  The emergence of pre-trained AI systems with powerful capabilities across a
diverse and ever-increasing set of complex domains has raised a critical
challenge for AI safety as tasks can become too complicated for humans to judge
directly. Irving et al. [2018] proposed a debate method in this direction with
the goal of pitting the power of such AI models against each other until the
problem of identifying (mis)-alignment is broken down into a manageable
subtask. While the promise of this approach is clear, the original framework
was based on the assumption that the honest strategy is able to simulate
deterministic AI systems for an exponential number of steps, limiting its
applicability. In this paper, we show how to address these challenges by
designing a new set of debate protocols where the honest strategy can always
succeed using a simulation of a polynomial number of steps, whilst being able
to verify the alignment of stochastic AI systems, even when the dishonest
strategy is allowed to use exponentially many simulation steps.
