We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able to flip a decision made by the agent. Such a disturbance may, for instance, occur when the intended action of the agent cannot be executed due to a malfunction of an actuator in the environment. In this work, we introduce the concept of resilience in the stochastic setting and present a comprehensive set of fundamental problems. Specifically, we discuss such problems for Markov decision processes with reachability and safety objectives, which also smoothly extend to stochastic games. To account for the stochastic setting, we provide various ways of aggregating the amounts of disturbances that may have occurred, for instance, in expectation or in the worst case. Moreover, to reason about infinite disturbances, we use quantitative measures, like their frequency of occurrence.

翻译：本研究探讨不确定性环境下的弹性策略问题。弹性策略使智能体能够做出对扰动具有鲁棒性的决策。我们特别关注那些能够翻转智能体决策的扰动类型，例如当智能体预期动作因环境中执行器故障而无法实施时可能发生的扰动。本文在随机环境中引入弹性概念，并提出一系列基础性问题。具体而言，我们针对具有可达性与安全性目标的马尔可夫决策过程展开讨论，这些讨论可自然延伸至随机博弈场景。为适应随机环境特性，我们提供了多种扰动量的聚合方法，例如基于期望值或最坏情况的度量方式。此外，为处理无限扰动情形，我们采用量化指标（如扰动发生频率）进行分析。