ATCS C Learning and Optimization - theory and practice

2018 Spring

Lecturer: Jian Li

TA: Chuheng Zhang  zhangchuheng123 at live dot com

Room: 6B108

time: every monday 9:50am-12:15am


Prerequisite: undergrad machine learning (e.g., machine learing in coursera by Andrew Ng) , some basic knowledge about deep learning

There are some overlaps with my previous course ATCS16 and ATCS17.


We intend to cover a subset of the following topics (tentative):

(1) Classical machine learning and prediction algorithms: Adaboost, gradient boosting, random forestSVD, principle component analysis (PCA)Nonnegative matrix factorization (NMF), topic modeling, matrix completion, dictionary learning, spectral clustering, Gaussian process

(2) Deep Learning: review basics very very quickly (CNN, RNN, autoencoder, GAN please see my undergrad course), word2vec, attention, other GANs, e.g. WGAN, seq2seq, meta-learning, optimization and generalization issues, Deep reinforcement learning

(3) Continuous optimization: Gradient Descent, Stochastic Gradient Descent, mirror descent, variance reduction, proximal method, distributed(ADMM), (Maybe) non-convex optimization, frank-wolfe, Online learning, Universal portfolio, Multiplicative weighting method

I won't stickly follow the above order....I may skip something mentioned above and cover something not mentioned above...It is a graduate course.

I will be talking about several applications of ML and optimization in Finance, and of course in typical CS areas like vision, nlp, social networks as well...

Some knowledge about convex optimization may be useful. See Johns class http://itcs.tsinghua.edu.cn/~john/convex2013.html and a previous course by myself. But it will be fine if you didn't take those courses. Basic machine learning knowledge will be very useful. If you don't know any machine learning, I would suggest you to read some notes from Andrew Ng's undergrad lecture notes

The course is a blending of theory and practice. We will cover both the underlying mathematics as well as interesting heuristics.

A similar previous course.


Grading:

  1. Homeworks (30pts, 1 homework every two or three weeks, the homeworks may have some small coding assignments)
  2. 10 pts for taking notes: Each student should take notes for 1 or 2 lectures, using LaTex (use this template sample.tex algorithm2e.sty).
  3. Course projects (mid report 5pts, final report 45 pts, presentation 10pts)
  4. No exam. 

     


Schedule:

 

Feb 26. (quickly) review supervised learning

Additive model,

Adaboost,

Gradient boosting, xgboost

random forests (not covered in class, but you need to know).

Slides (based on this page)

Reading:

Additive models, Adaboost, gradient boosting: The element of statistical learning, Ch 9 and 10

Random forest: The element of statistical learning, Ch 9 and 10

XGBoost: A Scalable Tree Boosting System

Further reading:

Some learning theory about boosting: Foundation of Machine learning, Ch. 6.

lightGBM (another popular GDBT implementation)

Awesome Random Forest http://jiwonkim.org/awesome-random-forest/

Mar 5 Online Learning, The expert problem. Multiplicative weights method (with application to zero-sum game), Gradient descent for online learning, Universal Porfolio Multiplicative weights method: a meta-algorithm and its applications. (A survey) Sanjeev Arora, Elad Hazan, and Satyen Kale. [pdf]

The method can be used to solve approximately the zero-sum game and linear program, and is also closely related to Adaboost.

Online convex programming and generalized infinitesimal gradient ascent. M. Zinkevich.

Mar 12 (Cont.)Universal Portfolio, Online-to-Batch, Norm, Fenchel Conjugate, Some basics (strongly convex, Bregman Divergence) Proof follows: Universal Portfolios With and Without Transaction Costs

Online to Batch: http://ttic.uchicago.edu/~tewari/lectures/lecture13.pdf

Mar 19 Online Mirror Descent, Follow the Regularized Leader, UCB for multi-armed bandit

Mirror Descent

(equivalence of FTRL and OMD)

www-stat.wharton.upenn.edu/~rakhlin/courses/stat991/papers/lecture_notes.pdf

Mar 26 UCB for multi-armed bandit (cont.)

epsilon-greedy algorithm

Deep learning basics (slides1)

Peter Auer, Nicolo Cesa-Bianchi, and Paul Fischer. Finite-time analysis of the multiarmed bandit problem, 2002

BP follows the description from http://www.offconvex.org/

Apr 2 Deep learning basics (CNN slides2, RNN slides3)  Unfortunately, I will not be in town. So TA will go over the slides (probably in Chinese.....) Again, I expect you to know basic deep learning already.
Apr 9 Topic modeling (nonnegative matrix factorization, anchor word assumption)

Word2Vec

Slides

Learning Topic Models - Going beyond SVD

(an more practical algorithm) A Practical Algorithm for Topic Modeling with Provable Guarantees

Mikolov, Tomas; Sutskever, Ilya; Chen, Kai; Corrado, Greg S.; Dean, Jeff (2013). Distributed representations of words and phrases and their compositionality.

