Diagnostic information for the optimization algorithm

[roliveira]

Is your feature request related to a problem? Please describe.

When running an optimization experiment, the optimization algorithm may occasionally propose a step size that either violates user‑defined bounds or triggers back-tracking. This can occur at any batch. Before introducing any specific adjustments to the optimization experiment, we need to diagnostic the results and pinpoint the root causes of these large update proposals.

Describe the solution you'd like To be able to make an informed decision about the quality of the optimization experiment, and propose adjustments to improve my results. I'd like to have an informative and standarized output for:

• the gradient estimation
• the line search
• bound and backtracking conditions

Describe alternatives you've considered N/A

Additional context Once we can reliably pinpoint the culprit (e.g. poor curvature estimate, inedequate step sizing, poor perturbation sampling, etc.), we can open follow‑on issues to propose mitigations.