吴恩达机器学习课程:Gradient Descent For Linear Regression

Gradient Descent For Linear Regression

Which of the following are true statements? Select all that apply.

• To make gradient descent converge, we must slowly decrease α over time.
  错误。一般来说越接近局部最低时，曲线的导数越小，梯度下降的幅度就越小（即梯度下降会自动选择较小的幅度）。所以不一定要动态调整α（学习率）的值。
• Gradient descent is guaranteed to find the global minimum for any function J(θ₀, θ₁)
  错误：对一个代价函数J(θ₀, θ₁)，若它拥有处在局部最优解的初始值θ₀, θ₁，则在这一点的导数为0，此时采取梯度下降的算法将无法得到全局最优解。
• Gradient descent can converge even if α is kept fixed. (But α cannot be too large, or else it may fail to converge.)
  正确。原因同第一项。
• For the specific choice of cost function J(θ₀, θ₁)used in linear regression, there are no local optima (other than the global optimum).
  正确。对一个特定的初始值，不能得到代价函数的局部最优解，持续尝试不同的参数组合才能得到局部最优解（或全局最优解），尝试完所有参数组合后才能确定全局最优解。