Topics On Optimization and Machine Learning

Credits
6
Types
Specialization compulsory (Computer Networks and Distributed Systems)
Requirements
This subject has not requirements , but it has got previous capacities
Department
AC
Mail
jose.maria.barcelo@upc.edu
The goal of this course is giving the student a background in the methodologies in the advanced design of mechanisms using non-lineal convex optimization, machine learning, and deep learning that can be applied to computer networks and distributed systems. In particular, we will explore non-linear optimization techniques, kernel machine learning methods, and generative AI models.

Teachers

Person in charge

Others

Weekly hours

Theory
4
Problems
0
Laboratory
0
Guided learning
0
Autonomous learning
7.11

Competences

Technical Competences of each Specialization

Computer networks and distributed systems

  • CEE2.1 - Capability to understand models, problems and algorithms related to distributed systems, and to design and evaluate algorithms and systems that process the distribution problems and provide distributed services.
  • CEE2.2 - Capability to understand models, problems and algorithms related to computer networks and to design and evaluate algorithms, protocols and systems that process the complexity of computer communications networks.
  • CEE2.3 - Capability to understand models, problems and mathematical tools to analyze, design and evaluate computer networks and distributed systems.

    • Generic Technical Competences

    Generic

  • CG3 - Capacity for mathematical modeling, calculation and experimental designing in technology and companies engineering centers, particularly in research and innovation in all areas of Computer Science.

    • Transversal Competences

    Reasoning

  • CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.

    • Basic

  • CB6 - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.
  • CB8 - Capability to communicate their conclusions, and the knowledge and rationale underpinning these, to both skilled and unskilled public in a clear and unambiguous way.

    • Objectives

    1. Capacity to formulate a convex optimization problem
      Related competences: CG3, CEE2.3, CB6, CTR6,
    2. Capacity to solve non linear optimization problems.
      Related competences: CG3, CEE2.3, CB6, CTR6,
    3. Capacity to apply to a real problem topics related to optimization
      Related competences: CG3, CEE2.2, CEE2.3, CEE2.1, CB8, CTR6,
    4. Capacity to understand basic machine learning algorithms
      Related competences: CG3, CEE2.3, CB6, CTR6,
    5. Capacity to apply machine learning algorithms to real scenarios.
      Related competences: CG3, CEE2.2, CEE2.3, CEE2.1, CB8, CTR6,
    6. Capacity to understand neural networks and deep learning algorithms
      Related competences: CG3, CEE2.3, CB6, CTR6,
    7. Capacity to apply neural networks and deep learning algorithms to real scenarios
      Related competences: CG3, CEE2.2, CEE2.3, CEE2.1, CB8, CTR6,

    Contents

    1. Convex Optimization basics
      In this topic we will introduce the main concepts of non-linear optimization with special emphasis in convex optimization. Specifically we will see: convex sets, convex functions, convex optimization problems (COP) and duality (Lagrange dual function, KKT optimality conditions), methods for solving COP's (General Descent Methods, Interior Point Methods)
    2. Kernel methods in machine learning
      Examples of how optimisation is applied in the field of machine learning in computer networks and distributed networks. In particular, it will explain how reproduction of kernel Hilbert spaces (RKHS), supervised methods with kernels including kernel ridge regression (KRR), Gaussian processes, support vector machines (for classification and for regression), and the PCA kernel work.
    3. Deep learning models and Generative AI
      This topic covers the basic concepts related to deep learning and generative AI models applied to computer networks and distributed systems. In particular, Bayesian neural networks, Monte Carlo models, variational inference, LLMs, transformers, latent variable models (EM, ELBO, etc.), generative AI models such as autoregressive, flow, diffusive and variational models (VAE) will be covered.

    Activities

    Activity Evaluation act


    Convex Optimization basics


    Objectives: 1 2 3
    Contents:
    Theory
    18h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Kernel methods in machine learning


    • Theory: Development of the theory. Embedded in the theory there will be some classes devoted to exercises.
    Objectives: 4 3
    Contents:
    Theory
    18h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Deep learning models and Generative AI


    • Theory: Development of the theory. Embedded in the theory there will be some classes devoted to exercises.
    Objectives: 3 6
    Contents:
    Theory
    18h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Delivery of the programming project using nonlinear optimisation


    Objectives: 2 3
    Week: 9 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Delivery of the sensor calibration project using machine learning techniques (KRR, SVR, GP),


    Objectives: 5 4 3
    Week: 14 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Delivery of the project using a neural network


    Objectives: 3 6 7
    Week: 18 (Outside class hours)
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Teaching methodology

    During the initial sessions of each topic, the main results will be explained in the blackboard. The student will solve some exercises to prove their skills in the topic. Finally, the students develop projects according to the topics studied.

    Evaluation methodology

    The evaluation is based on the development of 3 projects (each project is worth the same) and 2 written exams. The final grade for the course (FM) will be:

    FM = 0.6*(P1+P2+P3) + 0.2*Ex1 + 0.2*Ex2.

    For each project, a research report is submitted where the proposed problem is analysed, the resolution methodology is described and the results and conclusions are described. Students will be assessed on their ability to demonstrate understanding and comprehension of the theory, ability to reason and communicate results (competences CG3, CEE2.2, CEE2.3, CEE2.1, CB8, CTR6).

    In the written exams, they will be given a list of theoretical concepts related to the subject topics on which they have to demonstrate an understanding and comprehension. In the exam they will be asked to explain their understanding of these concepts (competences CG3, CEE2.3, CB6, CTR6).

    Bibliography

    Basic

    Web links

    Previous capacities

    Recommended to have previously followed the course "Statistical Analysis of Networks and Systems (SANS-MIRI)"