Avoiding Catastrophe in Continuous Spaces by Asking for Help

Most reinforcement learning algorithms with formal regret guarantees assume all mistakes are reversible and rely on essentially trying all possible options. This approach leads to poor outcomes when some mistakes are irreparable or even catastrophic. We propose a variant of the contextual bandit problem where the goal is to minimize the chance of catastrophe. Specifically, we assume that the payoff each round represents the chance of avoiding catastrophe that round, and try to maximize the product of payoffs (the overall chance of avoiding catastrophe). To give the agent some chance of success, we allow a limited number of queries to a mentor and assume a Lipschitz continuous payoff function. We present an algorithm whose regret and rate of querying the mentor both approach 0 as the time horizon grows, assuming a continuous 1D state space and a relatively "simple" payoff function. We also provide a matching lower bound: without the simplicity assumption: any algorithm either constantly asks for help or is nearly guaranteed to cause catastrophe. Finally, we identify the key obstacle to generalizing our algorithm to a multi-dimensional state space.