Summary Mastering Atari Go Chess and Shogi Planning with a Learned Model arxiv.org
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One Line
MuZero is an exceptional algorithm that outperforms previous reinforcement learning methods and achieves the same level of performance as AlphaZero without needing prior knowledge of the environment's dynamics.
Slides
Slide Presentation (11 slides)
Key Points
- The MuZero algorithm combines tree-based planning with a learned model to achieve superhuman performance in a range of challenging domains.
- MuZero learns a model that predicts the reward, action-selection policy, and value function, which are relevant for planning.
- MuZero achieved a new state of the art in evaluations on 57 different Atari games and matched the superhuman performance of the AlphaZero algorithm in Go, chess, and shogi.
- MuZero bridges the gap between high-performance planning algorithms and model-free RL algorithms, achieving superhuman performance in both logically complex and visually complex domains.
- MuZero's combination of planning and a learned model allows for powerful learning and planning methods to be applied to real-world domains without a perfect simulator.
Summaries
24 word summary
MuZero is a superhuman algorithm that excels in challenging domains without knowing the environment's dynamics. It surpasses previous RL approaches and matches AlphaZero's performance.
78 word summary
MuZero is an algorithm that achieves superhuman performance in challenging domains like Atari games, Go, chess, and shogi. It doesn't require knowledge of the environment's dynamics, but instead trains a model to predict reward, action-selection policy, and value function for planning. MuZero surpasses previous RL approaches in Atari games and matches AlphaZero's performance in board games. It combines a learned model with Monte Carlo Tree Search and introduces a variant called MuZero Reanalyze for improved learning and planning.
158 word summary
The MuZero algorithm combines tree-based planning and a learned model to achieve superhuman performance in challenging domains such as Atari games, Go, chess, and shogi. Unlike previous methods, MuZero does not require knowledge of the environment's dynamics. Instead, it trains a model that predicts the reward, action-selection policy, and value function needed for planning. MuZero surpasses previous state-of-the-art RL approaches in Atari games and matches AlphaZero's performance in Go, chess, and shogi. It even slightly exceeds AlphaZero's performance in Go while using fewer computations. MuZero combines a learned model with Monte Carlo Tree Search (MCTS) to solve board games and Atari games. It generates training data by playing games with MCTS and uses a replay buffer. MuZero also introduces a variant called MuZero Reanalyze and demonstrates its effectiveness in learning and planning in the Atari environment. Overall, MuZero showcases its power in solving board games and Atari games through its superior performance compared to random and human players.
483 word summary
The MuZero algorithm is a powerful approach that combines tree-based planning with a learned model to achieve superhuman performance in various challenging domains, including Atari games, Go, chess, and shogi. What sets MuZero apart from previous model-based reinforcement learning methods is that it does not require knowledge of the underlying dynamics of the environment. Instead, it learns a model that predicts the reward, action-selection policy, and value function needed for planning.
MuZero addresses the struggles faced by previous RL planning approaches when dealing with complex and unknown dynamics in real-world problems. By incorporating a learned model into its training procedure and combining it with tree-based search, MuZero achieves state-of-the-art performance in visually complex domains like Atari games, while maintaining superhuman performance in precision planning tasks such as chess, shogi, and Go.
Building upon the search and policy iteration algorithms of AlphaZero, MuZero trains a model that predicts the policy, value function, and immediate reward at each step based on observations. This end-to-end trained model accurately estimates these quantities.
In evaluations, MuZero surpasses previous state-of-the-art model-free RL approaches in Atari games and matches the superhuman performance of AlphaZero in Go, chess, and shogi. Despite using fewer computations per node in the search tree, MuZero even slightly exceeds AlphaZero's performance in Go. The scalability in planning and efficient learning demonstrated by MuZero make it applicable to a wide range of real-world problems.
