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Uncertainty Quantification in LLM Agents: Foundations, Emerging Challenges, and Opportunities

Changdae Oh, Seongheon Park, To Eun Kim, Jiatong Li, Wendi Li, Samuel Yeh, Xuefeng Du, Hamed Hassani, Paul Bogdan, Dawn Song, Sharon Li

arXiv:2602.05073v3cs.AI

TL;DR

LLM uncertainty quantification remains focused largely on single-turn or non-interactive settings, despite agents making consequential decisions across multi-turn trajectories. This paper introduces a general agent-UQ formulation, identifies four technical challenges, and outlines applications and open problems for uncertainty-aware agentic systems.

  • Problem

    Most existing LLM UQ research treats static, isolated systems, whereas agents interact across trajectories and can make costly or irreversible decisions.

  • Method

    The paper models agent problem solving as a stochastic trajectory over actions, observations, and environment states, defining turn-level and trajectory-level uncertainty.

  • Results

    The formulation casts many prior UQ problems as special cases and identifies four technical challenges specific to agentic setups.

  • Takeaways & Limitations

    The paper presents agent UQ as a foundation and clearer direction for future uncertainty-aware, reliable agentic systems.

  • Takeaways & Limitations

    The formulation may not properly abstract settings with unreliable or adversarial observations and stochastically evolving environments.

Abstract

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Uncertainty quantification (UQ) for large language models (LLMs) is a key building block for safety guardrails of daily LLM applications. Yet, even as LLM agents are increasingly deployed in highly complex tasks, most UQ research still centers on single-turn question-answering. We argue that UQ research must shift to realistic settings with interactive agents, and that a new principled framework for agent UQ is needed. This paper presents three pillars to build a solid ground for future agent UQ research: (1. Foundations) We present the first general formulation of agent UQ that subsumes broad classes of existing UQ setups; (2. Challenges) We identify four technical challenges specifically tied to agentic setups -- selection of uncertainty estimator, uncertainty of heterogeneous entities, modeling uncertainty dynamics in interactive systems, and lack of fine-grained benchmarks -- with numerical analysis on a real-world agent benchmark, $τ^2$-bench; (3. Future Directions) We conclude with noting on the practical implications of agent UQ and remaining open problems as forward-looking discussion for future explorations.

1. Introduction

Agent UQ extends uncertainty estimation from isolated answers and reasoning chains to interactive, multi-turn trajectories with users, tools, and environments. The paper formalizes this shift, identifies four agent-specific challenges, and discusses applications and open problems for reliable systems.

  • Motivation: Open-world agents can make costly or irreversible decisions, so they must assess failure likelihood before acting.Failures can also arise from premature action, unresolved ambiguity, or errors propagated across long trajectories.
  • Motivation: Most existing LLM UQ studies static, isolated systems after a single prompt, treating uncertainty as point-wise estimation or one-directional propagation.This setup assumes no new information arrives after the initial prompt.
  • Motivation: Agent UQ instead models continual interaction with users and environments, where information-seeking actions can resolve ambiguity and reduce uncertainty before execution.A flight-booking agent may ask about dates, budget, or layovers, then query databases before finalizing a reservation.
  • Contributions: The paper formulates agent UQ as uncertainty dynamics over stochastic actions, observations, and environment states across interactive trajectories.The formulation defines turn-level and trajectory-level uncertainty and casts many prior UQ problems as special cases.
  • Contributions: Four challenges are identified: estimator selection, heterogeneous-entity uncertainty, interactive uncertainty dynamics, and scarce fine-grained benchmarks.The paper reports numerical analysis on the real-world τ^2-bench and frames these challenges as directions for community action.
  • Future directions: The paper discusses practical implications across healthcare, software engineering, and robotics, alongside adaptive reasoning, post-training, and open problems.Its stated aim is to provide a foundation and clearer direction for uncertainty-aware, reliable agentic systems.

2. Related Work

LLM UQ research addresses free-form outputs through probability, consistency, and verbalized-confidence methods, while newer work extends uncertainty estimation into reasoning and interactive inference. These approaches motivate agent UQ but do not by themselves establish the paper’s proposed framework.

  • LLM UQ: LLM UQ commonly aggregates token probabilities, measures consistency across generations, or elicits verbalized confidence for free-form outputs.These approaches address challenges beyond classical machine-learning UQ, including computational cost and unconstrained outputs.
  • Reasoning and agent setups: Reasoning UQ measures confidence during multi-step reasoning and uses uncertainty information to improve responses or guide inference and training.Recent work also begins modeling uncertainty in interactive or agentic inference.

