gradientpõhise

Gradient-based optimization is a class of algorithms used in machine learning and optimization problems to minimize or maximize a function. These algorithms are particularly useful when the function is differentiable, meaning it has a gradient that can be computed. The gradient is a vector of partial derivatives that points in the direction of the steepest ascent of the function. By following the negative of the gradient, gradient-based optimization algorithms can efficiently find the minimum of a function.

One of the most well-known gradient-based optimization algorithms is gradient descent. In gradient descent, the algorithm starts with an initial guess for the minimum and iteratively updates the guess by moving in the direction of the negative gradient. The size of the step taken in each iteration is determined by a learning rate parameter. If the learning rate is too small, the algorithm may converge slowly. If it is too large, the algorithm may overshoot the minimum and fail to converge.

There are several variants of gradient descent, including stochastic gradient descent (SGD), mini-batch gradient descent, and momentum-based methods. SGD updates the parameters using a single training example at a time, which can be more efficient than using the entire dataset. Mini-batch gradient descent uses a subset of the training data to compute the gradient, balancing between the efficiency of SGD and the stability of batch gradient descent. Momentum-based methods add a term to the update rule that depends on the previous updates, which can help the algorithm escape local minima and converge more quickly.

Gradient-based optimization algorithms are widely used in machine learning because they can handle large-scale problems and are relatively easy to implement. However, they can be sensitive to the choice of learning rate and may struggle with non-convex functions. In such cases, other optimization algorithms, such as those based on second-order derivatives or evolutionary algorithms, may be more appropriate.