Logical Reasoning

Decentralized Distributed Proximal Policy Optimization (DD-PPO) is a method for distributed reinforcement learning in resource-intensive simulated environments. DD-PPO is distributed (uses multiple machines), decentralized (lacks a centralized server), and synchronous (no computation is ever `stale'), making it conceptually simple and easy to implement. 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, 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: $$ L^{v}\left({\theta}\right) = \hat{\mathbb{E}}\_{t}\left[\frac{\pi\_{\theta}\left(a\_{t}\mid{s\_{t}}\right)}{\pi\_{\theta\_{old}}\left(a\_{t}\mid{s\_{t}}\right)})\hat{A}\_{t}\right] = \hat{\mathbb{E}}\_{t}\left[r\_{t}\left(\theta\right)\hat{A}\_{t}\right] $$ As a general abstraction, DD-PPO implements the following: at step $k$, worker $n$ has a copy of the parameters, $\theta^k_n$, calculates the gradient, $\delta \theta^k_n$, and updates $\theta$ via $$ \theta^{k+1}\_n = \text{ParamUpdate}\Big(\theta^{k}\_n, \text{AllReduce}\big(\delta \theta^k\_1, \ldots, \delta \theta^k\_N\big)\Big) = \text{ParamUpdate}\Big(\theta^{k}\_n, \frac{1}{N} \sum_{i=1}^{N} { \delta \theta^k_i} \Big) $$ where $\text{ParamUpdate}$ is any first-order optimization technique (e.g. gradient descent) and $\text{AllReduce}$ performs a reduction (e.g. mean) over all copies of a variable and returns the result to all workers. Distributed DataParallel scales very well (near-linear scaling up to 32,000 GPUs), and is reasonably simple to implement (all workers synchronously running identical code).

• 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.

Recurrent Event Network (RE-NET) is an autoregressive architecture for predicting future interactions. The occurrence of a fact (event) is modeled as a probability distribution conditioned on temporal sequences of past knowledge graphs. RE-NET employs a recurrent event encoder to encode past facts and uses a neighborhood aggregator to model the connection of facts at the same timestamp. Future facts can then be inferred in a sequential manner based on the two modules.