ATCS ¨C Selected Topics in Learning, Prediction, and Optimization (with application in Finance)
2019 Spring
Lecturer: Jian Li ( lapordge at gmail dot com)
TA: Xu Jin ( jxu3425 at gmail dot com )
time: every Tue 9:50am-12:15am
Room: 6B307 £¨Áù½Ì£©
We intend to cover a subset of the following topics (tentative):
(1) I assume you already know all basics (convex optimization and machine learning, stochastic gradient descent, gradient boosting, deep learning basics, CNN, RNN, please see my undergrad course). I will recall some details when necessary.
(2) Online learning and sequential prediction. Multi-armed bandit, Universal portfolio, Multiplicative weighting method, online convex optimization, (maybe) online learning and pricing derivatives
(3) learning theory: VC, Margin theory, Generalization
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 (trading, pricing derivatives etc), and of course in typical CS areas like vision, nlp, social networks as well...
Some knowledge about convex optimization may be useful. See 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.
Grading:
Schedule:
Feb 26 | The expert problem.
Multiplicative weights method Using MW to solve Zero sum game Basics of Stock and Future Markets |
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.¡¡ |
Mar 5 | Cover's
universal portfolio. Gradient descent for online learning Basics of Forward contract and futures |
Online convex
programming and generalized infinitesimal gradient ascent. M. Zinkevich.¡¡Universal Portfolios¡¡ Universal Portfolios With and Without Transaction Costs¡¡ |
Mar 12 | Online Mirror Descent Basics of options, binomial tree |
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Mar 19 | Online Mirror Descent and Follow the
Regularized leader Blackwell approachability Theorem Basics of Stochastic calculus |
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Mar 26 | Blackwell approachability Theorem and
Online Learning Online to Batch Conversion Ito formula, idea of Delta hedge |
Blackwell Approachability and No-Regret Learning are
Equivalent Online to batch
https://ttic.uchicago.edu/~tewari/lectures/lecture13.pdf ¡¡ |
Apr 2 | Rademacher complexity, VC-dimension BSM formula |
[Book] Foundation of Machine Learning, Chapter 3 |
Apr 9 | the Relaxation technique Cover's Bit Prediction, its connection with rademacher complexity |
The material can be found in Lecture notes for STAT928: Statistical Learning and Sequential Prediction |
Apr 16 | Interval Regret, Sleeping expert, Dynamic regret. Pricing derivatives thru online learning |
¡¡Online Trading Algorithms and Robust Option Pricing¡¡ Robust Option Pricing: Hannan and Blackwell Meet Black and Scholes¡¡ |
Apr 23 |
Pricing derivatives thru online learning Online learnability and littlestone dimension |
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May 7 | Online learnability and
littlestone dimension Multi-armed bandits, UCB, EXP3, Contextual bandit EXP4 Very brief mentioning of the portfolio theory |
https://haipeng-luo.net/courses/CSCI699/ Portfolio theory: https://en.wikipedia.org/wiki/Modern_portfolio_theory Fama and French Three Factor Model https://www.investopedia.com/terms/f/famaandfrenchthreefactormodel.asp |
May 14 | Generalization, Algorithmic Stability. Stability for SGD
(convex). Some basics of the stock markets. |
Train faster, generalize
better: Stability of stochastic gradient descent
the worldquat paper i mentioned: 101 Formulaic Alphas |
May 21 | Stability for SGD (convex) , Convergence of SGD
(convex), Stability of SGLD (nonconvex). |
On Generalization Error Bounds of Noisy Gradient Methods for Non-Convex Learning |
May 28 | Generalization via Compression Framework | ¡¡ Stronger generalization bounds for deep nets via a compression approach ¡¡ |
Jun 4 | Neural Tangent Kernel and Overparameterized Neural network | Class based on paper On exact computation with an
infinitely wide neural net See the references in this paper for several previous papers on this topic. ¡¡ |
Jun 11 | (Project presentation) | ¡¡ |
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References:
[Book] Introduction to online convex optimization
[Book] Learning, Prediction and Games
[Book] Options, Futures and Other Derivatives
[Book] Foundation of Machine Learning
[Book] Understanding Machine Learning: From Theory to Algorithms
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).
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