To solve board games and Atari games, MuZero combines a learned model with Monte Carlo Tree Search (MCTS). The value function in MuZero is bounded within the [0, 1] interval, allowing for combining value estimates with probabilities using the pUCT rule. The network architecture and hyperparameters used by MuZero are similar to those of AlphaZero.
During training, MuZero generates training data by playing games with MCTS using the latest checkpoint of the network. It keeps an in-memory replay buffer of the most recent games or sequences. The network input representation varies depending on the game, and the dynamics function takes the hidden state produced by the representation function as input.
MuZero also introduces a variant called MuZero Reanalyze, which re-executes its search using the latest model parameters. This fresh policy serves as the policy target for most updates during MuZero training.
The evaluation of MuZero shows that it outperforms both random and human players in most games, whether starting from random no-op or human positions. Its normalized scores are significantly higher than those of random and human players, confirming its effectiveness in learning and planning in the Atari environment.
Overall, MuZero's effectiveness in learning and planning in the Atari environment is demonstrated through its superior performance compared to random and human players in a wide range of games. It highlights the benefits of models in precision planning domains like Go. By combining a learned model with MCTS, MuZero effectively plans and makes decisions, showcasing its power in solving board games and Atari games.
516 word summary
The MuZero algorithm combines tree-based planning with a learned model to achieve superhuman performance in a range of challenging domains, including Atari games, Go, chess, and shogi. Unlike previous model-based reinforcement learning (RL) methods, MuZero does not require knowledge of the underlying dynamics of the environment. Instead, it learns a model that predicts the reward, action-selection policy, and value function necessary for planning.
Previous approaches to planning in RL have struggled with real-world problems that have complex and unknown dynamics. MuZero addresses this issue by combining a tree-based search with a learned model. This allows it to achieve state-of-the-art performance in visually complex domains like Atari games while maintaining superhuman performance in precision planning tasks like chess, shogi, and Go.
MuZero builds upon the search and policy iteration algorithms of AlphaZero but incorporates a learned model into the training procedure. The model predicts the policy, value function, and immediate reward at each step based on observations. It is trained end-to-end to accurately estimate these quantities.
In evaluations, MuZero outperformed previous state-of-the-art model-free RL approaches in Atari games and matched the superhuman performance of AlphaZero in Go, chess, and shogi. It even slightly exceeded AlphaZero's performance in Go despite using fewer computations per node in the search tree. MuZero demonstrated scalability in planning and efficient learning, making it applicable to a wide range of real-world problems.
To solve board games and Atari games, MuZero combines a learned model with Monte Carlo Tree Search (MCTS). The value function in MuZero is bounded within the [0, 1] interval, allowing for combining value estimates with probabilities using the pUCT rule. The network architecture and hyperparameters used by MuZero are similar to those of AlphaZero.
During training, MuZero generates training data by playing games with MCTS using the latest checkpoint of the network. It keeps an in-memory replay buffer of the most recent games or sequences. The network input representation varies depending on the game, and the dynamics function takes the hidden state produced by the representation function as input.
MuZero also introduces a variant called MuZero Reanalyze, which re-executes its search using the latest model parameters. This fresh policy is used as the policy target for most updates during MuZero training.
In evaluations of individual games with random no-op starts and games starting from human positions, MuZero outperformed both random and human players in most games. Its normalized scores were significantly higher than those of random and human players, confirming the effectiveness of MuZero in learning and planning in the Atari environment.
The evaluation also analyzed the impact of search depth in the MCTS tree on performance. Deeper searches led to better performance, highlighting the importance of planning and searching in the MuZero algorithm.
Overall, the evaluation demonstrated the effectiveness of the MuZero algorithm in learning and planning in the Atari environment. It outperformed random and human players in a wide range of games and showed that models are particularly beneficial in precision planning domains like Go. MuZero combines a learned model with MCTS to effectively plan and make decisions, showcasing its power in solving board games and Atari games.
