Constrained Policy Optimization (1705.10528v1)

Abstract: For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact with or around humans should satisfy safety constraints. Recent advances in policy search algorithms (Mnih et al., 2016, Schulman et al., 2015, Lillicrap et al., 2016, Levine et al., 2016) have enabled new capabilities in high-dimensional control, but do not consider the constrained setting. We propose Constrained Policy Optimization (CPO), the first general-purpose policy search algorithm for constrained reinforcement learning with guarantees for near-constraint satisfaction at each iteration. Our method allows us to train neural network policies for high-dimensional control while making guarantees about policy behavior all throughout training. Our guarantees are based on a new theoretical result, which is of independent interest: we prove a bound relating the expected returns of two policies to an average divergence between them. We demonstrate the effectiveness of our approach on simulated robot locomotion tasks where the agent must satisfy constraints motivated by safety.

Constrained Policy Optimization: Bridging Safety and Performance in Reinforcement Learning

The paper "Constrained Policy Optimization" by Joshua Achiam, David Held, Aviv Tamar, and Pieter Abbeel presents a novel approach to reinforcement learning (RL) tailored for environments where strict behavioral constraints must be enforced. The authors introduce Constrained Policy Optimization (CPO), which pioneers integrating safety constraints directly into the learning algorithm, thereby extending the usability of RL in real-world applications where safety is paramount.

Overview of the Approach

Traditional policy search algorithms in RL focus solely on maximizing expected return, often assuming unconstrained exploration. However, this paradigm is not viable in many practical scenarios, such as robotics or autonomous driving, where unsafe actions during the learning phase can lead to catastrophic outcomes. This paper addresses this limitation by embedding constraints within the iterative policy optimization process.

The authors formulate the constrained reinforcement learning problem using Constrained Markov Decision Processes (CMDPs). They propose a policy search method that provably ensures near-constraint satisfaction at each iteration, leveraging a trust-region optimization approach. The core innovation of CPO is its ability to guarantee that policy updates will respect predefined constraints, such as safety limits, while still improving the expected reward.

Theoretical Contributions

One of the notable theoretical contributions of this work is a new performance bound that relates the difference in expected returns between two policies to the average divergence between them. This bound tightens previously known results for policy search using trust regions and forms the theoretical backbone of CPO.

The main theorem presented shows that the difference in performance between two policies, $\pi'$ and $\pi$, can be bounded by a term involving the KL divergence between the policies. This allows the authors to propose a trust-region method where the surrogate objective and constraints can be reliably estimated from samples, bypassing the need for off-policy evaluation.

Algorithmic Implementation

CPO is implemented by approximating the constrained policy update using linear and quadratic approximations to the objective and constraints. The update rule is derived through a dual optimization problem, where the dual variables are computed to enforce constraint satisfaction strictly. This dual-based approach ensures that every policy update generated by CPO respects the safety constraints, which sets it apart from primal-dual methods that only guarantee constraint satisfaction asymptotically.

To handle high-dimensional policy spaces, such as those represented by neural networks, the authors leverage the conjugate gradient method for computing needed matrix-vector products without explicit matrix inversion, making CPO computationally feasible for large-scale problems.

Experimental Evaluation

The effectiveness of CPO is demonstrated through experiments on high-dimensional simulated robot locomotion tasks, including variations of robotic control environments with safety constraints. The results show that CPO successfully trains neural network policies that satisfy constraints throughout training while maximizing reward. The experiments include comparisons with primal-dual optimization (PDO) methods, where CPO consistently outperforms PDO in enforcing constraints, keeping constraint violations significantly low without compromising on the performance in return.

Implications and Future Directions

The implications of this research are substantial for the field of RL, particularly for applications requiring safe interactions. The ability to integrate and enforce safety constraints during the training phase expands the applicability of RL to areas such as autonomous vehicle navigation, robotic surgery, and industrial automation, where ensuring operational safety alongside learning efficiency is critical.

Future developments might explore extensions of CPO to handle non-linear constraints and more complex safety definitions. Additionally, integrating CPO with other advances in deep RL, such as model-based planning and hierarchical RL, could further improve its scalability and efficiency. The robustness of CPO in real-world deployment could be studied, including its adaptability to dynamic environments where constraints may evolve over time.

In conclusion, "Constrained Policy Optimization" offers a significant step towards realizing safer RL algorithms capable of operating within stringent safety requirements. It provides a foundation for more reliable and practical AI systems that can safely learn and adapt within the constraints of real-world environments.