This paper introduces Batch-Constrained Deep Q-learning (BCQ), a novel off-policy deep reinforcement learning algorithm that can learn effectively from arbitrary, fixed batch data without exploration. The authors highlight a critical issue in off-policy reinforcement learning: extrapolation error, which arises when the dataset is uncorrelated with the true distribution of the current policy. This error leads to inaccurate value estimates and poor performance in off-policy learning. BCQ addresses this by constraining the policy to select actions that are similar to those in the batch data, thereby minimizing the mismatch between the policy's state-action visitation and the batch. The algorithm uses a state-conditioned generative model to produce only previously seen actions, combined with a Q-network to select the highest valued action similar to the data in the batch. This approach ensures that the policy remains close to on-policy behavior with respect to the available data, leading to more accurate value estimates. The authors demonstrate that BCQ outperforms existing off-policy algorithms like DDPG and DQN in several tasks, including those with imperfect demonstrations. Experiments on the MuJoCo environment show that BCQ achieves stable value learning and strong performance in batch settings. It is particularly effective in scenarios where data is noisy or incomplete, as it avoids extrapolation error by focusing on actions present in the batch. The algorithm is also efficient, requiring fewer training steps than traditional deep reinforcement learning methods. The paper concludes that BCQ provides a robust solution for off-policy learning in batch settings, offering a foundation for future research in reinforcement learning. It emphasizes the importance of addressing extrapolation error in practical applications where data collection is limited or costly.This paper introduces Batch-Constrained Deep Q-learning (BCQ), a novel off-policy deep reinforcement learning algorithm that can learn effectively from arbitrary, fixed batch data without exploration. The authors highlight a critical issue in off-policy reinforcement learning: extrapolation error, which arises when the dataset is uncorrelated with the true distribution of the current policy. This error leads to inaccurate value estimates and poor performance in off-policy learning. BCQ addresses this by constraining the policy to select actions that are similar to those in the batch data, thereby minimizing the mismatch between the policy's state-action visitation and the batch. The algorithm uses a state-conditioned generative model to produce only previously seen actions, combined with a Q-network to select the highest valued action similar to the data in the batch. This approach ensures that the policy remains close to on-policy behavior with respect to the available data, leading to more accurate value estimates. The authors demonstrate that BCQ outperforms existing off-policy algorithms like DDPG and DQN in several tasks, including those with imperfect demonstrations. Experiments on the MuJoCo environment show that BCQ achieves stable value learning and strong performance in batch settings. It is particularly effective in scenarios where data is noisy or incomplete, as it avoids extrapolation error by focusing on actions present in the batch. The algorithm is also efficient, requiring fewer training steps than traditional deep reinforcement learning methods. The paper concludes that BCQ provides a robust solution for off-policy learning in batch settings, offering a foundation for future research in reinforcement learning. It emphasizes the importance of addressing extrapolation error in practical applications where data collection is limited or costly.