Lyapunov-based Safe Policy Optimization for Continuous Control (1901.10031v2)

Abstract: We study continuous action reinforcement learning problems in which it is crucial that the agent interacts with the environment only through safe policies, i.e.,~policies that do not take the agent to undesirable situations. We formulate these problems as constrained Markov decision processes (CMDPs) and present safe policy optimization algorithms that are based on a Lyapunov approach to solve them. Our algorithms can use any standard policy gradient (PG) method, such as deep deterministic policy gradient (DDPG) or proximal policy optimization (PPO), to train a neural network policy, while guaranteeing near-constraint satisfaction for every policy update by projecting either the policy parameter or the action onto the set of feasible solutions induced by the state-dependent linearized Lyapunov constraints. Compared to the existing constrained PG algorithms, ours are more data efficient as they are able to utilize both on-policy and off-policy data. Moreover, our action-projection algorithm often leads to less conservative policy updates and allows for natural integration into an end-to-end PG training pipeline. We evaluate our algorithms and compare them with the state-of-the-art baselines on several simulated (MuJoCo) tasks, as well as a real-world indoor robot navigation problem, demonstrating their effectiveness in terms of balancing performance and constraint satisfaction. Videos of the experiments can be found in the following link: https://drive.google.com/file/d/1pzuzFqWIE710bE2U6DmS59AfRzqK2Kek/view?usp=sharing.

• The paper presents Lyapunov-based algorithms that leverage projection techniques for safe policy updates in constrained MDPs.
• It integrates both θ-projection and a-projection methods to enforce safety constraints during reinforcement learning training.
• Empirical results show faster convergence and lower constraint violations, making the approach promising for robotics and autonomous systems.

Lyapunov-Based Safe Policy Optimization for Continuous Control

The research introduces an innovative approach to reinforcement learning (RL) in continuous action spaces, with a focus on ensuring agent safety through compliance with constraints. The core contribution of the paper is a set of algorithms that leverage the theoretical properties of Lyapunov functions to ensure safe policy optimization. Specifically, the authors address Constrained Markov Decision Processes (CMDPs) using two novel methods for safe policy updates: the $\theta$-projection and the $a$-projection.

Overview

In RL, particularly when interacting with physical systems, safety constraints are critical. Unsafe policies can drive systems to states that are not desirable or potentially harmful. This paper proposes a formulation grounded in CMDPs, where constraints are imposed on the expected cumulative costs associated with state transitions. The novelty lies in integrating Lyapunov functions, a concept from control theory traditionally used to analyze system stability, into policy optimization algorithms for CMDPs. By implementing these functions, the proposed algorithms maintain safety constraints without hampering the agent's performance objective.

Algorithms

The paper details two principal algorithms:

1. $\theta$-Projection Approach: This method incorporates the Lyapunov constraints directly during parameter updates. It attempts to minimize the expected cumulative cost while ensuring that each policy update respects the constraints derived from Lyapunov functions. This is achieved through a projection of the policy parameters onto the feasible region demarcated by these constraints.
2. $a$-Projection Approach: Alternatively, the $a$-projection injects a safety layer into the policy network that dynamically projects actions onto a safety constraint set during execution. This technique allows the integration of safety checks directly into the action decision process, reducing the conservativeness of policy updates compared to the $\theta$-projection.

Both methods use policy gradient techniques, such as Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO), which are augmented with Lyapunov constraints to ensure safety both during training and in the final learned policy.

Results

Empirical results indicate strong performance of the proposed methods in simulated environments like MuJoCo tasks and a real-world indoor robot navigation scenario. The Lyapunov-based algorithms exhibit efficient learning by balancing performance and constraint satisfaction. The $a$-projection approach, in particular, is shown to be less conservative, yielding faster convergence with lower constraint violations.

Implications

The integration of Lyapunov functions in RL for constraint satisfaction opens new possibilities for safely deploying RL in domains like robotics and autonomous vehicles, where safety constraints are non-negotiable. The proposed approaches ensure that policies remain within the feasible set throughout training, limiting potential damages from exploration. This methodological advancement suggests that similar techniques could be employed to enhance safety protocols in various applications involving RL and CMDPs.

Future Directions

Future research could focus on refining the implementation of Lyapunov functions to address limitations regarding the computational complexity introduced by the constraints. Developing more sophisticated mechanisms for handling infinite state spaces or extending these frameworks to environments where model-based approaches can offer complementary benefits might prove valuable. Also, the exploration of scalability and robustness in more complex, real-world settings remains an open avenue for future studies.

In conclusion, this paper provides a significant contribution to the safe deployment of RL systems in continuous action domains, ensuring that while agents strive for optimal performance, they adhere to safety constraints throughout their operation.