I'm trying to solve the optimization problem

$\min_x \frac{1}{n} \sum_{i=1}^n f_i(x)$

where $f_i$ are (strongly) convex, smooth, lower semi-continuous, etc. However, I am not able to do conventional stochastic gradient descent (SGD), because the $f_i$ are distributed in multiple machines. I understand there are several ways to handle this situation, but suppose I do SGD in a deterministic cyclic way:

k = 1;

while 1

```
for i from 1 to n
$x_{k+1} = x_k - \eta_k * \nabla f_i(x)$;
k = k + 1;
end
```

end

Do whatever you like on the step size $\eta_k$.

**Question**: is there any rate of convergence in terms of $k$? A possible result could be like:
for $x_k$ to be an $\epsilon$ accurate solution, $k$ needs to be at least $\frac{nC}{\epsilon^2}$,
where the constant $C$ can be the strong convexity modulus of $f_i$, or Lipstchitz continuous constant of $f_i$ or its gradient, or norm of $\nabla f_i$, etc.

I am aware of results for cyclic coordinate descent: On the Finite Time Convergence of Cyclic Coordinate Descent Methods. Ankan Saha and Ambuj Tewari, Siam Journal of Optimization, 23(1):576-601, 2013.

Thanks in advance.