In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we first derive a formula for computing the gradient of the Lagrangian function for percentile risk-constrained MDPs. Then, we devise policy gradient and actor-critic algorithms that (1) estimate such gradient, (2) update the policy parameters in the descent direction, and (3) update the Lagrange multiplier in the ascent direction. For these algorithms we prove convergence to locally-optimal policies. Finally, we demonstrate the effectiveness of our algorithms in an optimal stopping problem and an online marketing application.

本文研究利用概率风险约束的马尔可夫决策过程，通过计算梯度并设计算法实现了局部最优策略，解决了累积成本最小化的顺序决策问题，例子包括最优停止问题和在线营销应用。

具有分位风险标准的风险受限强化学习