Gradient Episodic Memory for Continual Learning

Presented by

• Yu Xuan Lee
• Tsen Yee Heng

Background and Introduction

Supervised learning consist of a training set [math]\displaystyle{ D_{tx}=(x_i,y_i)^n_{i=1} }[/math], where [math]\displaystyle{ x_i \in X }[/math] and [math]\displaystyle{ y_i \in Y }[/math]. Empirical Risk Minimization (ERM) is one of the common supervised learning method used to minimize a loss function by having multiple passes over the training set.

[math]\displaystyle{ \frac{1}{|D_{tr}|}\textstyle \sum_{(x_i,y_i) \in D_{tr}} \ell (f(x_i),y_i) }[/math]

where [math]\displaystyle{ \ell :\mathcal {Y} \times \mathcal {Y} \to [0, \infty) }[/math]

Different to machine learning, datas are being observed sequentially, occurred recurrently, and stored limitedly for learning humans. Thus, the iid assumption is not applicable to ERM. One of the characteristics of ERM is "catastrophic forgetting", which is the problem of recalling past knowledge upon acquiring new ones. To overcome this problem, Gradient Episodic Memory (GEM) is introduced to alleviates forgetting on previous acquired knowledge, while solving new problems more efficiently.

Framework for Continual Learning

Task Descriptor

Task descriptor are integers [math]\displaystyle{ t_i=I \in \mathbb{Z} }[/math] which occurs in a collection where [math]\displaystyle{ t_1,...,t_n \in \mathcal{T} }[/math].