Reward Constrained Policy Optimization (1805.11074v3)

Abstract: Solving tasks in Reinforcement Learning is no easy feat. As the goal of the agent is to maximize the accumulated reward, it often learns to exploit loopholes and misspecifications in the reward signal resulting in unwanted behavior. While constraints may solve this issue, there is no closed form solution for general constraints. In this work we present a novel multi-timescale approach for constrained policy optimization, called `Reward Constrained Policy Optimization' (RCPO), which uses an alternative penalty signal to guide the policy towards a constraint satisfying one. We prove the convergence of our approach and provide empirical evidence of its ability to train constraint satisfying policies.

• The paper introduces RCPO, a multi-timescale algorithm that incorporates adaptive penalty signals into the reward function to enforce constraints in reinforcement learning.
• It leverages actor-critic methods and temporal-difference learning to guarantee convergence and improve sample efficiency in varied simulated environments.
• Empirical evaluations demonstrate that RCPO outperforms traditional methods by reducing hyperparameter tuning and achieving consistent performance across grid-world and robotic simulations.

Reward Constrained Policy Optimization: An Overview

The paper, "Reward Constrained Policy Optimization," by Tessler, Mankowitz, and Mannor, introduces a novel approach to tackling the inherent challenges in Reinforcement Learning (RL) when dealing with constraints. The core issue addressed by the authors is the tendency of RL agents to exploit loopholes in the reward signal, leading to undesired behaviors. Though constraints can mitigate these unintended behaviors, the absence of a closed-form solution for general constraints presents a significant hurdle.

Core Contributions

The authors propose Reward Constrained Policy Optimization (RCPO), a multi-timescale algorithm designed to guide policy optimization such that constraints are satisfied. This approach incorporates a penalty signal into the reward function, directing the policy towards compliance with the constraint. The authors provide convergence proofs and demonstrate the empirical effectiveness of RCPO in training constraint-satisfying policies.

Theoretical Foundations

The paper establishes solid theoretical underpinnings for RCPO, leveraging well-defined constructs in Markov Decision Processes (MDPs) and Constrained MDPs (CMDPs). The introduction of a penalized reward function enables the use of actor-critic methods, allowing the estimation of value functions using Temporal-Difference (TD) learning, which is critical for the algorithm's efficiency.

The authors make several assumptions that secure the convergence of RCPO, such as the boundedness of the value function and the existence of locally feasible policies. Notably, they extend these to accommodate general constraints, which distinguishes RCPO from conventional methods that are limited to recursive BeLLMan equation-satisfying constraints.

Empirical Evaluation

RCPO's effectiveness is validated through experiments in both grid-world environments and more complex six-domain robotic simulations using Mujoco. The authors evidence that RCPO consistently outperforms traditional constraint handling techniques, particularly demonstrating superior sample efficiency and stability.

One of the notable empirical results is the comparison with the reward shaping approach. By automating the adjustment of penalty coefficients, RCPO mitigates the time-consuming and computationally intensive process of hyper-parameter tuning often encountered in reinforcement learning applications.

Key Findings

The experimental results showcase RCPO's ability to adaptively and efficiently guide policies to satisfy constraints while avoiding the pitfalls of fixed penalty coefficients, which may lead to sub-optimal solutions. The authors demonstrate that traditional methods like direct Lagrange multipliers and fixed penalty coefficients are domain-dependent and often result in inconsistent performance across tasks.

Implications and Future Directions

RCPO opens new avenues for effectively incorporating constraints into reinforcement learning frameworks. The ability to handle general constraints without predefined penalty coefficients not only simplifies the training process but also offers broader applicability across different RL domains.

Looking forward, possible extensions of this work could include integration with existing techniques like Constrained Policy Optimization (CPO) to develop hybrid algorithms that maintain feasibility guarantees during training. Additionally, further research could explore RCPO's applicability to more complex multi-agent environments and its performance under varying numbers of constraints.

In summary, RCPO presents a robust, theoretically-founded, and empirically validated approach to constrained reinforcement learning. It represents a meaningful advancement in policy optimization, suggesting practical improvements in various real-world applications requiring adherence to behavioral constraints.