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Reinforcement learners are agents that learn to pick actions that lead tohigh reward. Ideally, the value of a reinforcement learner's policy approachesoptimality--where the optimal informed policy is the one which maximizesreward. Unfortunately, we show that if an agent is guaranteed to be"asymptotically optimal" in any (stochastically computable) environment, thensubject to an assumption about the true environment, this agent will be either"destroyed" or "incapacitated" with probability 1. Much work in reinforcementlearning uses an ergodicity assumption to avoid this problem. Often, doingtheoretical research under simplifying assumptions prepares us to providepractical solutions even in the absence of those assumptions, but theergodicity assumption in reinforcement learning may have led us entirely astrayin preparing safe and effective exploration strategies for agents in dangerousenvironments. Rather than assuming away the problem, we present an agent,Mentee, with the modest guarantee of approaching the performance of a mentor,doing safe exploration instead of reckless exploration. Critically, Mentee'sexploration probability depends on the expected information gain fromexploring. In a simple non-ergodic environment with a weak mentor, we findMentee outperforms existing asymptotically optimal agents and its mentor.

Curiosity Killed or Incapacitated the Cat and the Asymptotically Optimal Agent