Adaptive multi-fidelity optimization with fast learning rates

Leverage adaptive multi-fidelity optimization to efficiently optimize complex functions within limited budgets. This technique intelligently balances approximation cost and bias with fast learning rates, accelerating convergence and improving results for resource-constrained tasks like hyperparameter tuning.

intermediate1 hour5 steps

The play

Identify Multi-Fidelity Approximations
Determine different levels of approximation (fidelities) for your target function, such as varying dataset sizes, model complexities, or simulation resolutions. Each fidelity should offer a different trade-off between speed/cost and accuracy.
Quantify Cost and Bias per Fidelity
For each identified fidelity, estimate its computational cost (e.g., training time, resource usage) and its bias relative to the true, high-fidelity function. This helps in strategic decision-making during optimization.
Define Budget and Optimization Goal
Establish your total computational budget (e.g., total compute hours, maximum iterations) and clearly define the objective function and performance metrics for your optimization task (e.g., minimize validation loss, maximize accuracy).
Implement Adaptive Multi-Fidelity Strategy
Integrate an adaptive multi-fidelity optimization algorithm (e.g., using a specialized library or framework) that dynamically selects fidelities based on estimated cost, bias, and current optimization progress to efficiently explore the search space.
Monitor and Refine Optimization
Track the optimization process, analyze convergence, and adjust parameters or fidelity definitions as needed. The goal is to achieve optimal performance within your defined budget by intelligently leveraging different fidelities.

Starter code

def multi_fidelity_objective(params, fidelity_level):
    """
    Simulates an objective function with varying fidelity levels.
    Lower fidelity_level means faster computation (lower cost) but higher bias.

    Args:
        params (dict): Optimization parameters (e.g., learning_rate, batch_size).
        fidelity_level (int): Represents the approximation level (e.g., 1=low, 5=high).
                              Higher level means more accurate but more expensive.

    Returns:
        float: The simulated objective value (e.g., validation loss).
    """
    # Example: A simple quadratic function for optimization params
    base_loss = (params.get('learning_rate', 0.01) - 0.005)**2 + \
                (params.get('batch_size', 32) - 64)**2 / 1000

    # Simulate bias: lower fidelity adds more noise/bias
    # Higher fidelity_level (max 5) means less bias
    bias = (5 - fidelity_level) * 0.5
    
    # Simulate cost (not returned, but conceptually present):
    # cost_factor = fidelity_level * 0.1 

    return base_loss + bias

# Example usage:
# Evaluate a parameter set at low fidelity (e.g., quick check)
# loss_low_fidelity = multi_fidelity_objective({'learning_rate': 0.008, 'batch_size': 50}, fidelity_level=1)
# print(f"Low fidelity loss: {loss_low_fidelity:.4f}")

# Evaluate the same parameter set at high fidelity (e.g., for final validation)
# loss_high_fidelity = multi_fidelity_objective({'learning_rate': 0.008, 'batch_size': 50}, fidelity_level=5)
# print(f"High fidelity loss: {loss_high_fidelity:.4f}")

Source

Paperarxiv.org