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Gradient Descent & Local Optima

Task Description: Gradient descent algorithm is widely used in machine learning optimisations. In this task, you can check the influence of initialisation, learning rate, and number of optimisation steps in obtaining the optimum.

Objective: Minimize $f(x)$ Update Rule: $x_{t+1} = x_t - \eta \nabla f(x_t)$

Initialization ($x_0$): 0

Learning Rate ($\eta$): 0.05

Optimization Steps: 20

Observe the trajectory arrows. Red indicates the path; the Cyan point represents the final converged state $\theta^*$.