introduce "nudging" function for learning rate

ultralytics/engine/trainer.py

@@ -209,6 +209,13 @@ class BaseTrainer:
             self.lf = one_cycle(1, self.args.lrf, self.epochs)  # cosine 1->hyp['lrf']
         else:
             self.lf = lambda x: max(1 - x / self.epochs, 0) * (1.0 - self.args.lrf) + self.args.lrf  # linear
+            # NOTE for testing
+            # lambda x: max(1 - x / epochs, 0) * (1.0 - lrf) + lrf
+            self.lf = [self.lf(n) for n in range(self.epochs)]
+            
+            # NOTE need to figure out how to make this work, especially for stagnating loss
+            nudge_lr(self.lf, ...)
+
         self.scheduler = optim.lr_scheduler.LambdaLR(self.optimizer, lr_lambda=self.lf)
 
     def _setup_ddp(self, world_size):
@@ -772,3 +779,30 @@ class BaseTrainer:
             f'{len(g[1])} weight(decay=0.0), {len(g[0])} weight(decay={decay}), {len(g[2])} bias(decay=0.0)'
         )
         return optimizer
+
+def nudge_lr(series:list[float], start:int, end:int, amplitude:float) -> list[float]:
+    """
+    Adds a decaying 'nudge' in a linearly decreasing learning rate series to help overcome stagnating loss.
+
+    Args:
+        series (list[float]): The input series of values.
+        start (int): The starting index of the range to nudge.
+        end (int): The ending index of the range to nudge.
+        amplitude (float): The amplitude of the modified bump to add.
+
+    Returns:
+        list[float]: The modified series with the nudge applied.
+    """
+    _series = [s for s in series.copy()]  # avoid inplace modification
+    D = end - start
+    s_half = start + D // 2
+    s1, s2 = slice(start, s_half),  slice(s_half, end)
+    
+    # Calculate the values for the augmentation
+    y = [amplitude * (1 - math.exp(-2 * (v / (D)) ** 2)) for v in range(D)]
+    
+    # Insert new values
+    _series[s1] = [v + y[e - start] for e,v in enumerate(_series[s1], start=start)]
+    _series[s2] = [v + y[end - e - 1] for e,v in enumerate(_series[s2], start=s_half)]
+    
+    return _series