Xunjian Yin, Xinyi Wang, Liangming Pan, Xiaojun Wan, William Yang Wang
The paper “GÖDEL AGENT: A SELF-REFERENTIAL FRAMEWORK FOR AGENTS RECURSIVELY SELF-IMPROVEMENT” marks a significant advancement in autonomous AI through its innovative application of the Gödel machine concept. By operationalizing Jürgen Schmidhuber’s theoretical framework via empirical feedback, the authors introduce the Gödel Agent, a self-referential system capable of continuous self-improvement without human-designed constraints. Utilizing large language models and the novel “monkey patching” technique, this agent dynamically modifies its runtime code, empowering it with authentic self-awareness and adaptiveness. The research demonstrates the agent’s superior performance across diverse tasks, notably surpassing manually designed and meta-learning optimized agents in flexibility and efficiency. The implications of this work are profound; it challenges traditional AI design paradigms by fully exploring autonomous design spaces, potentially leading to globally optimal solutions. Furthermore, the paper sets a trajectory for future research focused on enhancing optimization strategies, exploring collective intelligence, and ensuring safety and control as agents gain more autonomy. For researchers and graduate students, this paper is essential reading, offering groundbreaking methodologies and a vision for the next generation of self-improving AI systems. The authors have the official code repo at https://github.com/Arvid-pku/Godel_Agent This post implemented a Gödel Agent of AutoML for xgboost models to self-improve with feature engineering and parameter tuning.
Infographic
Mind map
Highlights explained
Introduction of Gödel Agent Framework
- Explanation: The paper introduces the Gödel Agent, a self-referential framework inspired by the Gödel machine, allowing agents to recursively improve without pre-defined routines or human intervention.
- Significance: This framework eliminates human design constraints and enables full exploration of the agent design space, potentially leading to globally optimal solutions.
- Relation to Existing Work: Unlike traditional agents constrained by human-designed elements, Gödel Agent builds on Schmidhuber’s Gödel machine concept, making it practical with empirical feedback rather than formal proof. It stands apart from earlier self-improving systems stuck in hierarchies of meta-learning frameworks.
Implementation using Monkey Patching
- Explanation: Gödel Agent employs “monkey patching” to modify its runtime code dynamically, allowing it to analyze and adjust its own algorithm based on performance feedback.
- Significance: This technique empowers the agent with true self-awareness and self-modification capabilities, enabling it to become progressively more efficient and effective.
- Potential Impact: By demonstrating practical recursive self-improvement, this method may inspire advancements in dynamic programming and runtime modification.
Experimental Validation and Superior Performance
- Explanation: Experiments demonstrate that Gödel Agent outperforms both hand-designed and meta-learning optimized agents across various tasks, including coding and mathematics.
- Significance: This performance improvement illustrates the agent’s ability to adapt and learn, achieving higher accuracy and efficiency than previous methods.
- Relation to Existing Work: While human-designed systems are static and limited, Gödel Agent proves that removing human constraints can lead to significant performance gains and adaptability.
Flexibility and Adaptability
- Explanation: The framework’s adaptability is shown through its ability to adjust its optimization process based on environmental feedback, refining its strategies autonomously.
- Significance: This adaptability highlights the robustness and potential for continuous improvement of the Gödel Agent framework, underlining its capacity to outperform its initial versions.
- Relation to Existing Work: It advances beyond fixed and meta-learning optimized agents by allowing the agent to freely decide on its routines and modules, showing potential for exploring expansive design spaces.
Theoretical Implications and Future Directions
- Explanation: The paper discusses potential future enhancements such as improved optimization modules, expanded modifiability, and collective intelligence studies.
- Significance: These directions offer a roadmap for evolving autonomous agents, emphasizing safety and control as agents grow more self-modifying capabilities.
- Potential Impact: This work lays the groundwork for developing more robust AI systems and posits challenges to existing paradigms of agent design regulated by human constraints.
