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ΧΕΙΜΕΡΙΝΟ ΕΞΑΜΗΝΟ 2021-2022

ΑΙΘΟΥΣΑ 2041 Κτ. Επιστημών, ΚΑΘΕ ΠΕΜΠΤΗ 5μμ-8μμ

This is a joint course (senior undergraduate - ECE Masters program - MLDS Masters Program).

The course description is as follows:

• Brief summary of Linear Algebra concepts (vectors, planes, vector and matrix norms).
• Vectors and matrices in Matlab.
• Brief summary of functions of several variables (gradient, Hessian, level sets).
• Convex sets (definition and examples), operations on convex sets that preserve convexity.
• Convex functions (definition, examples), operations on convex functions that preserve convexity.
• Convex optimization problems (definition, examples), optimal points.
• Unconstrained optimization (characterization of optimal solution, gradient method, convergence analysis, Newton method, local convergence analysis).
• Convex optimization with constraints (Farkas Lemma, Fritz John conditions, conditions Karush-Kuhn-Tucker (KKT) - examples).
• Duality, Lagrangian, dual function, weak and strong duality – examples of dual problems.
• Convex optimization with affine equality constraints (Newton method, primal-dual).
• General convex optimization problems (barrier function, interior point method, primal-dual).
• Alternating Direction Method of Multipliers
• Introduction to distributed optimization

The Lab part of the course consists of four (4) projects which contain theoretical questions as well as matlab (or octave) code implementing selected optimization algorithms.

Grading;

• Final Exam 6/10,
• Projects (4/10).

Our main source will be the textbook

S. Boyd and L. Vandenberghe. "Convex Optimization," Cambridge University Press, 2004 (I uploaded the textbook in the "Εγγραφα" section).

See also the video series of recent Boy's lectures 

https://www.youtube.com/playlist?list=PLoROMvodv4rMJqxxviPa4AmDClvcbHi6h

Another excellent source is the book

A. Beck, Introduction to nonlinear optimization (2nd edition), SIAM.

Uncertainty and probabilistic reasoning. Robotic perception and action. Recursive state estimation: state space, belief space, prediction and correction, Bayes filter. Estimation filters: linear Kalman filter, extended Kalman filter, unscented Kalman filter, histogram filter, particle filter. Probabilistic motion models: velocity model, odometry model, sampling and probability density. Probabilistic observation models: beam model, scan model, feature model, sampling and probability density. Robot localization: Markov, Gaussian, Grid, Monte-Carlo. Robotic mapping: occupancy grid maps, feature maps, simultaneous localization and mapping (SLAM). Decision making under uncertainty, Markov decision processes (MDPs), optimal policies, value iteration, policy iteration. Partial observability, partially observable MPDs (POMDPs), augmented MDPs. Reinforcement learning, prediction and control, trial and error, approximate representations. Multi-robot planning, coordination, and learning.
syllabus

This is a joint course (ECE senior undergraduate, ECE Masters).

We will follow, mainly, the following sourse:

M. Mitzenmacher and E. Upfal. "Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis." Cambridge University Press, 2018 (second edition).

The lectures are scheduled as follows:

Monday: 14:00-16:00, Room 145Π58

Tuesday: 13:00-15:00, Room 137Π39

Some other useful sources will appear at the end of this description.

In order to give the most accurate view of the course, the description will be updated during the semester

• Randomized algorithms for checking polynomial and matrix equalities

• Randomized min-cut algorithm

• Discrete random variables: Bernoulli, binomial, geometric

• The coupon collector problem

• Probabilistic analysis of Quick-sort

• Inequalities: Markov, Chebyshev

• Randomized median algorithm

• Inequalities: Chernoff, Hoeffding

• The balls-and-bins problem

• Multinomial and Poisson random variables

• Random graphs

• Randomized algorithm for Hamiltonian cycle

• Probabilistic Method and its applications: large cut-sets, thresholds in random graphs

• Satisfiability problems (SAT)

• Martingales, Hoeffding-Azuma Inequality, and applications.

• Machine Learning related topics

The grade will be derived from

• written exam (6/10 with threshold 3)
• projects (theoretical questions, matlab code) (4/10) (please, try to avoid chapGTP or any other electronic help)
  
• bonus projects (approx 2/10) (tentative...)
  

Other useful sources (the list will be updated regularly...)

• N. Alon and J. E. Spencer. "The Probabistic Method." Wiley, fourth edition, 2015.
• R. Vershynin. "High-dimensional Probability." (excellent book, somewhat advanced) Available at: https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf

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