Agentic Calibration of Grey-Box Simulation Models: An LLM-Driven Alternative
Authors: David Gómez-Guillén, Mireia Diaz, Josep Lluis Arcos, Jesús Cerquides
Organizations: Unit of Infections and Cancer – Information and Interventions (UNIC-I&I), Cancer Epidemiology Research Program, Catalan Institute of Oncology-IDIBELL, L’Hospitalet de Llobregat, Spain · Autonomous University of Barcelona (UAB), Spain · Centro de Investigación Biomédica en Red de Epidemiología y Salud Pública (CIBERESP), Ministerio de Ciencia, Innovación y Universidades, Madrid, Spain · Artificial Intelligence Research Institute, IIIA-CSIC, Spain
Abstract
Calibration of grey-box simulation models is a constrained optimization problem in which model evaluations are expensive, the parameter space can be high-dimensional, and the search must respect plausibility constraints. Although the simulation code is fully available to the analyst, the joint effect of multiple parameters remains difficult to predict analytically. Classical optimizers such as Nelder--Mead (NM) are simple to deploy but sample-inefficient, particularly under constraints. Modern Bayesian Optimization methods achieve competitive solutions with far fewer evaluations but require non-trivial modeling machinery for constraint handling. We introduce an agentic calibration method in which a large language model acts as the optimizer, with constraints incorporated as a plain-language section of the system prompt. We evaluate the agentic method, NM, and Bayesian Optimization (BO) on an anal cancer simulation model under both unconstrained and clinically constrained calibration. Under unconstrained calibration, the agentic method achieves substantially lower best error than BO and NM, while requiring fewer model evaluations. Under constrained calibration, the agentic method reaches comparable error levels and both outperform NM. These results are obtained at the cost of increased inference time per iteration. Agentic calibration achieves competitive performance with substantially fewer model evaluations, and constraint handling is essentially free at the modeller-facing interface through simple textual specifications rather than additional modelling machinery. The main trade-off lies in increased per-iteration inference cost, making the approach particularly suitable when simulation time dominates. Beyond performance, the per-iteration rationale makes the search auditable and explainable, so its decisions can be scrutinised and justified to third parties.
The performance of an LLM agent depends on the scaffold around a frozen model. A common way to improve that scaffold is to use a coding agent as an optimizer: it reads current scores and traces and iteratively edits the source, producing a new candidate each round. Each edit is chosen according to a belief about how the environment will respond: what went wrong, and which change should help. That belief is typically implicit. It lives in the coding agent's reasoning on the current call, or remains latent in its parameters, rather than as something written down. Later calls therefore see scores and traces, but they do not use that belief. We introduce Belief-Calibrated Optimization (BCO), a method that writes that belief down as a persistent in-context document and continually revises that document as new candidates are evaluated. The resulting document is a world model: the current account of how the environment responds to edits. Added to an otherwise standard loop, BCO reaches a higher train passrate than a matched control that lacks only the world model, on five benchmarks spanning memory QA, tool-use QA, code-as-action app agents, and terminal agents. The gap remains on every held-out split, which is not used to select the candidate. After a target-model swap, in which the frozen model is replaced and the scaffold is not, the selected BCO scaffold leads on the tasks we test, except where context-window overruns leave it unfinished. An offline ablation then asks whether that gap comes from what the world model says. A fresh predictor given the accumulated document forecasts how the environment will respond more accurately than predictors given either no document or a same-form copy whose content has been falsified. The comparison indicates that the document carries reusable information in its content, not only in its form.
Bayesian optimization (BO) has become the standard tool for sample-efficient optimization and owes its efficiency to uncertainty-aware search driven by generic statistical priors. Richer domain priors can improve BO in principle, but encoding them through tailored kernels or problem structure is difficult and rarely done in practice. LLMs can help sidestep this difficulty by making informal priors from natural language, code, and documentation directly available to the optimizer. However, existing LLM-based BO methods either insert the LLM into a fixed role (surrogate, acquisition proxy, or configuration interface) or hand it broad control, sacrificing the systematic exploration that makes BO reliable. We introduce agentic Bayesian optimization: a paradigm in which an LLM agent is the central decision maker in the BO loop while a Bayesian backend provides the uncertainty-aware optimization substrate. The agent configures the problem, queries the backend, selects and commits evaluations, and can revise the optimization strategy during the run by tightening bounds, switching acquisition functions, proposing targeted evaluations, or even reframing the problem following new instructions or observed evidence. We instantiate this idea in Sara, a surrogate-augmented autoresearch agent, and lenz, a modular BoTorch-based backend that the agent can inspect and modify through a structured interface. Across synthetic and real-world benchmarks, Sara preserves the reliability of state-of-the-art BO without prior knowledge, outperforms LLM-based baselines, and uses natural-language priors to improve beyond standard BO. We further demonstrate the practical value of agentic BO in dynamic settings, where Sara reconfigures the full optimization problem on the fly as requirements change, a capability not previously available in standard BO.
LLM agents operate in two distinct regimes: open-weight agents amenable to reinforcement learning (RL) and black-box agents whose behaviour must be controlled purely at test time. Although black-box agents are often backed by state-of-the-art proprietary LLMs, API-only access precludes parameter-level optimization, rendering most RL methods inapplicable. To address this limitation, we turn to a known equivalence between RL and Bayesian inference. We propose Agentic Monte Carlo (AMC) to directly sample from the optimal policy of a black-box agent rather than training it through RL. The optimal policy is a posterior over trajectories whose prior we define as the fixed black-box LLM agent. We employ Sequential Monte Carlo to sample from this posterior by learning a value function to steer the agent while leaving the underlying black-box model unchanged. We validate AMC on three diverse environments from the AgentGym benchmark, demonstrating significant improvements over prompting baselines and even outperforming Group Relative Policy Optimization (GRPO) as we scale the test-time compute of our method. AMC demonstrates the feasibility of performing principled RL-style optimization of black-box LLM agents. Code is available at https://github.com/layer6ai-labs/Agentic-Monte-Carlo
Dae Yon Hwang, Raunaq Suri, Valentin Villecroze +4