Bayesian Optimisation (BO) is a well-established technique for optimising black-box functions—functions whose underlying structure is complex, expensive to evaluate, or unknown. It has proven particularly effective in hyperparameter tuning for complex machine learning models, design optimisation in engineering, and scientific experiments where evaluations are costly.

Now, imagine injecting the power of Large Language Models (LLMs)—like GPT-style models—into this Bayesian Optimisation process. The result is what we will call LLAMBO: Large Language Models to Enhance Bayesian Optimisation

In this blog post, we explore how LLMs can provide valuable domain knowledge and informed prior information, enabling Bayesian Optimisation to converge to better optima faster. We’ll discuss the conceptual pipeline, outline a code example, and wrap up with a use case demonstrating the synergy of LLMs and Bayesian Optimisation.

1. What is Bayesian Optimisation?

Bayesian Optimisation is a strategy to optimize expensive black-box functions. It typically involves:

• Surrogate Modelling: We model the objective function f(x)  with a surrogate (often a Gaussian Process or a Random Forest). This surrogate is used to predict the likely outcome of f(x) without an actual (potentially expensive) evaluation.
• Acquisition Function: We use an acquisition function (like Expected Improvement or Upper Confidence Bound) to find the most promising region to sample next, trading off exploration and exploitation.
• Iterate: We evaluate the black-box function at the new candidate point, update the surrogate model with the new data point, and repeat until convergence or resource limits.

2. Motivation for LLAMBO

While Bayesian Optimisation can be quite powerful on its own, it often starts from scratch or with minimal domain insights. Large Language Models (LLMs), trained on massive corpora, can bring contextual knowledge to this process:

• Domain-Specific Heuristics: LLMs can generate initial guesses about parameter ranges or conditions that are likely to be promising.
  
• Prior Knowledge: Instead of a flat prior over the search space, LLMs can help shape an informed prior that captures domain insights.
• Interpretability: LLMs can provide human-readable rationales or heuristics, which can inform domain experts about why certain regions might be more promising.

By integrating LLM outputs into the Bayesian Optimisation framework (particularly into the surrogate model or the acquisition function), we can significantly reduce the search space and speed up the convergence to an optimum.

3. Methodology and Workflow

Below is a high-level methodology for LLAMBO:

1. Identify the Black-Box Function: For example, let’s say we want to optimize hyperparameters of a neural network.
2. LLM-Assisted Prior Generation: We prompt a Large Language Model (e.g., GPT-4) with domain-relevant information to generate:
   [2.1] A plausible range for each hyperparameter.
   [2.2] Insights on how parameters interact (e.g., “If the batch size is large, you can often increase the learning rate.”).
3. Train the Surrogate Model: Initialise the Bayesian Optimisation process. Instead of a uniform prior, use the LLM outputs to either:
   [3.1] Weight certain regions more heavily.
   [3.2] Provide an initial dataset of promising candidate points to start with.
4. Optimise the Acquisition Function: The standard Bayesian Optimisation loop still applies, but it is guided by an LLM-informed surrogate model or acquisition strategy.
5. Iterate: Evaluate the black-box function at selected points, update the surrogate, and refine the acquisition function. In each iteration, we can re-prompt or re-check the LLM if necessary for updated heuristics.

4. Agentic Use Case: LLM-Driven Robotics Tuning

Consider an autonomous robotics agent that must continually optimise its control parameters (e.g., joint torque limits, speed profiles, or sensor fusion strategies) in a dynamic environment. Evaluating each new configuration in real hardware is expensive and time-consuming. Here’s how LLAMBO can be agentically applied:

1. Agent Observes the Environment: The agent monitors real-time data - like changes in surface friction, temperature, or payload weight - that affect control performance.
2. LLM-Enhanced Knowledge: The agent maintains a prompt history with an LLM, describing the robot’s domain, prior experiments, and performance logs.
3. Generate Prior & Heuristics: On each iteration, the agent queries the LLM for suggestions about parameter bounds, potential stability constraints, and typical pitfalls. For instance, the LLM may suggest “Under increased payload, reduce joint accelerations to maintain balance.”
4. Bayesian Optimisation Loop:
   [4.1] Surrogate Update: The agent’s surrogate model is updated with the newly tested parameter set (e.g., “Torque limit=20 Nm, Speed=1.2 m/s” -> “Task Completion Time=4.5s”).
   [4.2] Acquisition Function: The agent computes the next best parameter combination - balancing exploration (untried parameter ranges) vs. exploitation (likely optimal settings).
5. Actuate & Evaluate: The agent physically adjusts the robot’s controls to the new parameters, evaluates performance, and logs the outcome.
6. Iterate: If performance is still suboptimal, the agent repeats the process, each time benefiting from LLM knowledge that focuses on plausible parameter ranges or known mechanical constraints.

Why an Agentic Approach Is Powerful: The agent runs autonomously, using LLM insights to continually refine its prior, accelerating the path to an optimal solution without requiring constant human intervention. This is particularly valuable in changing environments or tasks, where an agent must adapt on the fly.

Below is a Python-like pseudocode showing how to integrate an LLM-based prior into Bayesian Optimisation with the popular bayes_opt library:

import numpy as np
from bayes_opt import BayesianOptimization

# Mock function to represent an LLM-based prior generation
def llm_generate_prior(agent_context):
    """
    In reality, the agent would prompt an LLM with the current context.
    We'll just return some hypothetical insights for demonstration.
    """
    param_ranges = {
        'torque_limit': (10, 40),
        'speed': (0.5, 2.0),
    }
    # The LLM suggests initial points that are “safe bets”
    initial_points = [
        {'torque_limit': 20, 'speed': 1.0},
        {'torque_limit': 25, 'speed': 1.2},
    ]
    return param_ranges, initial_points

# Black-box function representing real-world robot performance
def evaluate_robot(torque_limit, speed):
    """
    A toy example returning negative of “time to complete a task”.
    In reality, you’d measure actual performance from a robot’s sensors.
    """
    # Let's say optimum is near torque_limit=30, speed=1.5
    time_to_complete = 10 - ( -(torque_limit - 30)**2 / 400 ) - ( -(speed - 1.5)**2 * 4 )
    # We want to MINIMIZE time_to_complete, so we return its negative
    return -time_to_complete

# 1. Generate LLM-based prior
agent_context = "Robot arm with a heavier payload. Past logs suggest moderate torque and speed."
param_ranges, initial_points = llm_generate_prior(agent_context)

# 2. Initialize Bayesian Optimization
optimizer = BayesianOptimization(
    f=evaluate_robot,         # The black-box function to minimize (we can just invert sign).
    pbounds=param_ranges,
    verbose=2,
    random_state=42,
)

# 3. Seed the optimizer with LLM-based initial points
for init_pt in initial_points:
    optimizer.probe(params=init_pt, lazy=True)

# 4. Maximize with negative objective to effectively minimize time_to_complete
optimizer.maximize(
    init_points=0,   # We already seeded points from the LLM
    n_iter=10,
    acq="ei",
    xi=0.01
)

print("Best found parameters:", optimizer.max)

In a real agentic system, each iteration might:

1. Gather new sensor feedback on performance.
2. Pass updated context to the LLM for refined hints.
3. Update the Bayesian Optimisation loop.
4. Apply the best suggestion to the robot.

6. Summary and Conclusion

LLAMBO—Large Language Models to Enhance Bayesian Optimisation - enables you to incorporate rich, contextual knowledge into each stage of the optimisation process. For agentic applications like robotics tuning, self-driving labs, or intelligent manufacturing, the ability to adaptively refine priors and parameter search ranges via LLM prompts can significantly reduce the time and cost needed to reach a high-quality solution.

Whether you’re tuning a robotics system, searching for optimal hyperparameters in machine learning, or optimising any complex process, LLAMBO can help integrate human-like domain knowledge from LLMs into a more systematic Bayesian Optimisation flow. This approach not only accelerates and improves the search, but also makes the entire optimisation journey more explainable and adaptive - paving the way for fully agentic and autonomous solutions.