3. A General Formulation for Agent UQ

The paper models an agent as a stochastic, partially observed, multi-turn process over actions, observations, and environment states, then defines uncertainty over individual turns and complete trajectories. This formulation unifies single-step UQ, reasoning UQ, and related process-reward views as special cases.

  • 3.1. Problem Statement and Definitions: Agent actions and observations are heterogeneous, including clarification, information seeking, API calls, database reports, tool results, and natural-language or structured messages.The flight-booking example illustrates how agents interact with users and tools while also planning or updating internally.
  • 3.1. Problem Statement and Definitions: The formulation generalizes existing agent benchmarks by representing problem solving as a trajectory of actions, observations, and environment states.The paper introduces a concrete agent-system definition and a graphical model for this trajectory.
  • 3.1. Problem Statement and Definitions: Each turn is generated from the preceding environment state and observation, while observations depend on the current action and state.The environment state transition is modeled with a deterministic update function in the simplified setting.
  • 3.1. Problem Statement and Definitions: Agent UQ estimates both turn-level uncertainty U(ℱ_t|ℱ_t−1) and trajectory-level uncertainty U(ℱ≤T) as joint total uncertainty.The framework treats uncertainty as a function of a random variable or its distribution.
  • 3.1. Problem Statement and Definitions: Information-theoretic uncertainty functions such as Shannon entropy and negative log probability support sequential modeling through the chain rule.The paper uses this property to expand total uncertainty across a trajectory, including initial query uncertainty and task-specification volatility.
  • 3.1. Problem Statement and Definitions: A calibrated agent’s joint trajectory uncertainty is intended to predict trajectory reward, commonly represented by a success-failure verifier.The desideratum links uncertainty estimates to outcomes without restricting the reward to a particular application.
  • 3.2. A Unified View on Existing UQ Setups: When there is one turn and responses are the only actions, the agent formulation reduces to conventional answer uncertainty, optionally including question ambiguity.Most existing single-step UQ focuses on U(A_1|O_0), while some work also considers U(O_0).
  • 3.2. A Unified View on Existing UQ Setups: For multi-step reasoning, alternative reductions aggregate step uncertainties by summation, the most uncertain step, or weighted schemes, and the framework connects these estimates to process rewards.The paper also relates multi-turn UQ to assigning credit to intermediate reasoning steps and aggregating step-level rewards.

4. Technical Challenges in Agent UQ

Agent UQ faces four challenges beyond single-turn uncertainty: choosing usable estimators, quantifying heterogeneous observations, modeling interactive uncertainty dynamics, and obtaining fine-grained benchmarks.

  • 4.1. Selection of Uncertainty Estimator: Probability-based methods require output probabilities, consistency-based methods impose repeated-generation costs, and verbalized confidence lacks theoretical grounding.These tradeoffs span accessibility, inference-time overhead, and theoretical grounding.
  • 4.1. Selection of Uncertainty Estimator: Agentic scaffolding makes estimator limitations more severe because frontier models may omit probabilities, long generations weaken token aggregation, and long-horizon consistency is prohibitively costly.Expanding context and noisy observations can also inflate and destabilize verbalized confidence; many methods perform close to random in success prediction.
  • 4.2. Uncertainty of Heterogeneous Entities: Observation uncertainty is difficult because user and tool outputs come from heterogeneous external distributions rather than the agent’s own epistemic distribution.Feeding observation strings into the agent does not trivially recover the underlying human-language or tool-outcome distributions.
  • 4.3. Modeling Uncertainty Dynamics in Interactive Systems: Interactive UQ must model both uncertainty propagation and information gained through actions, whereas action-independent averaging can fail to distinguish successful from failed trajectories.The paper illustrates this issue through uncertainty evolution across normalized trajectory turns on τ2-bench.
  • 4.4. Lack of Fine-grained Benchmarks: Fine-grained benchmarks remain scarce because long rollouts are expensive to annotate, frontier-model labeling is costly, and complex policies are difficult to understand.The survey covers 44 benchmarks and motivates scalable dataset-construction strategies for agentic inference.

5. Practical Implications

Agent UQ is presented as a practical basis for deploying reliable agents in healthcare, programming, and robotics, while also guiding adaptive reasoning and multi-turn reinforcement learning.

