```markdown
### Image Description

The image presents a conclusion regarding the number of iterations needed until \( f(x) - p^\star \leq \epsilon \) is bounded above by the expression:

\[ 
\frac{f(x^{(0)}) - p^\star}{\gamma} + \log_2 \log_2 (\epsilon_0 / \epsilon) 
\]

#### Key Points:
- **Constants**: 
  - \( \gamma \) and \( \epsilon_0 \) depend on \( m \), \( L \), and \( x^{(0)} \).
- **Second Term**: 
  - It is small (around the order of 6) and nearly constant for practical purposes.
- **Unknowns in Practice**: 
  - Constants \( m \), \( L \), and hence \( \gamma \), \( \epsilon_0 \) are usually unknown.
- **Qualitative Insight**: 
  - Provides understanding of convergence properties, explaining two algorithm phases.

The slide is from a lecture by A. d'Aspremont on Convex Optimization M2, slide 22 of 53.
```