G-CoS: An Interpretable Gain-Cost Framework for User Satisfaction Estimation in Generative Information Retrieval

User satisfaction serves as a key indicator of search experience in Generative Information Retrieval (GenIR) systems, and its accurate estimation is essential for system optimization. Extensive research in traditional IR has established interaction signals (e.g., dwell time, clicks, query reformulations) as reliable indicators of user satisfaction. However, prevailing approaches for satisfaction estimation in GenIR (e.g., LLM-as-a-judge) primarily rely on textual content and fail to account for user interactions during the search process. In this work, empirical analysis of real-world data shows that user satisfaction correlates negatively with interaction signals reflecting interaction cost, and positively with response quality. Building on these findings, we propose the Gain-aware Cost-sensitive Satisfaction estimator (G-CoS), an interpretable gain-cost framework for user satisfaction estimation in GenIR. G-CoS models user satisfaction as a dynamic trade-off between Response Quality and multidimensional Interaction Cost. Experimental results demonstrate that G-CoS outperforms LLM-as-a-judge methods, interaction sequence models, as well as machine learning models using the same gain and cost features. Moreover, the learned parameters reveal interpretable associations between gain-cost dynamics and user satisfaction. This work contributes an interpretable framework for user satisfaction estimation and offers insights for GenIR system optimization.