Multimodal web agents that process both screenshots and accessibility trees are increasingly deployed to interact with web interfaces, yet their dual-stream architecture opens an underexplored attack surface: an adversary who injects content into the webpage DOM simultaneously corrupts both observation channels with a consistent deceptive narrative. Our vulnerability analysis on MiniWob++ reveals that attacks including a visual component far outperform text-only injections, exposing critical gaps in text-centric VLM safety training. Motivated by this finding, we propose Dual-Modality Multi-Stage Adversarial Safety Training (DMAST), a framework that formalizes the agent-attacker interaction as a two-player zero-sum Markov game and co-trains both players through a three-stage pipeline: (1) imitation learning from a strong teacher model, (2) oracle-guided supervised fine-tuning that uses a novel zero-acknowledgment strategy to instill task-focused reasoning under adversarial noise, and (3) adversarial reinforcement learning via Group Relative Policy Optimization (GRPO) self-play. On out-of-distribution tasks, DMAST substantially mitigates adversarial risks while simultaneously doubling task completion efficiency. Our approach significantly outperforms established training-based and prompt-based defenses, demonstrating genuine co-evolutionary progress and robust generalization to complex, unseen environments.

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