AttributeError: 'str' object has no attribute 'set_params' when tuning a boosted classifier

### Describe the bug

Using `GridSearchCV` or `RandomizedSearchCV` to perform parameters tuning on an `AdaBoostClassifier`, the model doesn't fit when `base_estimator__`  parameters are searched, no matter what the base estimator is.

### Steps/Code to Reproduce

```python
from sklearn.datasets import load_iris
from sklearn.model_selection import RandomizedSearchCV, GridSearchCV

from sklearn.ensemble import AdaBoostClassifier
from sklearn.tree import DecisionTreeClassifier, ExtraTreeClassifier


X, y = load_iris(as_frame=True, return_X_y=True)
ada_base_estimator = ExtraTreeClassifier() # change the weak classifier here. 
ada = AdaBoostClassifier(ada_base_estimator)

model_params = {
    #'n_estimators': loguniform_int(50, 1000), # [50, 75, 100, 150, 200, 250, 500]
    #'learning_rate' : loguniform(0.0001, 10),
    #'base_estimator__class_weight': [{0:2,1:1}, {0:3,1:1}, {0:5,1:1}]
    'base_estimator__min_samples_split': [2, 4, 6], # 
}


clf = GridSearchCV(ada, model_params, cv=5,  
                scoring='balanced_accuracy') 
best_model = clf.fit(X, y)
```

### Expected Results

No error thrown.

_Note:_
The error isn't thrown when only the parameters of the adaboost are specified (i.e. `learning_rate` and `n_estimators`)

### Actual Results

```python
---------------------------------------------------------------------------

AttributeError                            Traceback (most recent call last)

[<ipython-input-3-2ade04b86dfd>](https://localhost:8080/#) in <module>
     16 clf = GridSearchCV(ada, model_params, cv=5,  
     17                 scoring='balanced_accuracy') # 
---> 18 best_model = clf.fit(X, y)

12 frames

[/usr/local/lib/python3.8/dist-packages/sklearn/model_selection/_search.py](https://localhost:8080/#) in fit(self, X, y, groups, **fit_params)
    873                 return results
    874 
--> 875             self._run_search(evaluate_candidates)
    876 
    877             # multimetric is determined here because in the case of a callable

[/usr/local/lib/python3.8/dist-packages/sklearn/model_selection/_search.py](https://localhost:8080/#) in _run_search(self, evaluate_candidates)
   1387     def _run_search(self, evaluate_candidates):
   1388         """Search all candidates in param_grid"""
-> 1389         evaluate_candidates(ParameterGrid(self.param_grid))
   1390 
   1391 

[/usr/local/lib/python3.8/dist-packages/sklearn/model_selection/_search.py](https://localhost:8080/#) in evaluate_candidates(candidate_params, cv, more_results)
    820                     )
    821 
--> 822                 out = parallel(
    823                     delayed(_fit_and_score)(
    824                         clone(base_estimator),

[/usr/local/lib/python3.8/dist-packages/joblib/parallel.py](https://localhost:8080/#) in __call__(self, iterable)
   1083             # remaining jobs.
   1084             self._iterating = False
-> 1085             if self.dispatch_one_batch(iterator):
   1086                 self._iterating = self._original_iterator is not None
   1087 

[/usr/local/lib/python3.8/dist-packages/joblib/parallel.py](https://localhost:8080/#) in dispatch_one_batch(self, iterator)
    899                 return False
    900             else:
--> 901                 self._dispatch(tasks)
    902                 return True
    903 

[/usr/local/lib/python3.8/dist-packages/joblib/parallel.py](https://localhost:8080/#) in _dispatch(self, batch)
    817         with self._lock:
    818             job_idx = len(self._jobs)
--> 819             job = self._backend.apply_async(batch, callback=cb)
    820             # A job can complete so quickly than its callback is
    821             # called before we get here, causing self._jobs to

[/usr/local/lib/python3.8/dist-packages/joblib/_parallel_backends.py](https://localhost:8080/#) in apply_async(self, func, callback)
    206     def apply_async(self, func, callback=None):
    207         """Schedule a func to be run"""
--> 208         result = ImmediateResult(func)
    209         if callback:
    210             callback(result)

[/usr/local/lib/python3.8/dist-packages/joblib/_parallel_backends.py](https://localhost:8080/#) in __init__(self, batch)
    595         # Don't delay the application, to avoid keeping the input
    596         # arguments in memory
--> 597         self.results = batch()
    598 
    599     def get(self):

[/usr/local/lib/python3.8/dist-packages/joblib/parallel.py](https://localhost:8080/#) in __call__(self)
    286         # change the default number of processes to -1
    287         with parallel_backend(self._backend, n_jobs=self._n_jobs):
--> 288             return [func(*args, **kwargs)
    289                     for func, args, kwargs in self.items]
    290 

[/usr/local/lib/python3.8/dist-packages/joblib/parallel.py](https://localhost:8080/#) in <listcomp>(.0)
    286         # change the default number of processes to -1
    287         with parallel_backend(self._backend, n_jobs=self._n_jobs):
--> 288             return [func(*args, **kwargs)
    289                     for func, args, kwargs in self.items]
    290 

[/usr/local/lib/python3.8/dist-packages/sklearn/utils/fixes.py](https://localhost:8080/#) in __call__(self, *args, **kwargs)
    115     def __call__(self, *args, **kwargs):
    116         with config_context(**self.config):
--> 117             return self.function(*args, **kwargs)
    118 
    119 

[/usr/local/lib/python3.8/dist-packages/sklearn/model_selection/_validation.py](https://localhost:8080/#) in _fit_and_score(estimator, X, y, scorer, train, test, verbose, parameters, fit_params, return_train_score, return_parameters, return_n_test_samples, return_times, return_estimator, split_progress, candidate_progress, error_score)
    672             cloned_parameters[k] = clone(v, safe=False)
    673 
--> 674         estimator = estimator.set_params(**cloned_parameters)
    675 
    676     start_time = time.time()

[/usr/local/lib/python3.8/dist-packages/sklearn/base.py](https://localhost:8080/#) in set_params(self, **params)
    215 
    216         for key, sub_params in nested_params.items():
--> 217             valid_params[key].set_params(**sub_params)
    218 
    219         return self

AttributeError: 'str' object has no attribute 'set_params'
```