Apr 16 GloVe, Deep Walk,

Word2Vec as implicit matrix factorization

embedding in deep learning

Start Attention

Neural Word Embedding as Implicit Matrix Factorization

further reading:

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec.

Apr 23 Attention
slides(1)  slides(2)
Show, Attend and Tell: Neural Image Caption Generation with Visual Attention

Neural Machine Translation by Jointly Learning to Align and Translate

Self Attention for Machine Translation

ConvS2S

Attention Is All You Need
May 7 Finishing attention.

Normalization (batch norm, layer norm, group norm)

slides

(Very) Brief introduction to transfer learning and multi-task learning

slides

Start Generalization (algorithmic stability)
Reading:

How transferable are features in deep neural networks?

When Will You Arrive? Estimating Travel Time Based on Deep Neural Networks

further readings:

Sino Pan's slides

May 14 Generalization

Algorithmic stability, PAC Bayes

Generalization of SGD and SGLD (Langevin dynamics)

Train faster, generalize better: Stability of stochastic gradient descent

generalization of SGLD (this note provides a simple and elementary proof of the first result of the next paper, which uses techniques from SDE)

further readings:

Generalization Bounds of SGLD for Non-convex Learning

Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data
May 21 Convergence of GD (convex, strongly convex)

Stochastic GD, Variance Reduction

Accelerating Stochastic Gradient Descent using Predictive Variance

further readings:

Introductory Lectures on Stochastic Optimization

Potential-Function Proofs for First-Order Methods

Katyusha: The First Direct Acceleration of Stochastic Gradient Methods

Lower bound: Tight Complexity Bounds for Optimizing Composite Objectives

May 28 Heavy ball method (ODE interpretation and  convergence analysis)

Lower bound of first order method

Nesterov's acceleration (ODE interpretation and analysis)

further readings:

A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights

Potential-Function Proofs for First-Order Methods

Optimal bounds for convex functions:

(upper bound) Katyusha: The First Direct Acceleration of Stochastic Gradient Methods

(Lower bound:) Tight Complexity Bounds for Optimizing Composite Objectives

Nonconvex:

see table 1 and 2 in my paper: A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization.

Jun 4 Reinforcement learning.
policy iteration, value iteration, MC, TD, actor-critic

Berkeley Deep Reinforcement Learning course:

http://rll.berkeley.edu/deeprlcourse/

Jun 11 (last class) Policy Gradient, advantage, actor-critic, A3C Further reading: google the following

natural policy gradient (NPG)

TRPO (trust region policy optimization)

PPO(proximal policy optimization)

More material see

http://rll.berkeley.edu/deeprlcourse/

Course Project Presentation


References:

[Book] The elements of statistical learning [ESL]

[Book] Convex Optimization

[Book] Introduction to online convex optimization

[Book] Learning, Prediction and Games

[Book] Lectures on Modern Convex Optimization

Ankur Moitra's (MIT) lecture notes (Algorithmic machine learning) lecture notes

Berkeley Deep Reinforcement Learning course:

http://rll.berkeley.edu/deeprlcourse/

blog about nonconvex optimization:  https://www.offconvex.org/

 


Python is the default programming language we will use in the course.

If you haven't use it before, don't worry. It is very easy to learn (if you know any other programming language), and is a very efficient language, especially

for prototyping things related scientific computing and numerical optimization. Python codes are usually much shorter than C/C++ code (the lauguage has done a lot for you). It is also more flexible and generally faster than matlab.

A standard combination for this class is Python+numpy (a numeric lib for python)+scipy (a scientific computing lib for python)+matplotlab (for generating nice plots)

Another somewhat easier way is to install Anaconda (it is a free Python distribution with most popular packages).