Research map / Optimization / Nonconvex and smooth optimization
First-Order Algorithms Converge Faster than $O(1/k)$ on Convex Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Analyze fixed-step gradient descent with step size in (0,1/L] without bounded level set assumption | gradient descent on convex L-smooth problems · theory | convergence rate of f(x_k)-f*: O(1/k) to o(1/k) | Helped |
| Extend step sizes to range (0,(2-γ)/L) and line-search conditions | gradient descent · theory | convergence rate of f(x_k)-f*: O(1/k) to o(1/k) | Helped |
| Arbitrary sampling stochastic coordinate descent analyzed without bounded level set | stochastic coordinate descent · theory | convergence rate of expected f(x_k)-f*: O(1/k) to o(1/k) | Helped |
| Analysis of short-step and line-search proximal gradient on regularized problems | proximal gradient · theory | convergence rate of F(x_k)-F*: O(1/k) to o(1/k) | Helped |
| Analysis of proximal coordinate descent with arbitrary sampling and separable regularizer | proximal coordinate descent · theory | convergence rate of expected F(x_k)-F*: O(1/k) to o(1/k) | Helped |
| Tightness example f(x)=x^p with fixed step gradient descent | gradient descent, coordinate and proximal methods without line search · one-dimensional f(x)=x^p | convergence rate | No clear effect |
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