The expert problem.

Multiplicative weights method

Online gradient descent

1. 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.
2. Our exposition of expert problem follows this note
3. Online convex programming and generalized infinitesimal gradient ascent. M. Zinkevich
4. Selected Reading: Tracking the Best Expert (this can deal with dynamic regret)

Cover's universal portfolio.

2nd order bound

Online Mirror Descent: Fenchel conjugate function

(closely related to other notion of duality, such as polar dual, dual norm)

1. Universal Portfolios

2. Universal Portfolios With and Without Transaction Costs

3. The Squint paper by Koolen and Van Erven

4. Selected reading: online newton method (see this book Chapter 4) (this can solve the universal portfolio problem)

Interval regret, Sleeping Expert, Adaptive Regret

1. Online mirror descent (see this note or this(chapter 5))

2. selected reading: OMD is nearly optimal in a certain sense

Pure exploration: Median Elimination

1. Finite-time Analysis of the Multiarmed Bandit Problem

2. The non-stochastic multi-armed bandit problem

3. Action elimination and stopping conditions for the multi-armed bandit and reinforcement learning problems

Contextual bandit: EXP4

epsilon-greedy

1. A Tutorial on Thompson Sampling

2. The Epoch-Greedy Algorithm for Contextual Multi-armed Bandits

3. Taming the monster: A fast and simple algorithm for contextual bandits

Selected Reading:

1. Olivier Chapelle and Lihong Li. An empirical evaluation of Thompson sampling. In NIPS, 2011.
2. Russo, D. and B. Van Roy. 2014. “Learning to optimize via posterior sampling”. Mathematics of Operations Research. 39(4): 1221–1243. (Regret analysis of Thompson sampling, via a connection to UCB)

Hyperband

Bayesian Optimization

Online-to-batch

Introduction to Stock and Future Market

Efficient Market Hypothesis

1. Hyperband: A novel bandit-based approach to hyperparameter optimization

2. Practical Bayesian Optimization of Machine Learning Algorithms
3. Online to Batch

Selected Reading:

Gaussian process optimization in the bandit setting: No regret and experimental design

Brief Intro to Future and Option

No arbitrage argument

Basics of Brownian Motion

Ito Calculus

Binomial Tree model

Black-Scholes Merton (BSM) model

Pricing derivative via no regret online learning

1. See corresponding chapters in Options, Futures and Other Derivatives 

Feynman-Kac formula

Risk neutral valuation representation of BS formula

Fokker-Planck formula

Robust pricing options using online learning

Volatility smile

1. Online Trading Algorithms and Robust Option Pricing
2. Learning, Regret Minimization and Option Pricing
3. Robust option pricing: Hannan and Blackwell meet Black and Scholes

Selected Reading:

1. How to Hedge an Option Against an Adversary: Black-Scholes Pricing is Minimax Optimal

2. Minimax Option Pricing Meets Black-Scholes in the Limit

Rademacher complexity

Maxima of (sub)Gaussian process

Chaining

Packing/Covering number

VC-dimension

I mainly followed the very well written (by van Handel) [lecture note] Probability in High Dimension (chapter 5 and 7)

[Book] Neural Network Learning: Theoretical Foundations is also a very good source.

Pseudo-dimension, Fat-Shattering dimension

Rademacher complexity

Relation between these dimensions and covering/packing numbers.

1. [Book] Neural Network Learning: Theoretical Foundations (Chapter 11)

2. Rademacher and Gaussian complexities: Risk bounds and structural results

3. Scale-sensitive dimensions, uniform convergence, and learnability

Selected reading:

1. Local Rademacher Complexities

2. Fast rates in statistical and online learning

(overview) generalization bounds in deep learning

Rethinking generalization

Spectral norm generalization bound

Generalization via Compression

1. [Book] Neural Network Learning: Theoretical Foundations (Chapter 7,8)
2. Understanding deep learning requires rethinking generalization
3. Spectrally-normalized margin bounds for neural networks

4. Stronger generalization bounds for deep nets via a compression approach

Selected Reading:

1. A pac-bayesian approach to spectrally-normalized margin bounds for neural networks

2. Non-vacuous generalization bounds at the imagenet scale: a PAC-bayesian compression approach

3. Computing nonvacuous generalization bounds for deep (stochastic) neural networks with many more parameters than training data

4. Uniform convergence may be unable to explain generalization in deep learning

MMD, Universality, integral operator

generalization bound for kernel method

(overview) why existing (kernel) generalization bounds are not enough　

1. A Primer on Reproducing Kernel Hilbert Spaces

2. [Book] Learning with Kernels. Support Vector Machines, Regularization, Optimization, and Beyond. By Bernhard Schölkopf and Alexander J. Smola, Chapter 1 and 2

3. Universality, characteristic kernels and RKHS embedding of measures

4. A Kernel Two-Sample Test

Selected reading:

1. On Learning with Integral Operators

2. ON THE MATHEMATICAL FOUNDATIONS OF LEARNING

1. Reconciling modern machine-learning practice and the classical bias–variance trade-off

2. Deep double descent: Where bigger models and more data hurt

3. The generalization error of random features regression: Precise asymptotics and double descent curve

4. Surprises in high-dimensional ridgeless least squares interpolation

5. Optimal regularization can mitigate double descent

1. To understand deep learning we need to understand kernel learning

2. Rademacher and Gaussian complexities: Risk bounds and structural results

3. Learning Kernels Using Local Rademacher Complexity

4. Neural Tangent kernel
5. Training Neural Networks as Learning Data-Adaptive Kernels