Certified Zero-Shot Transfer of Information-Bottleneck Policies

Compression is known to improve policy transfer, yet when and why a compressed policy transfers to a new task remains poorly understood. Current empirical approaches evaluate compressed policies on held-out environments, which reveals the outcome of a transfer but not its cause, while theoretical approaches either bound value changes from the two tasks without reference to the policy or relate compression to lost value within a single task. This work aims to understand when and why a policy compressed with the information bottleneck (IB) on a source task transfers to a target task. Given models of both tasks, we answer when with a sufficient condition for near-optimal target return, and why with its terms, each of which names one cause: compression on the source, representation shift, or disagreement between the tasks’ optimal policies. We evaluate the condition in two settings. On tabular grid-worlds, where the IB is solved exactly, it certifies 88.6% of the successful transfers across 13,200 configurations with no false certifications. On neural IB policies trained on MiniGrid images, where the learned representation can itself shift between tasks, it remains sound, and its terms separate failures caused by representation shift from those caused by task disagreement.