[DOC] add missing torch entries in README and documentation (#239)

## Description
Added the missing `torch` integration entries in the README feature
table and created a full example page for TorchExperiment, following the
pattern of existing sklearn/sktime integrations.

## Related Issues
Fixes #211

## Type of Change
- [x] `[DOC]` - Documentation changes

## How was this solved?
- Added `torch` entry to the integrations table in
examples/integrations/README.md
- Created torch_experiment_example.py with a working example using
TorchExperiment+ `HillClimbing` optimizer
- Added a "PyTorch Lightning Integration" section in the Sphinx docs
(docs/source/examples/integrations.rst)
- Updated the README feature table's third column to "Problems &
Experiments" as suggested in the issue

## Checklist
- [x] PR title includes appropriate tag: `[BUG]`, `[ENH]`, `[DOC]` or
`[MNT]`
- [x] Linked to related issue (if applicable)
- [x] Code passes `make check` (lint, format, isort)
- [x] Tests added/updated for changes (if applicable)
- [x] Documentation updated (if applicable)

## Testing
The new example is auto-discovered by examples/test_examples.py and
passes.

---------

Co-authored-by: Abhishek <abhishekup082gmail.com@Abhisheks-MacBook-Air.local>

Author: Abhishek9639

docs/source/examples/integrations.rst

@@ -33,6 +33,31 @@ For time series forecasting and classification with sktime:
        pip install hyperactive[sktime-integration]
 
 
+PyTorch Lightning Integration
+-----------------------------
+
+For deep learning hyperparameter optimization with PyTorch Lightning:
+
+.. list-table::
+   :header-rows: 1
+   :widths: 30 70
+
+   * - Use Case
+     - Example
+   * - PyTorch Lightning Experiment
+     - `torch_experiment_example.py <https://github.com/SimonBlanke/Hyperactive/blob/master/examples/integrations/torch_experiment_example.py>`_
+
+.. note::
+
+   PyTorch Lightning integration requires additional dependencies:
+
+   .. code-block:: bash
+
+       pip install hyperactive[all_extras]
+
+   or install ``torch`` and ``lightning`` separately.
+
+
 Installing Extras
 -----------------
 

examples/integrations/torch_experiment_example.py

@@ -0,0 +1,111 @@
+"""Example: Hyperparameter tuning with TorchExperiment and PyTorch Lightning.
+
+This example demonstrates how to use the TorchExperiment class to
+optimize hyperparameters of a PyTorch Lightning model using Hyperactive.
+"""
+
+import lightning as L
+import numpy as np
+import torch
+from torch import nn
+from torch.utils.data import DataLoader
+
+from hyperactive.experiment.integrations import TorchExperiment
+from hyperactive.opt.gfo import HillClimbing
+
+
+# 1. Define a Lightning Module
+class SimpleLightningModule(L.LightningModule):
+    """Simple classification model for demonstration."""
+
+    def __init__(self, input_dim=10, hidden_dim=16, lr=1e-3):
+        super().__init__()
+        self.save_hyperparameters()
+        self.model = nn.Sequential(
+            nn.Linear(input_dim, hidden_dim),
+            nn.ReLU(),
+            nn.Linear(hidden_dim, 2),
+        )
+        self.lr = lr
+
+    def forward(self, x):
+        """Forward pass."""
+        return self.model(x)
+
+    def training_step(self, batch, batch_idx):
+        """Training step."""
+        x, y = batch
+        y_hat = self(x)
+        loss = nn.functional.cross_entropy(y_hat, y)
+        self.log("train_loss", loss)
+        return loss
+
+    def validation_step(self, batch, batch_idx):
+        """Validate a single batch."""
+        x, y = batch
+        y_hat = self(x)
+        val_loss = nn.functional.cross_entropy(y_hat, y)
+        self.log("val_loss", val_loss, on_epoch=True)
+        return val_loss
+
+    def configure_optimizers(self):
+        """Configure optimizers."""
+        return torch.optim.Adam(self.parameters(), lr=self.lr)
+
+
+# 2. Define a DataModule
+class RandomDataModule(L.LightningDataModule):
+    """Random data module for demonstration."""
+
+    def __init__(self, batch_size=32):
+        super().__init__()
+        self.batch_size = batch_size
+
+    def setup(self, stage=None):
+        """Set up train and validation datasets."""
+        dataset = torch.utils.data.TensorDataset(
+            torch.randn(200, 10),
+            torch.randint(0, 2, (200,)),
+        )
+        self.train, self.val = torch.utils.data.random_split(dataset, [160, 40])
+
+    def train_dataloader(self):
+        """Return training dataloader."""
+        return DataLoader(self.train, batch_size=self.batch_size)
+
+    def val_dataloader(self):
+        """Return validation dataloader."""
+        return DataLoader(self.val, batch_size=self.batch_size)
+
+
+# 3. Create the TorchExperiment
+datamodule = RandomDataModule(batch_size=16)
+datamodule.setup()
+
+experiment = TorchExperiment(
+    datamodule=datamodule,
+    lightning_module=SimpleLightningModule,
+    trainer_kwargs={
+        "max_epochs": 3,
+        "enable_progress_bar": False,
+        "enable_model_summary": False,
+        "logger": False,
+    },
+    objective_metric="val_loss",
+)
+
+# 4. Define search space and optimizer
+search_space = {
+    "hidden_dim": [16, 32, 64, 128],
+    "lr": np.logspace(-4, -1, 10).tolist(),
+}
+
+optimizer = HillClimbing(
+    search_space=search_space,
+    n_iter=5,
+    experiment=experiment,
+)
+
+# 5. Run optimization
+best_params = optimizer.solve()
+print(f"Best params: {best_params}")