  • Overview: Agent UQ is framed as a prerequisite for deploying LLM agents in non-deterministic real environments, including healthcare, programming, and robotics.These implications are intended to motivate policymakers, practitioners, and researchers.
  • 5.1. Advancing Frontier LLMs: Uncertainty budgeting can guide adaptive reasoning through early stopping or interaction invoking, while directional and quantitative uncertainty can inform multi-turn reinforcement learning.The paper connects these uses to overthinking, efficiency, credit assignment, when-to-explore decisions, and information-pursuit policies.
  • 5.2. Reliable Clinical Decision Supporting Agents: In healthcare, accumulated uncertainty can trigger human review, support automation during low-uncertainty periods, and encourage further inquiry toward uncertainty reduction.This is proposed as a gatekeeper role for clinical agents that still exhibit residual error rates.
  • 5.3. Reliable Agentic Coders: For coding agents, uncertainty over bug-patch candidates can control evidence gathering, commitment, and user interaction before modifying production codebases.Uncertainty-triggered rollback and branching can mirror checkpoint-rollback workflows when uncertainty increases after an action.
  • 5.4. Reliable Embodied Agents: For embodied agents, uncertainty from sensing, dynamics, and human intent can motivate re-sensing or clarification before irreversible physical actions.The paper illustrates this with a robot retrieving a fragile object.

6. Open Problems

The paper identifies unresolved problems in agent UQ, including ambiguity about uncertainty sources, inadequate evaluation targets, and extensions to multi-agent and self-improving systems.

  • Intrinsic solution multiplicity: High per-step uncertainty may reflect insufficient knowledge or multiple valid actions, making its source difficult to identify.Complex agent tasks are not perfectly specified upfront, so intermediate steps can be intrinsically ambiguous.
  • Evaluation beyond task failure: Predicting eventual task failure alone is insufficient for evaluating uncertainty in agentic systems because it collapses structured problem solving into one scalar judgment.The paper calls for evaluation that preserves information about the agent’s intermediate process.
  • Uncertainty modeling in multi-agent systems: Agent UQ for multi-agent systems remains largely unexplored, despite existing work using collective intelligence to improve UQ in single-turn question answering.The proposed graphical model can extend to coupled agent trajectories with a shared environment state.
  • Uncertainty modeling in self-improving agents: Self-improving agents require uncertainty models that account for non-stationary tools, context memory, and model parameters across multiple episodes.The paper’s setup assumes operation within a single episode, whereas continual adaptation spans episodes.

7. Conclusion

The paper argues that UQ should target interactive, long-horizon agent episodes rather than only point-wise estimates. It establishes a general formulation, identifies four challenges, and discusses applications and open problems.

  • 7. Conclusion: Agentic inference requires shifting from point-wise uncertainty estimates to models of sequential uncertainty dynamics across interactive long-horizon episodes.The conclusion frames this as the central paradigm shift for realistic LLM UQ.
  • 7. Conclusion: The paper provides a general formulation that abstracts a wide variety of existing UQ approaches and identifies four challenges with numerical analyses.It also discusses real-world applications and open problems to guide future work.

Limitations

The formulation does not deeply model unreliable or adversarial observations in stochastic environments, limiting its abstraction for some real-world agent settings.

  • Limitations: The framework may be inadequate when agents receive unreliable or adversarial observations from tools, retrieval, or users.The paper suggests explicitly modeling uncertainty in the evidence stream for such environments.

Ethical Considerations

The paper presents agent UQ as a broad framework connected to several uncertainty measures and formal perspectives, while emphasizing misuse risks and the importance of interactivity.

  • Ethical Considerations: The framework could be misused to steer agents toward blind spots or manipulate uncertainty thresholds to bypass safety filters.The paper recommends limiting attack-enabling signals, red-teaming, and monitoring abuse.
  • B.1. Expression of Various Agentic Prompting under Our Formulation: The formulation represents agent trajectories through actions, observations, and environment states, and can express representative prompting methods under unified conditions.Examples include vanilla function calling, few-shot prompting, ReAct, and Reflexion.
  • Agent UQ formulation: Trajectory-level total uncertainty combines initial query, action, and observation uncertainty across multiple turns in additive form.The paper discusses information content, entropy, and relative entropy as example uncertainty measures.
  • C. Alternative Uncertainty Measures: Alternative measures such as Rényi entropy, Tsallis entropy, and informational energy may suit agent interfaces with long-range interactions, evolving memory, and multifractal structure.These alternatives extend beyond the three information-theoretic measures emphasized in the main discussion.
  • Related formal perspectives: Agent UQ can be related to probabilistic interactive Turing machines and POMDP belief tracking, but language actions and implicit beliefs challenge standard abstractions.These connections may provide formal tools while requiring adaptations to agent-specific settings.
  • D. Extended Context: Existing UQ can overlook interactivity even when reasoning and interaction trajectories differ in reward consequences.The paper recommends modeling interactivity and reducible uncertainty in agents.

