Reading is not Reasoning: Bridging the Agentic Policy Gap in Vision-Text Compression

Multi-step language-model agents repeatedly process growing interaction histories, leading to substantial context costs. Vision--text compression reduces these costs by rendering history as images, but the resulting modality shift creates a marked capability gap. Through controlled evaluations of history recovery, matched-state decisions, and complete trajectories, we show that this gap cannot be explained by OCR quality alone. Visual-history agents exhibit systematic drift in action selection, query formulation, stopping, and evidence use, revealing an agentic policy gap. We introduce \textbf{CAPS}, a two-stage \textbf{C}ross-modal \textbf{A}gentic \textbf{P}olicy \textbf{S}elf-distillation framework that uses the same model's stronger text-history policy to supervise its visual-history counterpart. Offline trajectory self-distillation transfers successful text-policy behavior to visual-history inputs, while online policy self-distillation provides dense supervision on states visited by the visual-history policy during reinforcement learning. On SearchQA, CAPS improves over AgentOCR by 5.0\% and 3.4\% with 3B and 7B backbones, respectively. On full-history ALFWorld, the corresponding gains are 15.6\% and 14.5\%. Across settings, CAPS reduces average memory-context cost by up to 63.3\% and peak cost by up to 83.4\% relative to matched text-history policies. These results show that explicit cross-modal policy self-distillation can preserve agent capability under vision--text compression. Our code will be made publicly available in a future release.