Language models are often said to face a symbol grounding problem. While some have argued the problem can be solved without resort to other modalities, many have speculated that grounded learning is more efficient. We explore this question in Othello, a simplified, rule-based world that offers a controlled and interpretable testbed for studying world understanding. Building on prior work, we introduce VISOTHELLO, a multi-modal model trained jointly on move sequences and board images. Using the Othello rule understanding task, we examine whether multi-modal learning provides advantages over text-only approaches. We further evaluate robustness under semantically irrelevant perturbations and analyze the consistency of cross-modal alignment. Our results suggest that multi-modal training not only improves performance and robustness but also promotes convergence toward shared internal representations across different model architectures.

Solving combinatorial games has been a classic research topic in artificial intelligence because solutions can offer essential information to improve gameplay. Several definitions exist for `solving the game,' but they are markedly different regarding computational cost and the detail of insights derived. In this study, we introduce a novel definition called `semi-strongly solved' and propose an algorithm to achieve this type of solution efficiently. This new definition addresses existing gaps because of its intermediate computational cost and the quality of the solution. To demonstrate the potential of our approach, we derive the theoretical computational complexity of our algorithm under a simple condition, and apply it to semi-strongly solve the game of 6x6 Othello. This study raises many new research goals in this research area.

This paper presents novel game AI agents based on the AlphaZero framework, enhanced with Vision Transformers (ViT): AlphaViT, AlphaViD, and AlphaVDA. These agents are designed to play various board games of different sizes using a single model, overcoming AlphaZero's limitation of being restricted to a fixed board size. AlphaViT uses only a transformer encoder, while AlphaViD and AlphaVDA contain both an encoder and a decoder. AlphaViD's decoder receives input from the encoder output, while AlphaVDA uses a learnable matrix as decoder input. Using the AlphaZero framework, the three proposed methods demonstrate their versatility in different game environments, including Connect4, Gomoku, and Othello. Experimental results show that these agents, whether trained on a single game or on multiple games simultaneously, consistently outperform traditional algorithms such as Minimax and Monte Carlo tree search using a single DNN with shared weights, while approaching the performance of AlphaZero. In particular, AlphaViT and AlphaViD show strong performance across games, with AlphaViD benefiting from an additional decoder layer that enhances its ability to adapt to different action spaces and board sizes. These results may suggest the potential of transformer-based architectures to develop more flexible and robust game AI agents capable of excelling in multiple games and dynamic environments.

The game of Othello is one of the world's most complex and popular games that has yet to be computationally solved. Othello has roughly ten octodecillion (10 to the 58th power) possible game records and ten octillion (10 to the 28th power) possible game positions. The challenge of solving Othello, determining the outcome of a game with no mistake made by either player, has long been a grand challenge in computer science. This paper announces a significant milestone: Othello is now solved. It is computationally proved that perfect play by both players lead to a draw. Strong Othello software has long been built using heuristically designed search techniques. Solving a game provides a solution that enables the software to play the game perfectly.

This paper presents MiniZero, a zero-knowledge learning framework that supports four state-of-the-art algorithms, including AlphaZero, MuZero, Gumbel AlphaZero, and Gumbel MuZero. While these algorithms have demonstrated super-human performance in many games, it remains unclear which among them is most suitable or efficient for specific tasks. Through MiniZero, we systematically evaluate the performance of each algorithm in two board games, 9x9 Go and 8x8 Othello, as well as 57 Atari games. For two board games, using more simulations generally results in higher performance. However, the choice of AlphaZero and MuZero may differ based on game properties. For Atari games, both MuZero and Gumbel MuZero are worth considering. Since each game has unique characteristics, different algorithms and simulations yield varying results. In addition, we introduce an approach, called progressive simulation, which progressively increases the simulation budget during training to allocate computation more efficiently. Our empirical results demonstrate that progressive simulation achieves significantly superior performance in two board games. By making our framework and trained models publicly available, this paper contributes a benchmark for future research on zero-knowledge learning algorithms, assisting researchers in algorithm selection and comparison against these zero-knowledge learning baselines. Our code and data are available at https://rlg.iis.sinica.edu.tw/papers/minizero.

