Autonomous systems are increasingly used in highly variable and uncertain environments giving rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper first develops a sample-based method to upper bound the risk measure evaluation of a random variable whose distribution is unknown. These bounds permit us to generate high-confidence verification statements for a large class of robotic systems in a sample-efficient manner. Second, we develop a sample-based method to determine solutions to non-convex optimization problems that outperform a large fraction of the decision space of possible solutions. Both sample-based approaches then permit us to rapidly synthesize risk-aware policies that are guaranteed to achieve a minimum level of system performance. To showcase our approach in simulation, we verify a cooperative multi-agent system and develop a risk-aware controller that outperforms the system's baseline controller. Our approach can be extended to account for any g-entropic risk measure.

中文翻译：

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基于样本的连贯风险度量界限：在政策综合和验证中的应用


自主系统越来越多地用于高度可变和不确定的环境中，因此迫切需要在这些系统的策略的综合和验证中考虑风险。本文首先开发了一种基于样本的方法来对分布未知的随机变量的风险度量评估进行上限。这些界限使我们能够以样本有效的方式为一大类机器人系统生成高可信度的验证语句。其次，我们开发了一种基于样本的方法来确定非凸优化问题的解决方案，其性能优于大部分可能解决方案的决策空间。两种基于样本的方法都允许我们快速综合风险意识策略，以保证实现最低水平的系统性能。为了展示我们的模拟方法，我们验证了一个协作多智能体系统，并开发了一个优于系统基线控制器的风险感知控制器。我们的方法可以扩展到解释任何 g 熵风险度量。