WebRouter: Query-specific Router via Variational Information Bottleneck for Cost-sensitive Web Agent

LLM-brained web agents offer powerful capabilities for web automation but face a critical cost-performance trade-off. The challenge is amplified by web agents' inherently complex prompts that include goals, action histories, and environmental states, leading to degraded LLM ensemble performance. To address this, we introduce WebRouter, a novel query-specific router trained from an information-theoretic perspective. Our core contribution is a cost-aware Variational Information Bottleneck (ca-VIB) objective, which learns a compressed representation of the input prompt while explicitly penalizing the expected operational cost. Experiments on five real-world websites from the WebVoyager benchmark show that WebRouter reduces operational costs by a striking 87.8\% compared to a GPT-4o baseline, while incurring only a 3.8\% accuracy drop.