project_name=project_name,
    task_name=task_name,
    task_type=Task.TaskTypes.optimizer,
    reuse_last_task_id=False,
)

an_optimizer = HyperParameterOptimizer(
    base_task_id=base_task_id,
    hyper_parameters=[...],
        objective_metric_title="",
        objective_metric_series="",
        objective_metric_sign="max",
        optimizer_class=aSearchStrategy,
        execution_queue=execution_queue,
        spawn_project=None,
        save_top_k_tasks_only=None,
        max_iteration_per_job=1,
        total_max_jobs=max_jobs,
        max_number_of_concurrent_tasks=max_concurrent,
    )
    an_optimizer.start_locally()

Yes
But I want to verify how I can add a specific tag for each task run in the optimization task

What do you mean by verify? How are you currently running your HPO?

Hi @<1643060807786827776:profile|WorriedPeacock92> , you mean like this?
None