…ses (#3500)

## Typing Fixes for pyrefly errors ✅

### Original Issues (All Fixed)
- [x] Fix `_ExponentialLR.base_lrs` assignment type issue
(lr_finder.py:543)
- [x] Fix `_ExponentialLR.get_lr()` return type to match parent class
(lr_finder.py:545)
- [x] Fix `_ExponentialLR.get_lr()` list comprehension return type
(lr_finder.py:548)
- [x] Fix `_CosineAnnealingWarmRestarts.get_lr()` return type
(param_scheduler.py:900)
- [x] Fix `LRScheduler.get_param()` return type for single element
(param_scheduler.py:998)
- [x] Fix `LRScheduler.get_param()` return type for multiple elements
(param_scheduler.py:1000)

### Additional Improvements
- [x] Import `LRScheduler` directly from torch.optim.lr_scheduler (no
try/except)
- [x] Use `PyTorchLRScheduler` alias to avoid naming conflict with
ignite's LRScheduler
- [x] **Modernize ALL type hints to Python 3.10+ syntax in both files**:
  - `Union[A, B]` → `A | B`
  - `Optional[A]` → `A | None`
  - `List[T]` → `list[T]`
  - `Dict[K, V]` → `dict[K, V]`
  - `Tuple[T, ...]` → `tuple[T, ...]`

### Changes Made
1. **lr_finder.py**:
- Import: Removed try/except block, direct import as `from
torch.optim.lr_scheduler import LRScheduler as PyTorchLRScheduler`
- Class definition: Changed `class _ExponentialLR(_LRScheduler)` →
`class _ExponentialLR(PyTorchLRScheduler)`
   - Removed unused typing imports: `Dict`, `List`, `Optional`, `Union`
- Updated **all type hints throughout the entire file** to modern Python
3.10+ syntax

2. **param_scheduler.py**:
- Removed unused typing imports: `Dict`, `List`, `Optional`, `Union`,
`Tuple`
- Updated **all type hints throughout the entire file** to modern Python
3.10+ syntax
- Converted **50+ instances** of old typing syntax across the entire
file
- Line 872: `int | None` and `list[torch.Tensor | float]` for
`_CosineAnnealingWarmRestarts.get_lr()`
- Line 991: `torch.Tensor | float | list[torch.Tensor | float]` for
`LRScheduler.get_param()`

### Verification
- [x] Pyrefly check: All 6 original errors fixed, 0 errors in our files
- [x] Syntax validation: All files compile successfully
- [x] Code review: No issues found
- [x] Security scan (CodeQL): No vulnerabilities detected

### Result
All typing errors resolved with **comprehensive modernization of type
hints to Python 3.10+ syntax throughout both files**, following project
conventions established in PR #3497.

<!-- START COPILOT ORIGINAL PROMPT -->



<details>

<summary>Original prompt</summary>

> 
> ----
> 
> *This section details on the original issue you should resolve*
> 
> <issue_title>CI typing issue with
ignite/handlers/param_scheduler.py</issue_title>
> <issue_description>There is the following typing error revealed by
pyrefly:
> ```
> INFO Checking project configured at
`/home/runner/work/ignite/ignite/pyrefly.toml`
> ERROR `list[float]` is not assignable to attribute `base_lrs` with
type `list[Tensor | float]` [bad-assignment]
>    --> ignite/handlers/lr_finder.py:543:25
>     |
> 543 |         self.base_lrs = start_lrs
>     |                         ^^^^^^^^^
>     |
> ERROR Class member `_ExponentialLR.get_lr` overrides parent class
`_LRScheduler` in an inconsistent manner [bad-override]
>    --> ignite/handlers/lr_finder.py:545:9
>     |
> 545 |     def get_lr(self) -> List[float]:
>     |         ^^^^^^
>     |
> `_ExponentialLR.get_lr` has type `BoundMethod[_ExponentialLR, (self:
_ExponentialLR) -> list[float]]`, which is not assignable to
`BoundMethod[_ExponentialLR, (self: _ExponentialLR) -> list[Tensor |
float]]`, the type of `_LRScheduler.get_lr`
> ERROR Returned type `list[Tensor | Unknown]` is not assignable to
declared return type `list[float]` [bad-return]
>    --> ignite/handlers/lr_finder.py:548:16
>     |
> 548 | return [base_lr * (end_lr / base_lr) ** r for end_lr, base_lr in
zip(self.end_lrs, self.base_lrs)]
> |
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>     |
> ERROR Returned type `list[Tensor | float]` is not assignable to
declared return type `list[float]` [bad-return]
>    --> ignite/handlers/param_scheduler.py:900:16
>     |
> 900 |           return [
>     |  ________________^
> 901 | |             eta_min
> 902 | | + (base_lr - eta_min) * (1 + math.cos(math.pi *
self._lr_scheduler.T_cur / self._lr_scheduler.T_i)) / 2
> 903 | |             for base_lr in self._lr_scheduler.base_lrs
> 904 | |         ]
>     | |_________^
>     |
> ERROR Returned type `Tensor | float` is not assignable to declared
return type `float | list[float]` [bad-return]
>    --> ignite/handlers/param_scheduler.py:998:20
>     |
> 998 |             return lr_list[0]
>     |                    ^^^^^^^^^^
>     |
> ERROR Returned type `list[Tensor | float] | list[float]` is not
assignable to declared return type `float | list[float]` [bad-return]
>     --> ignite/handlers/param_scheduler.py:1000:20
>      |
> 1000 |             return lr_list
>      |                    ^^^^^^^
>      |
> Error: `list[float]` is not assignable to attribute `base_lrs` with
type `list[Tensor | float]`
> Error: Class member `_ExponentialLR.get_lr` overrides parent class
`_LRScheduler` in an inconsistent manner
> `_ExponentialLR.get_lr` has type `BoundMethod[_ExponentialLR, (self:
_ExponentialLR) -> list[float]]`, which is not assignable to
`BoundMethod[_ExponentialLR, (self: _ExponentialLR) -> list[Tensor |
float]]`, the type of `_LRScheduler.get_lr`
> Error: Returned type `list[Tensor | Unknown]` is not assignable to
declared return type `list[float]`
> Error: Returned type `list[Tensor | float]` is not assignable to
declared return type `list[float]`
> Error: Returned type `Tensor | float` is not assignable to declared
return type `float | list[float]`
> Error: Returned type `list[Tensor | float] | list[float]` is not
assignable to declared return type `float | list[float]`
>  INFO 6 errors (102 suppressed)
> Error: Process completed with exit code 1.
> ```</issue_description>
> 
> ## Comments on the Issue (you are @copilot in this section)
> 
> <comments>
> </comments>
> 


</details>



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- Fixes #3499

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Co-authored-by: copilot-swe-agent[bot] <[email protected]>
Co-authored-by: vfdev-5 <[email protected]>