This paper introduces the Lagrange Policy for Continuous Actions (LPCA), a reinforcement learning algorithm specifically designed for weakly coupled MDP problems with continuous action spaces. LPCA addresses the challenge of resource constraints dependent on continuous actions by introducing a Lagrange relaxation of the weakly coupled MDP problem within a neural network framework for Q-value computation. This approach effectively decouples the MDP, enabling efficient policy learning in resource-constrained environments. We present two variations of LPCA: LPCA-DE, which utilizes differential evolution for global optimization, and LPCA-Greedy, a method that incrementally and greadily selects actions based on Q-value gradients. Comparative analysis against other state-of-the-art techniques across various settings highlight LPCA's robustness and efficiency in managing resource allocation while maximizing rewards.

翻译：本文提出面向连续动作的拉格朗日策略（LPCA），一种专为连续动作空间中的弱耦合马尔可夫决策过程（MDP）问题设计的强化学习算法。LPCA通过引入弱耦合MDP问题的拉格朗日松弛，并在神经网络框架内进行Q值计算，解决了依赖连续动作的资源约束挑战。该方法有效解耦了MDP，使得在资源受限环境中能够进行高效策略学习。我们提出LPCA的两种变体：采用差分进化进行全局优化的LPCA-DE，以及基于Q值梯度逐步贪心选择动作的LPCA-Greedy方法。与多种场景下其他先进技术的对比分析表明，LPCA在管理资源分配并最大化奖励方面具有鲁棒性和高效性。