**ProxylessNet-CPU** is an image model learnt with the [ProxylessNAS](https://paperswithcode.com/method/proxylessnas) [neural architecture search](https://paperswithcode.com/method/neural-architecture-search) algorithm that is optimized for CPU devices. It uses inverted residual blocks (MBConvs) from [MobileNetV2](https://paperswithcode.com/method/mobilenetv2) as its basic building block.

**Proximal Policy Optimization**, or **PPO**, is a policy gradient method for reinforcement learning. The motivation was to have an algorithm with the data efficiency and reliable performance of [TRPO](https://paperswithcode.com/method/trpo), while using only first-order optimization. 

Let $r\_{t}\left(\theta\right)$ denote the probability ratio $r\_{t}\left(\theta\right) = \frac{\pi\_{\theta}\left(a\_{t}\mid{s\_{t}}\right)}{\pi\_{\theta\_{old}}\left(a\_{t}\mid{s\_{t}}\right)}$, so $r\left(\theta\_{old}\right) = 1$. TRPO maximizes a “surrogate” objective:

$$ L^{\text{CPI}}\left({\theta}\right) = \hat{\mathbb{E}}\_{t}\left[\frac{\pi\_{\theta}\left(a\_{t}\mid{s\_{t}}\right)}{\pi\_{\theta\_{old}}\left(a\_{t}\mid{s\_{t}}\right)})\hat{A}\_{t}\right] = \hat{\mathbb{E}}\_{t}\left[r\_{t}\left(\theta\right)\hat{A}\_{t}\right] $$

Where $CPI$ refers to a conservative policy iteration. Without a constraint, maximization of $L^{CPI}$ would lead to an excessively large policy update; hence, we PPO modifies the objective, to penalize changes to the policy that move $r\_{t}\left(\theta\right)$ away from 1:

$$ J^{\text{CLIP}}\left({\theta}\right) = \hat{\mathbb{E}}\_{t}\left[\min\left(r\_{t}\left(\theta\right)\hat{A}\_{t}, \text{clip}\left(r\_{t}\left(\theta\right), 1-\epsilon, 1+\epsilon\right)\hat{A}\_{t}\right)\right] $$

where $\epsilon$ is a hyperparameter, say, $\epsilon = 0.2$. The motivation for this objective is as follows. The first term inside the min is $L^{CPI}$. The second term, $\text{clip}\left(r\_{t}\left(\theta\right), 1-\epsilon, 1+\epsilon\right)\hat{A}\_{t}$ modifies the surrogate
objective by clipping the probability ratio, which removes the incentive for moving $r\_{t}$ outside of the interval $\left[1 − \epsilon, 1 + \epsilon\right]$. Finally, we take the minimum of the clipped and unclipped objective, so the final objective is a lower bound (i.e., a pessimistic bound) on the unclipped objective. With this scheme, we only ignore the change in probability ratio when it would make the objective improve, and we include it when it makes the objective worse. 

One detail to note is that when we apply PPO for a network where we have shared parameters for actor and critic functions, we typically add to the objective function an error term on value estimation and an entropy term to encourage exploration.

Proximal Policy Optimization Algorithms

ProxylessNet-CPU

ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware

• Parallel Layers – We use a “parallel” formulation in each Transformer block (Wang & Komatsuzaki, 2021), rather than the standard “serialized” formulation. Specifically, the standard formulation can be written as:   
    y = x + MLP(LayerNorm(x + Attention(LayerNorm(x)))   

Whereas the parallel formulation can be written as:   
    y = x + MLP(LayerNorm(x)) + Attention(LayerNorm(x))   

The parallel formulation results in roughly 15% faster training speed at large scales, since the MLP and Attention input matrix multiplications can be fused. Ablation experiments showed a small quality degradation at 8B scale but no quality degradation at 62B scale, so we extrapolated that the effect of parallel layers should be quality neutral at the 540B scale.

Source	ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com