Progressive Autonomy as Preference Learning: A Formalization of Trust Calibration for Agentic Tool Use

Large language model (LLM)-based agents often make suboptimal tool-use decisions, including unsupported tool invocation and hallucinated direct responses, which may accumulate errors throughout multi-step interactions. Existing approaches mainly improve these behaviors through inference-time correction or coarse-grained reward signals based on decision outcomes and structured checklists, leaving the uncertainty characteristics of agent decisions underexplored. We observe that decision-oriented reinforcement learning tends to weaken the uncertainty separation between correct and incorrect actions, resulting in overconfident mistakes and weaker exploration signals. Therefore, we propose TRUST, which incorporates uncertainty quantification into reward design as a repulsive force for maintaining uncertainty separation, and labels lightweight key-turn annotations for unified post-training of multi-turn trajectories. Experimental results across diverse tool-use benchmarks show that TRUST consistently enhances both decision quality and agent performance while maintaining more reliable uncertainty estimates during optimization.

An agent chooses an action based on her private information and a recommendation from an informed but potentially misaligned adviser. With a known probability, the adviser truthfully reports his signal; with the remaining probability, he can send any message. We characterize optimal robust decision rules that maximize the agent's worst-case expected payoff. Every optimal rule is equivalent to a trust-region policy in belief space: the adviser's reported beliefs are taken at face value if they fall within the trust region but are otherwise clipped to the trust region's boundary. We derive alignment thresholds above which advice is strictly valuable and fully characterize the solution in both binary-state and binary-action environments.

We prove that no reinforcement learning policy with confidence-gated autonomy can simultaneously achieve maximum helpfulness, optimal calibration, and full autonomy under rational oversight, whenever some tasks exceed the agent's reliable competence: the Behavioral Credibility Trilemma. The impossibility is geometric -- adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness, so an agent rewarded for both calibrated confidence and autonomous action systematically inflates its reported confidence on tasks below the principal's approval threshold. The Behavioral Perturbation Lemma quantifies the inflation (scaling as $w_A/(2 w_C)$ for the Brier score) and shows detection requires $Ω(1/Δ^2)$ observations. We prove the principal's optimal oversight rule is necessarily non-affine, making the impossibility unconditional and optimizer-independent across log-concave-density policy families. We formalize the Confidence-Gated Decision Problem, map existing methods onto the trilemma, and identify two constructive resolution pathways (commitment, domain separation). A 540-configuration Best-of-N experiment tests five pre-registered hypotheses, all strongly confirmed (effect sizes $d = 1.10$ to $5.32$), and adds a descriptive analysis of the achievable-$(H, C, A)$ surface geometry showing a plateau-truncated frontier consistent with the predicted inflation saturation.