Elements of Meta-Learning 关于元学习和强化学习

卡耐基梅隆大学 Probabilistic Graphical Models 课程

Posted by JoselynZhao on May 14, 2020

在这里插入图片描述 Goals for the lecture:

Introduction & overview of the key methods and developments. [Good starting point for you to start reading and understanding papers!]

Probabilistic Graphical Models | Elements of Meta-Learning

01 Intro to Meta-Learning

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Motivation and some examples

When is standard machine learning not enough? Standard ML finally works for well-defined, stationary tasks. 在这里插入图片描述 But how about the complex dynamic world, heterogeneous data from people and the interactive robotic systems? 在这里插入图片描述

General formulation and probabilistic view

What is meta-learning? Standard learning: Given a distribution over examples (single task), learn a function that minimizes the loss: 在这里插入图片描述 Learning-to-learn: Given a distribution over tasks, output an adaptation rule that can be used at test time to generalize from a task description 在这里插入图片描述

A Toy Example: Few-shot Image Classification 在这里插入图片描述 在这里插入图片描述

Other (practical) Examples of Few-shot Learning 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述

Gradient-based and other types of meta-learning

Model-agnostic Meta-learning (MAML) 与模型无关的元学习

  • Start with a common model initialization \(\theta\)
  • Given a new task \(T_i\) , adapt the model using a gradient step: 在这里插入图片描述
  • Meta-training is learning a shared initialization for all tasks: 在这里插入图片描述 在这里插入图片描述

Does MAML Work? 在这里插入图片描述

MAML from a Probabilistic Standpoint Training points: 在这里插入图片描述 testing points:在这里插入图片描述 MAML with log-likelihood loss对数似然损失: 在这里插入图片描述 在这里插入图片描述

One More Example: One-shot Imitation Learning 模仿学习 在这里插入图片描述

Prototype-based Meta-learning 在这里插入图片描述 Prototypes: 在这里插入图片描述 Predictive distribution: 在这里插入图片描述 Does Prototype-based Meta-learning Work? 在这里插入图片描述

Rapid Learning or Feature Reuse 特征重用 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述

Neural processes and relation of meta-learning to GPs

Drawing parallels between meta-learning and GPs In few-shot learning:

  • Learn to identify functions that generated the data from just a few examples.
  • The function class and the adaptation rule encapsulate our prior knowledge.

Recall Gaussian Processes (GPs): 高斯过程

  • Given a few (x, y) pairs, we can compute the predictive mean and variance.
  • Our prior knowledge is encapsulated in the kernel function.

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Conditional Neural Processes 条件神经过程 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述 在这里插入图片描述

On software packages for meta-learning A lot of research code releases (code is fragile and sometimes broken) A few notable libraries that implement a few specific methods:

  • Torchmeta (https://github.com/tristandeleu/pytorch-meta)
  • Learn2learn (https://github.com/learnables/learn2learn)
  • Higher (https://github.com/facebookresearch/higher)

在这里插入图片描述 Takeaways

  • Many real-world scenarios require building adaptive systems and cannot be solved using “learn-once” standard ML approach.
  • Learning-to-learn (or meta-learning) attempts extend ML to rich multitask scenarios—instead of learning a function, learn a learning algorithm.
  • Two families of widely popular methods:
    • Gradient-based meta-learning (MAML and such)
    • Prototype-based meta-learning (Protonets, Neural Processes, …)
    • Many hybrids, extensions, improvements (CAIVA, MetaSGD, …)
  • Is it about adaptation or learning good representations? Still unclear and depends on the task; having good representations might be enough.
  • Meta-learning can be used as a mechanism for causal discovery.因果发现 (See Bengio et al., 2019.)

02 Elements of Meta-RL

What is meta-RL and why does it make sense?

Recall the definition of learning-to-learn Standard learning: Given a distribution over examples (single task), learn a function that minimizes the loss: 在这里插入图片描述 Learning-to-learn: Given a distribution over tasks, output an adaptation rule that can be used at test time to generalize from a task description 在这里插入图片描述 Meta reinforcement learning (RL): Given a distribution over environments, train a policy update rule that can solve new environments given only limited or no initial experience. 在这里插入图片描述

Meta-learning for RL 在这里插入图片描述

On-policy and off-policy meta-RL

On-policy RL: Quick Recap 符合策略的RL:快速回顾 在这里插入图片描述 REINFORCE algorithm: 在这里插入图片描述

On-policy Meta-RL: MAML (again!)

  • Start with a common policy initialization \(\theta\)
  • Given a new task \(T_i\) , collect data using initial policy, then adapt using a gradient step: 在这里插入图片描述
  • Meta-training is learning a shared initialization for all tasks: 在这里插入图片描述 在这里插入图片描述 Adaptation as Inference 适应推理 Treat policy parameters, tasks, and all trajectories as random variables随机变量 在这里插入图片描述 meta-learning = learning a prior and adaptation = inference 在这里插入图片描述 Off-policy meta-RL: PEARL 在这里插入图片描述 在这里插入图片描述

Key points:

  • Infer latent representations z of each task from the trajectory data.
  • The inference networkq is decoupled from the policy, which enables off-policy learning.
  • All objectives involve the inference and policy networks. 在这里插入图片描述

Adaptation in nonstationary environments 不稳定环境 Classical few-shot learning setup:

  • The tasks are i.i.d. samples from some underlying distribution.
  • Given a new task, we get to interact with it before adapting.
  • What if we are in a nonstationary environment (i.e. changing over time)? Can we still use meta-learning? 在这里插入图片描述 Example: adaptation to a learning opponent 在这里插入图片描述Each new round is a new task. Nonstationary environment is a sequence of tasks.

Continuous adaptation setup:

  • The tasks are sequentially dependent.
  • meta-learn to exploit dependencies 在这里插入图片描述

Continuous adaptation

Treat policy parameters, tasks, and all trajectories as random variables 在这里插入图片描述

RoboSumo: a multiagent competitive env an agent competes vs. an opponent, the opponent’s behavior changes over time 在这里插入图片描述

Takeaways

  • Learning-to-learn (or meta-learning) setup is particularly suitable for multi-task reinforcement learning
  • Both on-policy and off-policy RL can be “upgraded” to meta-RL:
    • On-policy meta-RL is directly enabled by MAML
    • Decoupling task inference and policy learning enables off-policy methods
  • Is it about fast adaptation or learning good multitask representations? (See discussion in Meta-Q-Learning: https://arxiv.org/abs/1910.00125)
  • Probabilistic view of meta-learning allows to use meta-learning ideas beyond distributions of i.i.d. tasks, e.g., continuous adaptation.
  • Very active area of research.