update and expand scientific docstrings for optimizer, scheduler, trainer

- Expanded module-level and function/class docstrings in optimizer.py, scheduler.py, and trainer.py
- Described mathematical foundations, theoretical motivations, and provided detailed usage examples for students
- All docstrings in Russian, clear scientific style

test(training): add comprehensive tests for optimizer, scheduler, and trainer modules

- Added new test files for get_optimizer, get_linear_schedule_with_warmup, and Trainer
- Tests cover parameter handling, edge cases, and expected learning dynamics (lr schedules and loss behavior)
- Trainer now logs average epoch losses to self.loss_history for testability and analysis

refactor(training/trainer): log epoch loss to loss_history for downstream analysis and tests

BREAKING CHANGE: Trainer.loss_history is a new attribute consolidating average losses per epoch, enabling robust learning dynamics assertions in tests

llm/tests/training/test_scheduler.py

@@ -0,0 +1,62 @@
+import torch
+import torch.nn as nn
+from llm.training.scheduler import get_linear_schedule_with_warmup
+from llm.training.optimizer import get_optimizer
+
+class DummyModel(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.linear = nn.Linear(2, 2)
+
+def test_scheduler_warmup_and_decay():
+    model = DummyModel()
+    base_lr = 0.1
+    warmup_steps = 5
+    total_steps = 20
+    optimizer = get_optimizer(model, lr=base_lr, optimizer_type="sgd")
+    scheduler = get_linear_schedule_with_warmup(
+        optimizer, num_warmup_steps=warmup_steps, num_training_steps=total_steps)
+
+    lrs = [optimizer.param_groups[0]['lr']]  # lr до первого .step()
+    for _ in range(total_steps):
+        optimizer.step()
+        scheduler.step()
+        lrs.append(optimizer.param_groups[0]['lr'])
+
+    # Проверяем warmup: lr должен расти линейно в первых warmup_steps (начиная с шага 1)
+    for i in range(warmup_steps + 1):
+        expected = base_lr * min(i, warmup_steps) / max(1, warmup_steps)
+        assert abs(lrs[i] - expected) < 1e-6, f"Warmup step {i}: lr={lrs[i]}, expected={expected}"
+    # Проверяем decay: после warmup lr затухает
+    for i in range(warmup_steps + 1, total_steps + 1):
+        expected = base_lr * max(0.0, (total_steps - (i - 0)) / max(1, total_steps - warmup_steps))
+        assert abs(lrs[i] - expected) < 1e-6, f"Decay step {i}: lr={lrs[i]}, expected={expected}"
+    assert lrs[-1] == 0.0
+
+def test_scheduler_no_warmup():
+    model = DummyModel()
+    base_lr = 0.1
+    warmup_steps = 0
+    total_steps = 10
+    optimizer = get_optimizer(model, lr=base_lr, optimizer_type="adam")
+    scheduler = get_linear_schedule_with_warmup(
+        optimizer, num_warmup_steps=warmup_steps, num_training_steps=total_steps)
+    lrs = [optimizer.param_groups[0]['lr']]
+    for _ in range(total_steps):
+        optimizer.step()
+        scheduler.step()
+        lrs.append(optimizer.param_groups[0]['lr'])
+
+    for i in range(total_steps + 1):
+        expected = base_lr * max(0.0, (total_steps - i) / max(1, total_steps - warmup_steps))
+        assert abs(lrs[i] - expected) < 1e-6, f"Step {i}: lr={lrs[i]}, expected={expected}"
+    assert lrs[-1] == 0.0
+
+def test_scheduler_full_decay_to_zero():
+    model = DummyModel()
+    optimizer = get_optimizer(model, lr=1.0, optimizer_type="adamw")
+    scheduler = get_linear_schedule_with_warmup(optimizer, num_warmup_steps=2, num_training_steps=2)
+    scheduler.step()
+    scheduler.step()
+    for param_group in optimizer.param_groups:
+        assert param_group['lr'] == 0.0