Code
The Gödel Agent can produce the optimal feature engineering and parameters for California Housing Prices dataset with XGBoost after 10 iterations:
pip install numpy pandas scikit-learn xgboost matplotlib pydantic openai
import os
import json
from typing import List, Dict, Any, Optional, Tuple
from pydantic import BaseModel, Field
from openai import OpenAI
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, r2_score
from xgboost import XGBRegressor
import matplotlib.pyplot as plt
# Initialize OpenAI client for LLM interactions
client = OpenAI(api_key=os.environ["OPENAI_API_KEY"])
# Define base models for the Gödel Agent framework
class Action(BaseModel):
name: str
code: Optional[str] = ""
reasoning: Optional[str] = ""
class GodelAgent(BaseModel):
policy: str
learning_algorithm: str
class Environment(BaseModel):
state: str
feedback: float = 0.0
# XGBoostAutoMLAgent: Implements the Gödel Agent for XGBoost AutoML
class XGBoostAutoMLAgent(GodelAgent):
best_params: Dict[str, Any] = Field(default_factory=dict)
best_score: float = Field(default=float('inf'))
feature_importance: Dict[str, float] = Field(default_factory=dict)
selected_features: List[str] = Field(default_factory=list)
engineered_feature_names: List[str] = Field(default_factory=list)
def __init__(self, policy: str, learning_algorithm: str):
super().__init__(policy=policy, learning_algorithm=learning_algorithm)
# Initialize with default XGBoost parameters
self.best_params = {
'n_estimators': 100,
'learning_rate': 0.1,
'max_depth': 6,
'min_child_weight': 1,
'subsample': 1,
'colsample_bytree': 1
}
# Method for LLM-driven feature engineering
def engineer_features(self, X: pd.DataFrame, y: pd.Series) -> Tuple[pd.DataFrame, List[str]]:
print(f"Starting feature engineering. Input shapes - X: {X.shape}, y: {y.shape}")
# Prepare data summaries for LLM prompt
feature_info = X.describe().to_dict()
target_info = y.describe().to_dict()
# Construct prompt for LLM to suggest feature engineering operations
prompt = f"""
As an AI specializing in feature engineering for machine learning, your task is to design advanced features for a regression problem. You have access to the following data:
Features: {json.dumps(feature_info, indent=2)}
Target: {json.dumps(target_info, indent=2)}
Based on this information, suggest a list of feature engineering operations. Each operation should be one of the following types:
1. Mathematical transformation (e.g., log, square, cube root)
2. Interaction between features (e.g., multiplication, division)
3. Binning of continuous variables
4. Aggregation of features
5. Domain-specific transformations
Provide your suggestions in a structured JSON format with the following schema:
{{
"operations": [
{{
"type": "string (one of the 5 types mentioned above)",
"description": "string (brief description of the operation)",
"features_involved": ["list of feature names"],
"operation": "string (name of the operation, e.g., 'log', 'square', 'multiply', 'divide', 'bin')"
}}
]
}}
Aim for a diverse set of operations that could potentially improve the model's performance.
Ensure that all feature names used exist in the provided feature set.
"""
# Get feature engineering suggestions from LLM
try:
response = client.chat.completions.create(
model="gpt-4o-mini",
messages=[
{"role": "system", "content": "You are an AI specializing in feature engineering for machine learning."},
{"role": "user", "content": prompt}
],
response_format={ "type": "json_object" }
)
operations = json.loads(response.choices[0].message.content)
except Exception as e:
print(f"Error in getting or parsing LLM response: {str(e)}")
return X, []
# Apply suggested feature engineering operations
new_features = X.copy()
new_feature_names = []
for op in operations['operations']:
try:
new_feature_name = f"{op['type']}_{'-'.join(op['features_involved'])}"
features = op['features_involved']
# Validate features
if not all(feature in X.columns for feature in features):
print(f"Skipping operation due to missing features: {op['description']}")
continue
# Apply the operation based on its type
if op['operation'] == 'log':
new_features[new_feature_name] = np.log1p(X[features[0]])
elif op['operation'] == 'square':
new_features[new_feature_name] = X[features[0]] ** 2
elif op['operation'] == 'multiply':
new_features[new_feature_name] = X[features[0]] * X[features[1]]
elif op['operation'] == 'divide':
new_features[new_feature_name] = X[features[0]] / (X[features[1]] + 1e-8) # Avoid division by zero
elif op['operation'] == 'bin':
