Twiddle is an algorithm that tries to find a good choice of parameters \(p\) for an algorithm \(\mathcal{A}\) that returns an error.

The algorithm is quite simple to implement. I guess gradient descent might be better for most cases, but Twiddle does not require any knowledge about the algorithm \(\mathcal{A}\) which might be a big advantage. And you don't have to calculate the gradient of high dimensional functions, which is nice, too.

## The algorithm

Here is some pythonic pseudo code. `A`

is an algorithm that returns an error.

```
# Choose an initialization parameter vector
p = [0, 0, 0]
# Define potential changes
dp = [1, 1, 1]
# Calculate the error
best_err = A(p)
threshold = 0.001
while sum(dp) > threshold:
for i in range(len(p)):
p[i] += dp[i]
err = A(p)
if err < best_err: # There was some improvement
best_err = err
dp[i] *= 1.1
else: # There was no improvement
p[i] -= 2 * dp[i] # Go into the other direction
err = A(p)
if err < best_err: # There was an improvement
best_err = err
dp[i] *= 1.05
else: # There was no improvement
p[i] += dp[i]
# As there was no improvement, the step size in either
# direction, the step size might simply be too big.
dp[i] *= 0.95
```

## See also

- Twiddle - CS373 Unit 5 - Udacity: Explanation of Twiddle by Sebastian Thrun
- Numerische Optimierung in Matlab mit Twiddle-Algorithmus (German)