This paper proposes and analyzes two new policy learning methods: regularized policy gradient (RPG) and iterative policy optimization (IPO), for a class of discounted linear-quadratic control (LQC) problems over an infinite time horizon with entropy regularization. Assuming access to the exact policy evaluation, both proposed approaches are proven to converge linearly in finding optimal policies of the regularized LQC. Moreover, the IPO method can achieve a super-linear convergence rate once it enters a local region around the optimal policy. Finally, when the optimal policy for an RL problem with a known environment is appropriately transferred as the initial policy to an RL problem with an unknown environment, the IPO method is shown to enable a super-linear convergence rate if the two environments are sufficiently close. Performances of these proposed algorithms are supported by numerical examples.

翻译：本文针对无限时域上带熵正则化的一类折扣线性二次型控制(LQC)问题，提出并分析了两种新的策略学习方法：正则化策略梯度(RPG)和迭代策略优化(IPO)。假设可以获取精确的策略评估，两种方法均被证明在线性收敛速度下找到正则化LQC的最优策略。此外，IPO方法在进入最优策略邻域后能够实现超线性收敛速度。最后，当已知环境下的强化学习问题的最优策略被适当地迁移作为未知环境下的强化学习问题的初始策略时，若两种环境足够接近，IPO方法可实现超线性收敛速率。数值实验验证了所提算法的性能。