【Hackathon No.13】 (#33)

* add rfc of CyclicLR api

* fix typo

* update rfc of CyclicLR api

rfcs/APIs/20220314_api_design_for_CyclicLR.md

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+# paddle.optimizer.lr.CyclicLR设计文档
+
+| API名称                                                      | paddle.optimizer.lr.CyclicLR        |
+| ------------------------------------------------------------ | ----------------------------------- |
+| 提交作者<input type="checkbox" class="rowselector hidden">   | Asthestarsfalll                     |
+| 提交时间<input type="checkbox" class="rowselector hidden">   | 2022-03-14                          |
+| 版本号                                                       | V1.0                                |
+| 依赖飞桨版本<input type="checkbox" class="rowselector hidden"> | v2.2.0                              |
+| 文件名                                                       | 20220314_design_for_CyclicLR.md<br> |
+
+# 一、概述
+
+## 1、相关背景
+
+CyclicLR最早在论文[Cyclical Learning Rates for Training Neural Networks](https://arxiv.org/abs/1506.01186)中提出，它控制学习率以固定周期在base_lr和max_lr之间变化，它的调整是以batch.step进行的，同时，它还有3种内置的波幅调整策略：“triangular”、“triangular2”、“exp_range”。
+
+## 2、功能目标
+
+在 Paddle 框架中，新增 CyclicLR 优化调度器，调用路径为：[paddle.optimizer.lr](http://paddle.optimizer.lr/).CyclicLR。
+
+## 3、意义
+飞桨支持CyclicLR优化调度器
+
+# 二、飞桨现状
+
+目前paddle缺少相关功能实现。
+
+# 三、业内方案调研
+
+## Pytorch
+
+Pytorch中有API``，以及对应的`torch.optim.lr_scheduler.``CyclicLR(optimizer, base_lr, max_lr, step_size_up=2000, step_size_down=None,mode='triangular',gamma=1.,scale_fn=None,scale_mode='cycle',cycle_momentum=True,base_momentum=0.8, max_momentum=0.9, last_epoch=-1, verbose=False)`.
+
+在pytorch中，介绍为：
+
+```
+Sets the learning rate of each parameter group according to cyclical learning rate policy (CLR). The policy cycles the learning rate between two boundaries with a constant frequency, as detailed in the paper Cyclical Learning Rates for Training Neural Networks. The distance between the two boundaries can be scaled on a per-iteration or per-cycle basis.
+
+Cyclical learning rate policy changes the learning rate after every batch. step should be called after a batch has been used for training.
+
+This class has three built-in policies, as put forth in the paper:
+
+“triangular”: A basic triangular cycle without amplitude scaling.
+
+“triangular2”: A basic triangular cycle that scales initial amplitude by half each cycle.
+
+“exp_range”: A cycle that scales initial amplitude by \text{gamma}^{\text{cycle iterations}}gamma 
+cycle iterations at each cycle iteration.
+
+This implementation was adapted from the github repo: bckenstler/CLR
+```
+
+### 实现方法
+
+在实现方法上, Pytorch是直接通过python实现的，[代码位置](https://github.com/pytorch/pytorch/blob/master/torch/optim/lr_scheduler.py#L994)。
+
+核心代码为：
+
+```python
+def get_lr(self):
+    """Calculates the learning rate at batch index. This function treats
+        `self.last_epoch` as the last batch index.
+
+        If `self.cycle_momentum` is ``True``, this function has a side effect of
+        updating the optimizer's momentum.
+        """
+
+    if not self._get_lr_called_within_step:
+        warnings.warn("To get the last learning rate computed by the scheduler, "
+                      "please use `get_last_lr()`.", UserWarning)
+
+        cycle = math.floor(1 + self.last_epoch / self.total_size)
+        x = 1. + self.last_epoch / self.total_size - cycle
+        if x <= self.step_ratio:
+            scale_factor = x / self.step_ratio
+        else:
+			scale_factor = (x - 1) / (self.step_ratio - 1)
+
+		lrs = []
+		for base_lr, max_lr in zip(self.base_lrs, self.max_lrs):
+			base_height = (max_lr - base_lr) * scale_factor
+			if self.scale_mode == 'cycle':
+				lr = base_lr + base_height * self.scale_fn(cycle)
+			else:
+				lr = base_lr + base_height * self.scale_fn(self.last_epoch)
+				lrs.append(lr)
+
+         if self.cycle_momentum:
+         momentums = []
+         for base_momentum, max_momentum in zip(self.base_momentums, self.max_momentums):
+			base_height = (max_momentum - base_momentum) * scale_factor
+			if self.scale_mode == 'cycle':
+				momentum = max_momentum - base_height * self.scale_fn(cycle)
+			else:
+				momentum = max_momentum - base_height * self.scale_fn(self.last_epoch)
+			momentums.append(momentum)
+			for param_group, momentum in zip(self.optimizer.param_groups, momentums):
+				param_group['momentum'] = momentum
+
+		return lrs
+```
+
+
+
+## 其他实现
+
+https://github.com/bckenstler/CLR
+
+该仓库使用tensorflow2进行了实现
+
+介绍为：
+
+```
+A cyclical learning rate is a policy of learning rate adjustment that increases the learning rate off a base value in a cyclical nature. Typically the frequency of the cycle is constant, but the amplitude is often scaled dynamically at either each cycle or each mini-batch iteration.
+```
+
+
+
+### 实现方法
+
+直接使用python，[代码位置](https://github.com/bckenstler/CLR/blob/master/clr_callback.py#L5)
+
+核心代码为：
+
+```python
+def clr(self):
+	cycle = np.floor(1+self.clr_iterations/(2*self.step_size))
+	x = np.abs(self.clr_iterations/self.step_size - 2*cycle + 1)
+	if self.scale_mode == 'cycle':
+		return self.base_lr + (self.max_lr-self.base_lr)*np.maximum(0, (1-x))*self.scale_fn(cycle)
+	else:
+		return self.base_lr + (self.max_lr-self.base_lr)*np.maximum(0, (1-					x))*self.scale_fn(self.clr_iterations)
+```
+
+# 四、对比分析
+
+Pytorch官方文档中提到参考了上述tensorflow仓库进行修改实现，Pytorch与上述tensorflow仓库的主要区别如下：
+
+- 在该tensorflow仓库中，参数`step_size `表示从`base_lr`上升到`max_lr`（从`max_lr`下降到`base_lr`）的所需步数，而Pytorch使用两个参数`step_size_up`和`step_size_down`来分别表示学习率上升和下降所需的步数；
+- 引入动量衰减策略。
+
+其余实现基本相同，且Pytorch代码更易理解，故参考Pytorch进行实现。
+
+# 五、方案设计
+
+## 命名与参数设计
+
+API设计为`paddle.optimizer.lr.CyclicLR(base_learning_rate,max_learning_rate,step_size_up,step_size_down, mode='triangular',gamma=1.,scale_fn=None,scale_mode='cycle',last_epoch=-1,verbose=False)`
+
+去除了Pytorch中`momentum`的相关参数。
+
+同时，为了保持与paddle其他lrscheduler相关的api保持一致，将`base_lr`修改为`base_learning_rate`，`max_lr`修改为`max_learning_rate`。
+
+## 底层OP设计
+
+直接使用python实现，不再单独设计OP。
+
+## API实现方案
+
+主要参考Pytorch进行实现，实现位置为`paddle/optimizer/lr.py`。
+
+# 六、测试和验收的考量
+
+测试考虑的case如下：
+
+- 动态图，静态图，与numpy的结果保持一致；
+- 错误检查：`step_size_up`和 `step_size_down`数值小于等于0时能正确抛出错误；
+- 错误检查：`scale_mode`不在可选范围内时能正确抛出异常；
+
+# 七、可行性分析及规划排期
+
+方案仅使用python实现，工期上可以满足在当前版本周期内开发完成。
+
+# 八、影响面
+
+为独立新增API，对其他模块没有影响