For θ=4, gradient 6 and η=0.1, find the next gradient-descent parameter.
Answer and explanation
3.4
4−0.1×6=3.4.
Subjects
Optimization for ai
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Sample exercises
For L(w)=(w−2)², find the gradient at w=5.
Answer and explanation
6
2(w−2)=6.
What does subtracting a positive multiple of the gradient aim to do locally?
- Remove all data
- Always maximize loss
- Reduce the differentiable loss
- Guarantee a global optimum in any problem
Answer and explanation
Reduce the differentiable loss
The negative gradient is a local descent direction for sufficiently small steps.
Which can occur with an excessively large learning rate?
- Overshooting or divergence
- Guaranteed exact convergence in one step
- A negative dataset size
- Automatic data cleaning
Answer and explanation
Overshooting or divergence
Large steps can leave the local descent regime.
Why does a small gradient not always prove a global minimum?
Answer and explanation
It may indicate a local minimum, saddle, flat region or poor scaling. Global optimality needs stronger structure or analysis.
Credit stationary-point alternatives.
For f(w)=w², use central difference [f(2.1)−f(1.9)]/0.2. Find the result.
Answer and explanation
4
(4.41−3.61)/0.2=4.
Study notes
Gradient descent and learning-rate choices
Gradient descent uses θnew=θ−η∇L(θ) with a positive step size η. The negative gradient is locally downhill for a differentiable objective.
UniversityGradient descent and learning-rate choices · revision notes
Gradient descent uses θnew=θ−η∇L(θ) with a positive step size η. The negative gradient is locally downhill for a differentiable objective.
UniversityOne gradient-descent parameter update
The gradient and learning rate belong to the specified loss and parameterization.
UniversityOne gradient-descent parameter update · formula reference
The gradient and learning rate belong to the specified loss and parameterization.
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