arXiv:2402.08062v5 Announce Type: replace-cross Abstract: Most learning algorithms with formal regret guarantees assume that all mistakes are recoverable and essentially rely on trying all possible behaviors. This approach is problematic when some mistakes are "catastrophic", i.e., irreparable. We propose an online learning problem where the goal is to minimize the chance of catastrophe. Specifically, we assume that the payoff in each round represents the chance of avoiding catastrophe in that round and try to maximize the product of payoffs (the overall chance of avoiding catastrophe) while allowing a limited number of queries to a mentor. We also assume that the agent can transfer knowledge between similar inputs. We first show that in general, any algorithm either queries the mentor at a linear rate or is nearly guaranteed to cause catastrophe. However, in settings where the mentor policy class is learnable in the standard online model, we provide an algorithm whose regret and rate of querying the mentor both approach 0 as the time horizon grows. Although our focus is the product of payoffs, we provide matching bounds for the typical additive regret. Conceptually, if a policy class is learnable in the absence of catastrophic risk, it is learnable in the presence of catastrophic risk if the agent can ask for help.