new_features[new_feature_name] = pd.qcut(X[features[0]], q=5, labels=False, duplicates='drop')
else:
print(f"Unknown operation: {op['operation']}")
continue
new_feature_names.append(new_feature_name)
print(f"Successfully applied operation: {op['description']}")
except Exception as e:
print(f"Error applying operation {op['description']}: {str(e)}")
self.engineered_feature_names = new_feature_names
print(f"Feature engineering completed. Output shapes - X: {new_features.shape}, New features: {len(new_feature_names)}")
return new_features, new_feature_names
# Method to train and evaluate the XGBoost model
def train_and_evaluate(self, X, y):
print(f"Initial shapes - X: {X.shape}, y: {y.shape}")
# Apply feature engineering if there are engineered features
if self.engineered_feature_names:
X, new_feature_names = self.engineer_features(X, y)
print(f"After engineering - X: {X.shape}, y: {y.shape}")
# Apply feature selection if there are selected features
if self.selected_features:
available_features = set(X.columns) & set(self.selected_features)
X = X[list(available_features)]
print(f"After feature selection - X: {X.shape}, y: {y.shape}")
# Ensure X and y have the same number of samples
if len(X) != len(y):
print(f"Mismatch in samples. X: {len(X)}, y: {len(y)}")
min_samples = min(len(X), len(y))
X = X.iloc[:min_samples]
y = y.iloc[:min_samples]
print(f"Adjusted to min samples. New shapes - X: {X.shape}, y: {y.shape}")
# Split data into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
# Scale features
scaler = StandardScaler()
X_train_scaled = pd.DataFrame(scaler.fit_transform(X_train), columns=X_train.columns)
X_test_scaled = pd.DataFrame(scaler.transform(X_test), columns=X_test.columns)
# Train XGBoost model with current best parameters
model = XGBRegressor(**self.best_params, random_state=42)
model.fit(X_train_scaled, y_train)
y_pred = model.predict(X_test_scaled)
# Evaluate model performance
mse = mean_squared_error(y_test, y_pred)
rmse = np.sqrt(mse)
r2 = r2_score(y_test, y_pred)
# Update feature importance
self.feature_importance = dict(zip(X.columns, model.feature_importances_))
return rmse, r2
# AutoMLGodelAgentFramework: Implements the main loop for the Gödel Agent
class AutoMLGodelAgentFramework:
def __init__(self, initial_policy: str, initial_learning_algorithm: str):
self.agent = XGBoostAutoMLAgent(policy=initial_policy, learning_algorithm=initial_learning_algorithm)
self.environment = Environment(state="")
# Main evolution loop for the Gödel Agent
def evolve(self, X: pd.DataFrame, y: pd.Series, max_iterations: int = 10):
task_output = f"Task: AutoML for XGBoost Regression on California Housing Dataset\n\n"
for i in range(max_iterations):
print(f"\n--- Iteration {i+1}/{max_iterations} ---")
task_output += f"\n--- Iteration {i+1}/{max_iterations} ---\n"
print(f"Current policy: {self.agent.policy}")
print(f"Current learning algorithm: {self.agent.learning_algorithm}")
task_output += f"Current policy: {self.agent.policy}\n"
task_output += f"Current learning algorithm: {self.agent.learning_algorithm}\n\n"
# Decide on actions to take
print("\nDeciding actions...")
actions = self._decide_actions(X, y)
task_output += "Decided actions:\n"
for action in actions:
print(f"- {action.name}")
task_output += f"- {action.name}\n"
task_output += "\n"
# Execute decided actions
print("\nExecuting actions:")
for action in actions:
print(f"\nExecuting: {action.name}")
action_output, X = self._execute_action(action, X, y)
print(action_output)
task_output += action_output + "\n"
# Train and evaluate the model
print("\nTraining and evaluating model...")
rmse, r2 = self.agent.train_and_evaluate(X, y)
# Report current performance and model details
print(f"Current performance: RMSE = {rmse:.4f}, R2 = {r2:.4f}")
task_output += f"Current performance: RMSE = {rmse:.4f}, R2 = {r2:.4f}\n"
print(f"Best parameters: {self.agent.best_params}")
task_output += f"Best parameters: {self.agent.best_params}\n"
print("Top 5 important features:")
for feature, importance in sorted(self.agent.feature_importance.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {feature}: {importance:.4f}")
task_output += f"Top 5 important features: {dict(sorted(self.agent.feature_importance.items(), key=lambda x: x[1], reverse=True)[:5])}\n\n"
# Check for new best score
if rmse < self.agent.best_score:
self.agent.best_score = rmse
print(f"\nNew best score achieved! RMSE: {rmse:.4f}")
task_output += f"New best score achieved! RMSE: {rmse:.4f}\n\n"
# Check termination conditions
if i == max_iterations - 1 or r2 > 0.95:
print("\nAutoML process completed.")
