docs: add lambda parameter documentation with examples

README.md

@@ -116,6 +116,27 @@ embedding = np.random.randn(1024)  # replace with real embedding
 result = router.route(embedding)
 ```
 
+### Adjusting Lambda (Cost-Accuracy Tradeoff)
+
+The `lambda` parameter controls the tradeoff between accuracy and cost:
+- **lambda → 1.0**: Minimize cost (routes to cheaper models)
+- **lambda → 0.0**: Maximize accuracy (routes to the best model regardless of cost)
+- **Default: 0.999** (strongly cost-sensitive, as used in our RouterArena submission)
+
+```python
+# Cost-sensitive (default, as submitted to RouterArena)
+router = R2Router.from_pretrained(path, lambda_val=0.999)
+
+# Balanced accuracy vs cost
+router = R2Router.from_pretrained(path, lambda_val=0.5)
+
+# Accuracy-first (ignores cost, always picks highest quality)
+router = R2Router.from_pretrained(path, lambda_val=0.0)
+
+# Override lambda per query
+result = router.route_text("Solve this integral", lambda_val=0.5)
+```
+
 ### Train from Scratch
 
 ```python