SAIL: Learning What to Personalize from Sparse GUI Interaction History

Sparse interaction history is an ambiguous basis for personalization because observed actions may reflect the task, interface, or temporary context rather than transferable user tendencies. We introduce SAIL, a population relative framework for cold start GUI agents that compares historical behavior with plausible alternatives in the same context. SAIL aggregates these deviations into a compact probabilistic user state and applies query conditioned residual corrections to Population predictions. On FingerTip 20K, SAIL improves User Macro Sim1 by 7.48 points on average over the strongest prior history baselines and retains a 1.61 point average gain under a strict control matched for observable support, active capacity, and training budget. It also reaches 43.25% GUI execution success and retains personalization gains on held out users and Persona2Web. Controlled behavioral and adverse history tests show that task relevance alone does not determine history value: transferable user conditioned patterns help, while forced, misleading, or wrong user histories can still cause negative transfer. Overall, population relative modeling provides an effective way to extract transferable user information from sparse GUI interaction history.