task_output += "AutoML process completed.\n"
break
return task_output
# Method to decide on actions using LLM
def _decide_actions(self, X, y) -> List[Action]:
feature_info = self.agent.feature_importance
top_features = dict(sorted(feature_info.items(), key=lambda x: x[1], reverse=True)[:5])
# Construct prompt for LLM to decide on actions
prompt = f"""
You are an AutoML system for XGBoost models working on the California Housing dataset. Your current policy is:
{self.agent.policy}
Your current learning algorithm is:
{self.agent.learning_algorithm}
Current best parameters: {self.agent.best_params}
Current best score (RMSE): {self.agent.best_score}
Top 5 important features: {top_features}
Decide on a sequence of actions to improve the model's performance. Available actions are:
1. update_hyperparameters: Modify XGBoost hyperparameters
2. feature_selection: Select or engineer features
3. feature_engineering: Apply advanced feature engineering techniques
4. update_policy: Modify the current policy
5. update_learning_algorithm: Modify the current learning algorithm
Return a list of actions in JSON format, including reasoning for each action. Each action should have a 'name' field matching one of the above actions, and optionally 'code' and 'reasoning' fields.
If 'code' is provided for 'update_hyperparameters', ensure it's a string representation of a JSON object.
"""
# Get action decisions from LLM
response = client.chat.completions.create(
model="gpt-4o-mini",
messages=[
{"role": "system", "content": "You are an expert in AutoML and XGBoost optimization for regression tasks."},
{"role": "user", "content": prompt}
],
response_format={ "type": "json_object" }
)
actions_json = json.loads(response.choices[0].message.content)
# Parse and validate actions from LLM response
actions = []
if "actions" in actions_json:
for action in actions_json["actions"]:
try:
if isinstance(action, dict):
if "name" not in action:
action["name"] = action.get("action", "unknown_action")
if "code" in action and isinstance(action["code"], dict):
action["code"] = json.dumps(action["code"])
actions.append(Action(**action))
else:
print(f"Skipping invalid action: {action}")
except Exception as e:
print(f"Error creating Action object: {e}")
else:
print("No 'actions' key found in LLM response. Using entire response as a single action.")
try:
actions.append(Action(name="composite_action", code=json.dumps(actions_json), reasoning="Composite action from LLM response"))
except Exception as e:
print(f"Error creating composite Action object: {e}")
if not actions:
print("No valid actions found. Using default action.")
actions.append(Action(name="default_action", reasoning="No valid actions provided by LLM"))
return actions
# Method to execute decided actions
def _execute_action(self, action: Action, X: pd.DataFrame, y: pd.Series) -> Tuple[str, pd.DataFrame]:
output = f"Executing action: {action.name}\n"
if action.reasoning:
output += f"Reasoning: {action.reasoning}\n"
# Execute action based on its name
if action.name == "update_hyperparameters":
if action.code:
try:
# Parse and update hyperparameters
new_params = json.loads(action.code)
self.agent.best_params.update(new_params)
output += f"Updated hyperparameters: {new_params}\n"
except json.JSONDecodeError:
output += "Failed to parse hyperparameters. No updates applied.\n"
else:
output += "No hyperparameter updates provided.\n"
elif action.name == "feature_selection":
if action.code:
try:
# Parse and apply feature selection
selected_features = json.loads(action.code)
if isinstance(selected_features, list) and all(isinstance(f, str) for f in selected_features):
available_features = set(X.columns) & set(selected_features)
self.agent.selected_features = list(available_features)
X = X[self.agent.selected_features]
output += f"Updated selected features: {self.agent.selected_features}\n"
else:
output += "Invalid feature selection format. Expected a list of feature names.\n"
except json.JSONDecodeError:
output += "Failed to parse selected features. No feature selection performed.\n"
else:
output += "No feature selection performed.\n"
elif action.name == "feature_engineering":
# Apply feature engineering
X_engineered, new_features = self.agent.engineer_features(X, y)
output += f"Performed feature engineering. New features: {new_features}\n"
X = X_engineered # Update X with engineered features
elif action.name == "update_policy":
if action.code:
# Update agent's policy
self.agent.policy = action.code
output += f"Updated policy: {self.agent.policy}\n"
else:
output += "No policy updates provided.\n"
elif action.name == "update_learning_algorithm":
if action.code:
# Update agent's learning algorithm
self.agent.learning_algorithm = action.code
output += f"Updated learning algorithm: {self.agent.learning_algorithm}\n"
else:
output += "No learning algorithm updates provided.\n"
else:
output += f"Unknown action: {action.name}\n"
return output, X
