The paper introduces Constrained Policy Optimization (CPO), a novel policy search algorithm for constrained reinforcement learning. CPO is designed to address the challenge of training neural network policies in high-dimensional control tasks while ensuring that the policies satisfy specified constraints. The key contributions of CPO include: 1. **Theoretical Foundations**: The paper presents a new theoretical result that bounds the difference in returns between two policies in terms of an average divergence between them. This result is of independent interest and provides a tighter connection between the theory and practice of policy search in deep reinforcement learning. 2. **Algorithm Design**: CPO is derived from this theoretical foundation and is based on a trust region method. It guarantees that the policy updates will both improve the expected return and satisfy constraints. The algorithm is designed to handle high-dimensional policies and avoids the need for off-policy evaluation, which is often challenging in practice. 3. **Experimental Validation**: Extensive experiments on simulated robot locomotion tasks demonstrate that CPO can effectively enforce constraints while maximizing rewards. The results show that CPO outperforms other methods, such as primal-dual optimization, in terms of both constraint satisfaction and performance improvement. 4. **Applications**: CPO is particularly useful in domains where safety is a critical concern, such as industrial robotics, where the agent must interact with humans or other equipment. The ability to enforce constraints ensures that the agent's behavior remains safe throughout training. Overall, CPO represents a significant advancement in the field of constrained reinforcement learning, providing a practical and effective solution for training neural network policies in high-dimensional control tasks while ensuring that the policies satisfy specified constraints.The paper introduces Constrained Policy Optimization (CPO), a novel policy search algorithm for constrained reinforcement learning. CPO is designed to address the challenge of training neural network policies in high-dimensional control tasks while ensuring that the policies satisfy specified constraints. The key contributions of CPO include: 1. **Theoretical Foundations**: The paper presents a new theoretical result that bounds the difference in returns between two policies in terms of an average divergence between them. This result is of independent interest and provides a tighter connection between the theory and practice of policy search in deep reinforcement learning. 2. **Algorithm Design**: CPO is derived from this theoretical foundation and is based on a trust region method. It guarantees that the policy updates will both improve the expected return and satisfy constraints. The algorithm is designed to handle high-dimensional policies and avoids the need for off-policy evaluation, which is often challenging in practice. 3. **Experimental Validation**: Extensive experiments on simulated robot locomotion tasks demonstrate that CPO can effectively enforce constraints while maximizing rewards. The results show that CPO outperforms other methods, such as primal-dual optimization, in terms of both constraint satisfaction and performance improvement. 4. **Applications**: CPO is particularly useful in domains where safety is a critical concern, such as industrial robotics, where the agent must interact with humans or other equipment. The ability to enforce constraints ensures that the agent's behavior remains safe throughout training. Overall, CPO represents a significant advancement in the field of constrained reinforcement learning, providing a practical and effective solution for training neural network policies in high-dimensional control tasks while ensuring that the policies satisfy specified constraints.