Risk averse decision making under uncertainty in partially observable domains
is a fundamental problem in AI and essential for reliable autonomous agents. In
our case, the problem is modeled using partially observable Markov decision
processes (POMDPs), when the value function is the conditional value at risk
(CVaR) of the return. Calculating an optimal solution for POMDPs is
computationally intractable in general. In this work we develop a
simplification framework to speedup the evaluation of the value function, while
providing performance guarantees. We consider as simplification a
computationally cheaper belief-MDP transition model, that can correspond, e.g.,
to cheaper observation or transition models. Our contributions include general
bounds for CVaR that allow bounding the CVaR of a random variable X, using a
random variable Y, by assuming bounds between their cumulative distributions.
We then derive bounds for the CVaR value function in a POMDP setting, and show
how to bound the value function using the computationally cheaper belief-MDP
transition model and without accessing the computationally expensive model in
real-time. Then, we provide theoretical performance guarantees for the
estimated bounds. Our results apply for a general simplification of a
belief-MDP transition model and support simplification of both the observation
and state transition models simultaneously.

在部分可观察域中，面临不确定性的风险规避决策是人工智能领域的一个基本问题，对于可靠的自主代理至关重要。本研究使用部分可观察的马尔可夫决策过程（POMDPs）建模并采用回报的条件风险价值（CVaR）作为值函数。这项工作开发了一个简化框架，以加快值函数的评估速度，并提供性能保证。我们考虑了一种计算代价更低的信念 - MDP 转移模型作为简化方法，该模型可以对应于更廉价的观察或转移模型。我们的贡献包括一般的 CVaR 界限，通过假设两个累积分布之间的界限，可以使用一个随机变量 Y 来限制随机变量 X 的 CVaR。然后，我们推导出 POMDP 设置下 CVaR 值函数的界限，并展示了如何使用计算代价更低的信念 - MDP 转移模型来限制值函数，而无需实时访问计算代价高昂的模型。接着，我们提供了对估计边界的理论性能保证。我们的结果适用于对信念 - MDP 转移模型的一般简化，并可以同时简化观察和状态转移模型。