# Knowing When to Ask for Help: Bayesian Self-Escalation in Hierarchical LLM Agents

arXiv: https://arxiv.org/abs/2608.24087 · HTML: https://mlsanity.com/paper/2608.24087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 19 of 19)

- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Calibrated Learning to Defer with One-vs-All Classifiers](https://mlsanity.com/paper/2202.03673/) (2022)
- [When Does Confidence-Based Cascade Deferral Suffice?](https://mlsanity.com/paper/2307.02764/) (2023)
- [Partially Observed Markov Decision Processes. Problem Sets and Internet Supplement](https://mlsanity.com/paper/1604.08127/) (2016)
- [Agreement-Based Cascading for Efficient Inference](https://mlsanity.com/paper/2407.02348/) (2024)
- [Semantic Agreement Enables Efficient Open-Ended LLM Cascades](https://mlsanity.com/paper/2509.21837/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Competing-Hazards Systematization of Loss of Control in Autonomous Agents](https://mlsanity.com/paper/2609.38411/) (2026)

## Abstract (arXiv)

Current LLM agent systems decide delegation before reasoning begins (a router picks a model) or after a response is complete (a verifier scores it and may retry). We study a third regime: an agent that recognises, during its own reasoning, that it is unlikely to succeed and transfers control to a stronger model. We formulate intra-generation delegation as a Bayesian optimal-stopping problem over a learned competence posterior -- an online estimate of the agent's eventual task success whose sufficient statistics are learned from labelled trajectories, not read off raw entropy. We derive the myopic escalation threshold in closed form, characterise the optimal policy via dynamic programming, and prove that the optimal policy is a time-varying threshold with no shape assumption on the raw signal. We further prove exponential separation of the oracle belief at the Chernoff-information rate of the signal, a regret bound governed by the calibration of the posterior, and a finite-sample guarantee: with n labelled calibration trajectories the deployed plug-in policy's regret decays as 1/sqrt(n). A controlled simulation study confirms each prediction of the theory, including the predicted 1/sqrt(n) rate. We additionally report a real-model validation on a Qwen2.5-Coder 1.5B->7B code cascade (MBPP, 257 tasks), confirming two of three pre-registered predictions: the escalation frontier dominates post-hoc routing at equal cost, and the cumulative competence belief's discrimination rises over generation.