1572 word summary
The MuZero algorithm combines tree-based planning with a learned model to achieve superhuman performance in a range of challenging domains, without any knowledge of the underlying dynamics. MuZero learns a model that predicts the reward, action-selection policy, and value function, which are relevant for planning. In evaluations on 57 different Atari games, MuZero achieved a new state of the art. It also matched the superhuman performance of the AlphaZero algorithm in Go, chess, and shogi, without any knowledge of the game rules.
Constructing agents with planning capabilities has been a challenge in artificial intelligence. Tree-based planning methods have been successful in domains with a perfect simulator, but real-world problems often have complex and unknown dynamics. The MuZero algorithm addresses this issue by combining a tree-based search with a learned model. It predicts the quantities relevant for planning and achieves superhuman performance in visually complex domains like Atari games.
Previous work in model-based reinforcement learning (RL) has focused on reconstructing the true environmental state or sequence of full observations. However, these models struggle in visually rich domains like Atari games. Model-free RL methods estimate the optimal policy and value function directly from interactions with the environment, but they are not effective in domains that require precise lookahead, such as chess and Go. MuZero bridges this gap by achieving state-of-the-art performance in visually complex domains like Atari games while maintaining superhuman performance in precision planning tasks like chess, shogi, and Go.
MuZero builds upon AlphaZero's search and search-based policy iteration algorithms but incorporates a learned model into the training procedure. The main idea is to predict aspects of the future relevant for planning. The model receives observations as input and transforms them into a hidden state. This hidden state is updated iteratively by a recurrent process that predicts the policy, value function, and immediate reward at each step. The model is trained end-to-end to accurately estimate these quantities.
In evaluations, MuZero outperformed previous state-of-the-art model-free RL approaches in Atari games and achieved a new state of the art. It also matched the superhuman performance of AlphaZero in Go, chess, and shogi without any knowledge of the game rules. MuZero's performance in Go even slightly exceeded that of AlphaZero, despite using fewer computations per node in the search tree. MuZero demonstrated scalability in planning, even with longer searches than those seen during training. It also showed efficient learning with fewer simulations per move than the number of possible actions.
MuZero's combination of planning and a learned model allows for powerful learning and planning methods to be applied to real-world domains without a perfect simulator. It provides a bridge between high-performance planning algorithms and model-free RL algorithms, achieving superhuman performance in both logically complex and visually complex domains. MuZero's approach eliminates the need for knowledge of the environment's dynamics, making it applicable to a wide range of real-world problems.
The MuZero algorithm is a model-based reinforcement learning algorithm that combines a learned model with Monte Carlo Tree Search (MCTS) to solve board games and Atari games. In MuZero, the value function is bounded within the [0, 1] interval, which allows for combining value estimates with probabilities using the pUCT rule. However, since the value is unbounded in many environments, MuZero computes normalized Q value estimates by using the minimum and maximum values observed in the search tree.
In terms of hyperparameters, MuZero uses the same architectural choices and hyperparameters as AlphaZero for board games, including UCB constants, dirichlet exploration noise, and 800 simulations per search. For Atari games, MuZero uses 50 simulations per search to speed up experiments. The discount factor is assumed to be 1 in board games, and there are no intermediate rewards.
To generate training data, MuZero uses the latest checkpoint of the network to play games with MCTS. For board games, the search is run for 800 simulations per move, while for Atari games, 50 simulations per move are sufficient. The training job keeps an in-memory replay buffer of the most recent 1 million games for board games and the most recent 125 thousand sequences of length 200 for Atari games. MuZero uses an exploration scheme similar to AlphaZero for board games and samples actions from the visit count distribution throughout the duration of each game for Atari games.
The network input representation function varies depending on the game. For Go, chess, and shogi, the history over board states is encoded as the last 8 board states. In chess, the history is increased to the last 100 board states to allow correct prediction of draws. For Atari games, the input includes the last 32 RGB frames at resolution 96x96 along with the last 32 actions that led to each of those frames. RGB frames are encoded as one plane per color, rescaled to the range [0, 1], and historical actions are encoded as simple bias planes.
