What to Ask, When to Route: Value-Guided Skill Routing under Joint Task–Profile Uncertainty

Skill routing for LLM-based agents is typically performed from a single observed request, implicitly assuming that the available information is sufficient to identify the appropriate skill. In practice, the intended task, relevant user profile conditions, or both may be underspecified, making one-shot routing unreliable. We formulate personalized skill routing under joint task–profile uncertainty as a sequential clarify-or-route problem and propose VISTA, a training-free framework for resolving such decision-relevant uncertainty. VISTA identifies candidate-distinguishing task and profile factors, constructs a compact candidate-conditioned joint belief over plausible routing states, and evaluates task clarification, profile clarification, and immediate routing under a shared downstream utility. Based on this belief, value-of-information criteria determine whether clarification is worthwhile and which question offers the greatest expected routing benefit. We further construct a controlled counterfactual benchmark seeded by real user queries and profiles, comprising 213 cases and 2,160 simulated interactive episodes across task-only, profile-only, and joint ambiguity. The benchmark also includes explicit clarification-stopping controls and independent human validation. Experiments on two base LLMs show that VISTA improves cost-aware routing performance by 13.8% on average over interactive baselines while reducing clarification turns by 40.1%.