-Fu is formulated as a multi-task reinforcement learning environment. A task-specific neural network architecture, simplified state and action encoding schemes, a reward mechanism, and a dynamic learning-rate schedule are designed for the game environment. Based on Proximal Policy Optimization (PPO), a parallel training method is further proposed. The method aggregates episode samples generated from different opponent environments into a unified sample queue in the order of episode completion and dynamically adjusts the weights of samples from different opponents in the loss function based on their win rates. Experiments were conducted on the AutoDL platform using an NVIDIA RTX 4090 GPU. The proposed method enables joint training across multiple opponent environments. After approximately 15,000 training episodes, the trained agent achieved win rates exceeding 90% against all opponents and attained a level-clear rate of 79%, demonstrating strong game-playing performance and balanced performance across multiple opponent tasks. Furthermore, interdisciplinary analogies are used to interpret how parallel training improves sample efficiency and balanced performance across tasks. The proposed method is simple to implement, stable during training, and readily applicable to other complex multi-task environments.