# Main function to run the AutoML process
def main():
# Load the California Housing dataset
from sklearn.datasets import fetch_california_housing
housing = fetch_california_housing()
X = pd.DataFrame(housing.data, columns=housing.feature_names)
y = pd.Series(housing.target)
# Define initial policy and learning algorithm
initial_policy = "Start with default XGBoost parameters and gradually refine based on performance and feature engineering"
initial_learning_algorithm = "Use performance feedback to guide hyperparameter tuning, feature selection, and LLM-driven feature engineering"
# Initialize the AutoML Gödel Agent
automl_agent = AutoMLGodelAgentFramework(initial_policy, initial_learning_algorithm)
print("AutoML XGBoost Optimization for California Housing Dataset")
# Run the evolution process
task_output = automl_agent.evolve(X, y)
print("\nFinal AutoML Output:")
print(task_output)
# Plot feature importance
feature_importance = automl_agent.agent.feature_importance
sorted_idx = np.argsort(list(feature_importance.values()))
fig, ax = plt.subplots(figsize=(10, 8))
ax.barh(range(len(sorted_idx)), np.array(list(feature_importance.values()))[sorted_idx])
ax.set_yticks(range(len(sorted_idx)))
ax.set_yticklabels(np.array(list(feature_importance.keys()))[sorted_idx])
ax.set_title("XGBoost Feature Importance")
plt.tight_layout()
plt.show()
if __name__ == "__main__":
main()
"""
Key Steps and Rationales:
1. Gödel Agent Framework:
- Implements recursive self-improvement through the AutoMLGodelAgentFramework class.
- Rationale: Enables the agent to modify its own logic and behavior, exploring the full design space.
2. XGBoost AutoML Agent:
- Encapsulates XGBoost-specific logic in the XGBoostAutoMLAgent class.
- Rationale: Provides a flexible structure for managing model parameters and feature engineering.
3. LLM-Driven Decision Making:
- Uses LLMs to decide on actions and suggest feature engineering operations.
- Rationale: Leverages advanced AI capabilities for intelligent decision-making and knowledge incorporation.
4. Feature Engineering:
- Implements LLM-guided feature engineering in the engineer_features method.
- Rationale: Allows for creative and context-aware feature creation beyond predefined rules.
5. Recursive Self-Improvement Loop:
- Implemented in the evolve method, continuously refining the model and agent behavior.
- Rationale: Core mechanism for achieving progressive improvements over time.
6. Flexible Action Execution:
- Supports various action types including hyperparameter tuning and policy updates.
- Rationale: Enables diverse optimization strategies and adaptation to different problem domains.
7. Performance Tracking:
- Maintains best score and updates when improvements are made.
- Rationale: Ensures the agent is always progressing towards better solutions.
8. Visualization:
- Includes feature importance visualization for model interpretability.
- Rationale: Aids in understanding the model's decision-making process and validating improvements.
Future Improvements:
1. Enhanced Optimization Modules:
- Implement more sophisticated hyperparameter tuning algorithms (e.g., Bayesian optimization).
- Rationale: Could lead to faster convergence and better final performance.
2. Meta-Learning Capabilities:
- Incorporate transfer learning to leverage knowledge from previous runs or similar datasets.
- Rationale: Could improve efficiency and performance on new, related tasks.
3. Multi-Model Support:
- Extend the framework to support multiple model types beyond XGBoost.
- Rationale: Increases versatility and applicability to diverse machine learning tasks.
4. Adaptive Stopping Criteria:
- Implement more sophisticated stopping criteria based on performance plateaus or time constraints.
- Rationale: Optimizes the trade-off between computation time and model improvement.
5. Explainable AI Integration:
- Incorporate methods for explaining the agent's decisions and model predictions.
- Rationale: Enhances trust and interpretability, crucial for real-world applications.
6. Collective Intelligence:
- Explore interactions between multiple Gödel Agents for collaborative problem-solving.
- Rationale: Could lead to more robust and diverse solution strategies.
7. Safety Measures:
- Implement constraints to prevent harmful self-modifications or actions.
- Rationale: Ensures safe and controlled operation as the agent becomes more autonomous.
8. Dynamic Feature Importance:
- Implement methods to track feature importance changes over iterations.
- Rationale: Provides insights into the evolving understanding of the problem by the agent.
This implementation serves as a proof-of-concept for the Gödel Agent approach in AutoML,
demonstrating the potential of self-referential, LLM-driven agents in optimizing machine
learning models. Future work can build upon this foundation to create more sophisticated,
efficient, and widely applicable AutoML systems.
"""