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arXiv 1801.03326stat.MLcs.AI
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强化学习的期望策略变量

Expected Policy Gradients for Reinforcement Learning

Microsoft Research Cambridge(微软研究院剑桥分院);University of Oxford(牛津大学)

Kamil Ciosek, Shimon Whiteson

摘要:

我们提出了预期策略梯度(EPG),它统一了强化学习的随机策略梯度(SPG)和确定性策略梯度(DPG)。受预期Sarsa的启发,EPG在估计梯度时对动作进行积分(或求和),而不是仅依赖于采样轨迹中的动作。对于连续的行动空间,我们首先得到一个实际的结果,高斯政策和二次批评,然后将其扩展到一个普遍的分析方法,涵盖了广泛的一类演员和批评,包括高斯,指数家庭,并与有界支持的政策。对于高斯策略,我们引入了一种探索方法,该方法使用与评论家的缩放Hessian矩阵指数成比例的协方差。对于离散的动作空间,我们推导出一个基于softmax策略的EPG变体。我们还建立了一个新的一般策略梯度定理,其中随机策略梯度定理和确定性策略梯度定理是其特例。此外,我们证明了EPG降低了梯度估计的方差,而不需要确定性的政策,并具有很小的计算开销。最后,我们提供了一个广泛的EPG实验评估,并表明它优于现有的方法在多个具有挑战性的控制域。

英文摘要:

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains.

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