We consider the problem of designing policies for Markov decision processes
(MDPs) with dynamic coherent risk objectives and constraints. We begin by
formulating the problem in a Lagrangian framework. Under the assumption that
the risk objectives and constraints can be represented by a Markov risk
transition mapping, we propose an optimization-based method to synthesize
Markovian policies that lower-bound the constrained risk-averse problem. We
demonstrate that the formulated optimization problems are in the form of
difference convex programs (DCPs) and can be solved by the disciplined
convex-concave programming (DCCP) framework. We show that these results
generalize linear programs for constrained MDPs with total discounted expected
costs and constraints. Finally, we illustrate the effectiveness of the proposed
method with numerical experiments on a rover navigation problem involving
conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent
risk measures.

该研究旨在设计面向具有动态一致风险目标和约束的马尔可夫决策过程的策略。作者提出了一个基于优化的方法来综合最小化受约束的风险 - 厌恶问题的可行马尔可夫策略，并通过数值实验验证了该方法的有效性。