scipy.optimize.fmin_l_bfgs_b returns ‘ABNORMAL_TERMINATION_IN_LNSRCH’

scipy.optimize.fmin_l_bfgs_b: ‘ABNORMAL_TERMINATION_IN_LNSRCH’ Error

Understanding the Error

The “ABNORMAL_TERMINATION_IN_LNSRCH” error in scipy.optimize.fmin_l_bfgs_b signals an issue during the line search phase of the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS-B) optimization algorithm. This error indicates that the line search algorithm, responsible for finding the optimal step size along the search direction, has encountered a problem. Here’s a breakdown:

Common Causes

• Inadequate Search Interval: The line search algorithm may struggle to find a suitable step size within the defined search interval. This often occurs when the interval is too small or poorly defined.
• Numerical Instability: The optimization problem might exhibit numerical instability, leading to erratic behavior in the line search. This could be due to ill-conditioning, highly nonlinear function behavior, or excessive gradients.
• Poor Initialization: The starting point of the optimization (initial guess) might be far from the optimal solution, causing the algorithm to take large steps and struggle during line search.
• Constraints: If the problem involves bound constraints, the line search may fail to satisfy them due to a combination of factors like tight constraints or an inappropriate search direction.

Debugging Strategies

1. Inspect the Search Interval

Examine the fmin_l_bfgs_b parameters bounds and options, focusing on "maxcor" (maximum number of past gradient vectors to use), "ftol" (tolerance for function values), and "gtol" (tolerance for gradient values). Experiment with adjusting these parameters to see if it resolves the error.

2. Check Numerical Stability

• Rescale the problem variables to avoid overly large or small numbers. This can improve numerical stability.
• Ensure that your objective function and its gradient calculations are numerically stable and accurate.

3. Adjust Initialization

Try different starting points for your optimization. A well-chosen initial guess can significantly impact the algorithm’s performance.

4. Consider Alternatives

If you consistently face issues with fmin_l_bfgs_b, consider exploring alternative optimization algorithms available in SciPy, such as:

• scipy.optimize.minimize (with other methods like Nelder-Mead or BFGS)
• scipy.optimize.basinhopping (for global optimization)

Example:

Illustrating how to use fmin_l_bfgs_b and how the ‘ABNORMAL_TERMINATION_IN_LNSRCH’ error might occur.

import numpy as np
from scipy.optimize import fmin_l_bfgs_b

def objective_function(x):
    return x[0]**2 + x[1]**2

x0 = np.array([1, 1])
bounds = [(0, 10), (0, 10)]
result = fmin_l_bfgs_b(objective_function, x0, bounds=bounds, options={'ftol': 1e-10, 'gtol': 1e-10, 'maxcor': 10})

print(result)

Potential output:

     fun: 0.0
     jac: array([0., 0.])
 message: 'ABNORMAL_TERMINATION_IN_LNSRCH'
    nfev: 17
     nit: 4
 success: False
       x: array([0., 0.])

In this example, the line search may fail due to the chosen parameters, leading to the error.

Always remember to carefully examine the error message, the state of the optimization, and your problem setup. This will help you identify the root cause of the issue and take appropriate actions to resolve it.