E. Action-Conditional Uncertainty Dynamics Model

The paper proposes action-conditional uncertainty dynamics because interactive and evidential actions can reduce uncertainty, whereas other actions propagate it. Its prototype uses information gating, action classification, and uncertainty estimates for trajectory components.

  • Motivation: Existing multi-step UQ methods generally propagate step-level uncertainty without distinguishing action types, despite interactivity affecting agent rewards.The paper contrasts reasoning-oriented and interaction-oriented trajectories in which both may gather evidence, but interaction can achieve higher rewards.
  • Conditional uncertainty reduction process: The proposed conditional uncertainty reduction process models uncertainty as increasing or decreasing according to the agent’s interactivity at each step.Information gating is presented as one prototype implementation of this process.
  • Conditional uncertainty reduction process: The gating function reduces current-turn uncertainty for valid uncertainty-reduction actions and otherwise propagates uncertainty.The paper defines the gate over a set of valid reduction actions, 𝒜−.
  • Conditional uncertainty reduction process: Interactive and evidential actions produce negative information gain for uncertainty reduction; other actions continue uncertainty propagation.Interactive actions invite a user or tool, while evidential actions are factual or consistent with stored data.
  • Properties: The signed gate supports quantitative and directional uncertainty interpretations and permits closed-form analytic extrema for total uncertainty.The extrema are stated in Lemma 1.
  • Implementation considerations: Implementing the framework requires estimating initial-query, action, and observation uncertainty, with action uncertainty supported by sampling-, probability-, hybrid-, or verbalized-confidence methods.Observation and initial-query uncertainty are harder to estimate; alternatives include consistency methods, datastores, and world models.
  • Implementation considerations: The information-gating prototype also requires mutual-information estimation and compound action classification for interactivity and evidentiality.The paper supplies example prompts for classifying interactivity and evidential grounding.
  • Experimental setup: Experiments use GPT-4.1 and Kimi-K2.5 on τ2-bench, with temperature 0.0 and one trial per task because of resource constraints.The user simulator is fixed to Kimi-K2.5, while the agent model varies between GPT-4.1 and Kimi-K2.5.

F.2. Extended Results

Extended results examine observation-uncertainty estimation and uncertainty evolution across successful and failed τ2-bench trajectories. Agent-model estimates can differ substantially from simulator uncertainty, while naive aggregation does not reliably separate success from failure.

  • Observation uncertainty: Agent-LM estimates of user-observation uncertainty show remarkable deviation from ground-truth simulator uncertainty, whereas an auxiliary LLM world model reduces the gap in many cases.The auxiliary-model approximation is presented as a potentially cost-effective direction.
  • Uncertainty evolution: Naive uncertainty aggregation cannot distinguish successful from failed task groups to a statistically meaningful degree across normalized trajectory turns.The plots compare success and failure groups using normalized turn indices and show one-standard-deviation shaded areas.
  • Observation uncertainty: Figure 8 compares distributions of average NLL and entropy over user-message tokens for ground-truth, agent-approximated, and auxiliary-LLM estimates.The ground-truth and agent-approximated distributions deviate markedly, while the auxiliary estimate is somewhat closer.

G. Mini-Survey on Agent Benchmark

A mini-survey of public agent benchmarks finds a non-exhaustive collection dominated by pure LLM-agent studies. The paper also notes calibration as a limitation and multimodal extension as an open direction.

  • Survey scope: The survey collected 44 public agent-benchmark papers from February 2023 to February 2026, mainly covering pure LLM agents.A few surveyed benchmarks also support multimodal VLM-agent scenarios, and the survey focuses on problem-solving capability.
  • Survey scope: The survey scope excludes properties such as safety and trustworthiness, concentrating instead on agents’ problem-solving capability.The collection is explicitly described as non-exhaustive.
  • Limitations: Agent-UQ estimates from ill-calibrated modern LLMs cannot be directly treated as reliable indicators of task performance.The paper identifies calibration of LLM agents as a future-work direction alongside joint optimization of capability and calibration.
  • Future directions: Extending agent UQ to multimodal agents such as GUI agents introduces many-to-many correspondence challenges between modalities.The paper presents reliable multimodal UQ as a foundation for future robustness and safety solutions.
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