---
type: concept
x-llmwiki:
  schemaVersion: "0.1"
  contentHash: 5df099f6230f53728516f9ecf65f4411ba5eb9f35f57e6c507ff520814cc5a76
  pageDirectory: concepts
  sources:
    - hyperparameter-tuning-with-optuna-databricks-on-aws.md
  confidence: 1
  provenanceState: extracted
  freshnessStatus: unverified
  aliases:
    - optuna-objective-function
    - OOF
    - Objective function
    - Objective Function (Optuna)
  citations:
    - file: hyperparameter-tuning-with-optuna-databricks-on-aws.md
title: Optuna objective function
description: A user-defined function that defines the hyperparameter search space and returns a metric value for Optuna to minimize or maximize
tags:
  - machine-learning
  - optuna
  - optimization
timestamp: "2026-06-19T19:09:04.350Z"
---

# Optuna Objective Function

The **Optuna objective function** is a user-defined Python function that defines a hyperparameter optimization problem for [Optuna](/concepts/optuna.md), a popular hyperparameter optimization framework. The objective function receives a Trial object and returns a numerical value that represents the quality of a particular set of hyperparameters. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

## Structure

An objective function takes a single argument — a `trial` object — and returns a numerical value (typically a float) that Optuna minimizes or maximizes. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

The basic structure is:

```python
import sklearn

def objective(trial):
    # 1. Generate hyperparameters using the trial object
    regressor_name = trial.suggest_categorical('classifier', ['SVR', 'RandomForest'])
    
    if regressor_name == 'SVR':
        svr_c = trial.suggest_float('svr_c', 1e-10, 1e10, log=True)
        regressor_obj = sklearn.svm.SVR(C=svr_c)
    else:
        rf_max_depth = trial.suggest_int('rf_max_depth', 2, 32)
        regressor_obj = sklearn.ensemble.RandomForestRegressor(max_depth=rf_max_depth)
    
    # 2. Load and split data
    X, y = sklearn.datasets.fetch_california_housing(return_X_y=True)
    X_train, X_val, y_train, y_val = sklearn.model_selection.train_test_split(X, y, random_state=0)
    
    # 3. Train the model
    regressor_obj.fit(X_train, y_train)
    
    # 4. Evaluate and return objective value
    y_pred = regressor_obj.predict(X_val)
    error = sklearn.metrics.mean_squared_error(y_val, y_pred)
    return error  # An objective value linked with the Trial object
```

^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

## Components

### 1. Hyperparameter Generation via `trial.suggest_*` Methods

The objective function uses the Trial object's `suggest` methods to define the search space for each hyperparameter. Common methods include:

- `trial.suggest_float(name, low, high, log=True/False)` — For continuous parameters. The `log=True` option enables logarithmic sampling, useful when the search space spans multiple orders of magnitude. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]
- `trial.suggest_int(name, low, high)` — For integer parameters. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]
- `trial.suggest_categorical(name, choices)` — For categorical parameters. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

### 2. Model Training

After generating hyperparameters, the objective function typically creates a machine learning model using those parameters and trains it on training data. The function can use any machine learning framework, including scikit-learn, PyTorch, or TensorFlow. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

### 3. Evaluation and Return Value

The function evaluates the trained model and returns a numerical value that Optuna uses to guide the optimization process. Optuna tracks each trial's objective value to determine which hyperparameter combinations perform best. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

## Objective Value Semantics

By default, Optuna minimizes the objective value. If the goal is to maximize a metric (such as accuracy), the objective function should return the negative of that metric. Each return value is linked with the Trial object that generated the hyperparameters, allowing Optuna to build a history of tested configurations. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

## Best Practices

- Keep the objective function self-contained by including all necessary imports and data loading within the function. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]
- Use logarithmic sampling (`log=True`) for parameters that span many orders of magnitude, such as regularization strength. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]
- Return a single scalar value rather than a dictionary or list. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]
- Ensure data splitting happens inside the objective function to avoid data leakage across trials. ^[hyperparameter-tuning-with-optuna-databricks-on-aws.md]

## Related Concepts

- Optuna study — The optimization process that calls the objective function repeatedly.
- [Trial object](/concepts/optuna-trial-object.md) — Represents a single execution of the objective function.
- Hyperparameter optimization — The broader technique of finding optimal model parameters.
- Automated machine learning (AutoML) — Automated model selection and tuning pipelines.

## Sources

- hyperparameter-tuning-with-optuna-databricks-on-aws.md

# Citations

1. [hyperparameter-tuning-with-optuna-databricks-on-aws.md](/references/hyperparameter-tuning-with-optuna-databricks-on-aws-acf7dc85.md)
