# Robust QAOA Multi-Start Optimizer Check

This report checks whether the optimizer baseline is dominated by a single initial point.
For each graph/depth pair, 4 Nelder-Mead starts are evaluated with `maxiter=80`.
The selected multi-start optimizer row is the start with the highest ideal optimizer objective, then it is evaluated under the same noisy sweep as RA-QAOA.

## Robust vs Multi-Start Optimizer Summary

| depth | method | graph_count | mean_noisy_expected_cut | ci95_noisy_expected_cut | mean_success_probability | mean_noise_sensitivity | ci95_noise_sensitivity |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | multistart_optimizer | 60 | 8.743269 | 0.991982 | 0.131064 | 3.935351 | 0.272510 |
| 1 | robust | 60 | 7.676503 | 0.873080 | 0.096099 | 0.870598 | 0.206181 |
| 2 | multistart_optimizer | 60 | 9.311607 | 1.026264 | 0.247488 | 5.569979 | 0.399877 |
| 2 | robust | 60 | 7.750276 | 0.859378 | 0.127260 | 1.079351 | 0.232858 |

## p=2 Robust Minus Multi-Start Optimizer Deltas

| metric | graph_count | mean_delta_robust_minus_baseline | ci95_low | ci95_high | robust_better_rate |
| --- | --- | --- | --- | --- | --- |
| noise_sensitivity | 60 | -4.490628 | -4.999651 | -3.981605 | 1.000000 |
| noisy_expected_cut | 60 | -1.561331 | -1.738311 | -1.384351 | 0.000000 |
| success_probability | 60 | -0.120229 | -0.138023 | -0.102435 | 0.016667 |

## Interpretation

If multi-start keeps the same pattern as single-start, the conclusion is not an artifact of one initial point.
The performance optimizer remains a useful upper-performance comparison, while RA-QAOA remains a stability-oriented selector.