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Troubleshooting Your Gradient Descent Implementation with Backtracking Line Search

Discover effective solutions for the issues you're facing in implementing `gradient descent with backtracking line search` for optimization using Python. --- This video is based on the question https://stackoverflow.com/q/66874237/ asked by the user 'DockingBlade' ( https://stackoverflow.com/u/14728298/ ) and on the answer https://stackoverflow.com/a/66876240/ provided by the user 'wtw' ( https://stackoverflow.com/u/10349888/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions. Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Having trouble making update in gradient descent implementation? Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l... The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license. If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com. --- Troubleshooting Your Gradient Descent Implementation with Backtracking Line Search Implementing gradient descent can often feel daunting, especially when you encounter issues that prevent your code from running smoothly. If you've been working on a gradient descent implementation accompanied by a backtracking line search and have found that the updates to f(x0) are not functioning as expected, fear not! In this post, we will explore common pitfalls and provide solutions to help you optimize your code effectively. Understanding the Problem Many developers struggle with ensuring the accuracy of their gradient descent implementations, especially when dealing with complex functions. In the queried problem, the primary concern is that the value of f(x0) is not changing as anticipated after updates. This could stem from various issues, including improper handling of lambda expressions or mistakes in the backtracking line search procedure. Common Symptoms Here's what you may experience: The outputs remain static after multiple iterations. Large or unexpected numbers in the output, leading to errors or unrealistic function evaluations. Analyzing the Solution To resolve the issue, we will break down the critical components: 1. Correcting the Update Logic The first thing to inspect is how you're updating the algorithm's variables. It's vital to ensure that your update mechanism reflects changes properly. Debugging Tips: Utilize a debugger to step through your code, allowing for real-time observation. Insert print statements to monitor variable values and track where changes may not be taking effect. 2. Adjusting the Step Size A common fix for the problem where values do not change significantly is to lower the initial step size (t). This helps in preventing the calculations from scaling excessively – a factor that may produce large numbers leading to evaluation errors. Suggested Change: Consider starting with a smaller value: for instance, changing t = 0.001 instead of t = 1. 3. Evaluating the Line Search Technique Implementing an effective line search is vital for convergence. The current approach in the provided code employs a fixed ratio for reducing t, which may not always be ideal. It can be beneficial to explore alternative line search methods or leverage existing libraries: Recommended Library Usage: Python's SciPy library provides efficient optimization functions that can greatly simplify your task. Utilize the scipy.optimize.minimize() function to minimize the target function without dealing with custom implementations. Example Implementation: Here's a modified implementation utilizing SciPy: [[See Video to Reveal this Text or Code Snippet]] 4. Simplifying Function Definitions Lastly, revisiting the function definitions can reduce complexity and potential errors. Although lambda functions provide conciseness, they may not be necessary. Consider adopting regular function definitions for clarity and ease of debugging. Conclusion By methodically addressing the challenges faced in your gradient descent implementation, you can significantly improve the effectiveness of your optimization routine. By adjusting the step size, leveraging existing library optimizations, and maintaining clear function definitions, you'll be able to achieve better results efficiently. If you find that line search tactics are vital to your approach, consider exploring the line_search method from SciPy. Happy coding, and may your gradient descent implementation move smoothly from here onward!