In reinforcement learning, agents learn by performing actions and observing their outcomes. Sometimes, it is desirable for a human operator to textit{interrupt} an agent in order to prevent dangerous situations from happening. Yet, as part of their learning process, agents may link these interruptions, that impact their reward, to specific states and deliberately avoid them. The situation is particularly challenging in a multi-agent context because agents might not only learn from their own past interruptions, but also from those of other agents. Orseau and Armstrong defined emph{safe interruptibility} for one learner, but their work does not naturally extend to multi-agent systems. This paper introduces textit{dynamic safe interruptibility}, an alternative definition more suited to decentralized learning problems, and studies this notion in two learning frameworks: textit{joint action learners} and textit{independent learners}. We give realistic sufficient conditions on the learning algorithm to enable dynamic safe interruptibility in the case of joint action learners, yet show that these conditions are not sufficient for independent learners. We show however that if agents can detect interruptions, it is possible to prune the observations to ensure dynamic safe interruptibility even for independent learners.
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