The dynamics function takes as input the hidden state produced by the representation function or previous application of the dynamics function, concatenated with a representation of the action for the transition. Actions are encoded spatially in planes of the same resolution as the hidden state. The encoding varies depending on the game, with different encodings for Go, chess, shogi, and Atari.
The prediction function in MuZero uses the same architecture as AlphaZero, with one or two convolutional layers followed by a fully connected layer. The value and reward predictions are scaled using an invertible transform to ensure equivalent categorical representations. The representation and dynamics functions use the same architecture as AlphaZero, with 16 residual blocks.
During training, MuZero unrolls the network for K hypothetical steps and aligns it to sequences sampled from the trajectories generated by MCTS actors. The network has a loss for the value, policy, and reward targets at each unrolled step, and the total loss is summed to produce the total loss for the MuZero network. Gradient scaling is used to maintain a similar magnitude of gradient across different unroll steps.
MuZero also introduces a variant called MuZero Reanalyze, which revisits past time-steps and re-executes its search using the latest model parameters. This fresh policy is used as the policy target for 80% of updates during MuZero training. Other hyperparameters are adjusted to increase sample reuse and avoid overfitting of the value function.
In terms of evaluation, MuZero's relative strength in board games is measured by estimating Elo ratings through a tournament between iterations of MuZero and baseline players such as Stockfish, Elmo, or AlphaZero. In Atari games, mean reward over episodes is computed using different evaluation strategies, including random starts and human starts.
Overall, MuZero is a powerful algorithm that combines a learned model with MCTS to achieve impressive results in solving board games and Atari games.
The document presents an evaluation of the MuZero algorithm in the context of Atari games. The evaluation includes individual games with random no-op starts, as well as games starting from human positions. The results show that MuZero achieves impressive performance across a wide range of games.
In the evaluation of individual games with random no-op starts, MuZero outperforms both random and human players in most games. The normalized scores of MuZero are significantly higher than those of random and human players. MuZero achieves normalized scores that are several thousand percent higher than both random and human players in many games. This demonstrates the effectiveness of the MuZero algorithm in learning and planning in the Atari environment.
In the evaluation of games starting from human positions, MuZero again demonstrates its superiority. MuZero achieves higher scores than both random and human players in most games. The normalized scores of MuZero are consistently higher than those of random and human players. MuZero achieves normalized scores that are several thousand percent higher than both random and human players in many games. This further confirms the effectiveness of the MuZero algorithm in learning and planning in the Atari environment, even when starting from human positions.
The MuZero algorithm combines a learned model with Monte Carlo tree search (MCTS) to plan and make decisions in the Atari environment. The algorithm learns a model that predicts the next state and reward given the current state and action. This learned model is then used in MCTS to simulate future states and evaluate their potential outcomes. The algorithm uses a learning rule to update the model parameters based on the losses incurred during the planning process.
The evaluation also includes an analysis of the search depth in the MCTS tree and its impact on performance. The results show that deeper searches lead to better performance, as evidenced by the consistent improvement in scores with increasing search depth. This highlights the importance of planning and searching in the MuZero algorithm.
Furthermore, the evaluation compares the performance of MuZero in different games. The results show that MuZero performs better in precision planning domains, such as Go, compared to more complex and dynamic games like Ms. Pacman. This suggests that the benefit of models is greater in games that require precise planning and strategy.
Overall, the evaluation demonstrates the effectiveness of the MuZero algorithm in learning and planning in the Atari environment. MuZero outperforms both random and human players in a wide range of games, achieving significantly higher scores. The algorithm combines a learned model with MCTS to effectively plan and make decisions. The results highlight the importance of planning and searching in the MuZero algorithm, as well as the benefit of models in precision planning domains.