Lecture Note
University
Stanford UniversityCourse
CS229 | Machine LearningPages
2
Academic year
2023
anon
Views
24
Convergence in Gradient Descent: An Understanding In machine learning, gradient descent is a critical optimization process that aids in costfunction minimization and model performance. But how do you know whether it's operatingcorrectly? How do you tell if it's convergent and guiding you toward parameters that are nearthe cost function's global minimum? We will go into these issues in this post and discoverhow to spot a well-functioning gradient descent implementation. Gradient Descent: What Is It? An optimization technique called gradient descent aids in determining the minimum of acost function. The technique begins with a base set of parameters and iteratively reducesthese parameters to reduce the cost function. The cost function's negative gradient, or thedirection of the sharpest drop, is the direction in which the parameters are adjusted. Until thecost function achieves a minimum value, this process is repeated. Convergence and the Learning Curve A learning curve is a helpful tool for keeping track of the convergence of gradient descent.The cost function J, which is determined using the training set, and the value of J after eachgradient descent iteration are plotted on a learning curve. The cost J is on the vertical axiswhile the number of gradient descent iterations is on the horizontal axis. After each iteration,the cost J should go down if gradient descent is operating as intended. If J ever rises afterone cycle, either the learning rate Alpha was selected improperly—which typically indicatesthat Alpha is too large—or there may be a programming error. Looking at the learning curve is another method for ﬁguring out whether gradient descenthas converged. Gradient descent has more or less converged if the curve levels off andstops dropping. It is important to note that the number of gradient descent iterationsrequired to converge might vary signiﬁcantly between applications, making it challenging toanticipate in advance.
Selecting an Effective Learning Rate Alpha The gradient descent's convergence depends critically on the choice of the learning rateAlpha. It will take longer for the algorithm to converge if Alpha is too small, and it may neverconverge at all if Alpha is too large. Starting with a minimal value and gradually increasing ituntil the algorithm converges is a typical technique for choosing Alpha. A different approachis to grid search several Alpha values and choose the one that produces the best results. Test of Automatic Convergence An automatic convergence test is another method for determining when your model hasﬁnished training. When a speciﬁc stopping requirement is satisﬁed, such as a tiny change inthe cost function J or a slight change in the parameters, the convergence test halts thegradient descent iteration. It is practical to prevent performing gradient descent for too manyiterations by using the convergence test, which also conserves computer resources. Finally, knowing gradient descent convergence is crucial for enhancing model performance.You will be better able to select a descent learning rate Alpha and determine when yourmodel has ﬁnished training if you can identify what a well-running gradient descentimplementation looks like.
Checking Dradient Descent for Convergence
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