### Versions

```shell
System:
    python: 3.8.10 (default, Nov 14 2022, 12:59:47)  [GCC 9.4.0]
executable: /usr/bin/python3
   machine: Linux-5.10.147+-x86_64-with-glibc2.29

Python dependencies:
      sklearn: 1.2.0
          pip: 22.0.4
   setuptools: 57.4.0
        numpy: 1.21.6
        scipy: 1.7.3
       Cython: 0.29.33
       pandas: 1.3.5
   matplotlib: 3.2.2
       joblib: 1.2.0
threadpoolctl: 3.1.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: /usr/local/lib/python3.8/dist-packages/numpy.libs/libopenblasp-r0-2d23e62b.3.17.so
        version: 0.3.17
threading_layer: pthreads
   architecture: Haswell
    num_threads: 2

       user_api: openmp
   internal_api: openmp
         prefix: libgomp
       filepath: /usr/local/lib/python3.8/dist-packages/scikit_learn.libs/libgomp-a34b3233.so.1.0.0
        version: None
    num_threads: 2

       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: /usr/local/lib/python3.8/dist-packages/scipy.libs/libopenblasp-r0-8b9e111f.3.17.so
        version: 0.3.17
threading_layer: pthreads
   architecture: Haswell
    num_threads: 2
```

**IMPORTANT NOTE**:
This error isn't present on a previous version of scikit-learn (1.0.2) where the code posted works perfectly fine.

COMMENT:
`base_estimator` was renamed to `estimator` in v1.2. We are currently going through a deprecation cycle, but we missed the use case in `set_params`. The quick fix is to update the search parameters:

```python
model_params = {
    "estimator__min_samples_split": [2, 4, 6], # 
}
```

Labels: Bug