Recently, the seminal algorithms AlphaGo and AlphaZero have started a new era in game learning and deep reinforcement learning. While the achievements of AlphaGo and AlphaZero - playing Go and other complex games at super human level - are truly impressive, these architectures have the drawback that they require high computational resources. Many researchers are looking for methods that are similar to AlphaZero, but have lower computational demands and are thus more easily reproducible. In this paper, we pick an important element of AlphaZero - the Monte Carlo Tree Search (MCTS) planning stage - and combine it with temporal difference (TD) learning agents. We wrap MCTS for the first time around TD n-tuple networks and we use this wrapping only at test time to create versatile agents that keep at the same time the computational demands low. We apply this new architecture to several complex games (Othello, ConnectFour, Rubik's Cube) and show the advantages achieved with this AlphaZero-inspired MCTS wrapper. In particular, we present results that this agent is the first one trained on standard hardware (no GPU or TPU) to beat the very strong Othello program Edax up to and including level 7 (where most other learning-from-scratch algorithms could only defeat Edax up to level 2).

Language models like OpenAI's Generative Pre-Trained Transformers (GPT-2/3) capture the long-term correlations needed to generate text in a variety of domains (such as language translators) and recently in gameplay (chess, Go, and checkers). The present research applies both the larger (GPT-3) and smaller (GPT-2) language models to explore the complex strategies for the game of Othello (or Reverses). Given the game rules for rapid reversals of fortune, the language model not only represents a candidate predictor of the next move based on previous game moves but also avoids sparse rewards in gameplay. The language model automatically captures or emulates championship-level strategies. The fine-tuned GPT-2 model generates Othello games ranging from 13-71% completion, while the larger GPT-3 model reaches 41% of a complete game. Like previous work with chess and Go, these language models offer a novel way to generate plausible game archives, particularly for comparing opening moves across a larger sample than humanly possible to explore. A primary contribution of these models magnifies (by two-fold) the previous record for player archives (120,000 human games over 45 years from 1977-2022), thus supplying the research community with more diverse and original strategies for sampling with other reinforcement learning techniques.

Artificial intelligence (AI) has achieved superhuman performance in board games such as Go, chess, and Othello (Reversi). In other words, AI has become too strong an opponent for human players in such games. In this context, it is difficult for a human player to enjoy playing the games with the AI. To keep human players entertained and immersed in a game, the AI is required to dynamically balance its skill with that of the human player. To address this issue, we propose AlphaDDA, an AlphaZero-based AI with dynamic difficulty adjustment (DDA). AlphaDDA consists of a deep neural network (DNN) and a Monte Carlo tree search, as in AlphaZero. AlphaDDA estimates the value of the game state from only the board state using the DNN and changes its skill according to the value. AlphaDDA can adjust its skill using only the state of a game without any prior knowledge regarding an opponent. In this study, AlphaDDA plays Connect4, Othello, and 6x6 Othello, which is Othello using a 6x6 size board, with other AI agents. The other AI agents are AlphaZero, Monte Carlo tree search, the minimax algorithm, and a random player. This study shows that AlphaDDA can balance its skill with that of the other AI agents, except for a random player. The DDA ability of AlphaDDA is derived from an accurate estimation of the value from the state of a game. We believe that the AlphaDDA approach can be used for any game in which the DNN can estimate the value from the state.

"Many a true word hath been spoken in jest." "O, beware, my lord, of jealousy; It is the green-ey'd monster, which doth mock The meat it feeds on." "There was a star danced, and under that was I born." Who can write like Shakespeare? Or even spell like Shakespeare?

AlphaZero has achieved impressive performance in deep reinforcement learning by utilizing an architecture that combines search and training of a neural network in self-play. Many researchers are looking for ways to reproduce and improve results for other games/tasks. However, the architecture is designed to learn from scratch, tabula rasa, accepting a cold-start problem in self-play. Recently, a warm-start enhancement method for Monte Carlo Tree Search was proposed to improve the self-play starting phase. It employs a fixed parameter $I^\prime$ to control the warm-start length. Improved performance was reported in small board games. In this paper we present results with an adaptive switch method. Experiments show that our approach works better than the fixed $I^\prime$, especially for "deep," tactical, games (Othello and Connect Four). We conjecture that the adaptive value for $I^\prime$ is also influenced by the size of the game, and that on average $I^\prime$ will increase with game size. We conclude that AlphaZero-like deep reinforcement learning benefits from adaptive rollout based warm-start, as Rapid Action Value Estimate did for rollout-based reinforcement learning 15 years ago.