2021 Topics on Mathematical and Computing Science C

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Academic unit or major
Graduate major in Mathematical and Computing Science
Sumita Hanna  Kawase Yasushi  Ito Shinji  Takemura Kei 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Intensive ()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course offers basic knowledge on “online optimization” and advanced topics. The classes are given by three lecturers. The standard optimization problems assume that all the input data is given in advance, which is sometimes hard to satisfy in practice. On the other hand, in “online” optimization problems, a part of input data is given one by one. This course explains various models, typical problems, and algorithms with analysis techniques. The first half part of this course deals with competitive ratio analysis, and the latter focuses on regret analysis.

The aim of this course is to provide the concept of online optimization and basic theory, which are nowadays necessary in the real world. Recently online optimization has been attracting attention not only in optimization theory but also machine learning and artificial intelligence. The theory and algorithms are applied to make better services in practice.

The schedule of this course is irregular. The details are announced during the first class.
- 1st : June 11, period 5-6
- 2-13th : Every Tuesday from June 15, periods 5-6 & 7-8
- 14th : July 27, period 5-6

Student learning outcomes

The goal of this course is the following.
1) Students can show typical online optimization problems and explain the models.
2) Students can explain the notion of competitive ratio and a fundamental example of competitive ratio analysis.
3) Students can explain the notion of regret and a fundamental example of regret analysis.

Course taught by instructors with work experience

Applicable How instructors' work experience benefits the course
The lecturers have been working for research on online optimization as their business.


online optimization, competitive ratio, regret, game, machine learning

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

In each class, we focus on a specific topic by a standard type of lecture.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction Get the overall gist of this course
Class 2 Competitive analysis of deterministic algorithms (1/2)
Class 3 Competitive analysis of deterministic algorithms (2/2)
Class 4 Competitive analysis of randomized algorithms (1/2)
Class 5 Competitive analysis of randomized algorithms (2/2)
Class 6 Secretary problem
Class 7 Prophet inequality Midterm report
Class 8 Expert problem (1/2): greedy algorithm and regret
Class 9 Expert problem (2/2): multiplicative weight update method and regret analysis
Class 10 Online convex optimization
Class 11 Multi-armed bandit problem (1/2): adversarial model
Class 12 Multi-armed bandit problem (2/2): stochastic model
Class 13 Linear bandit problem Final report
Class 14 Review and exercise


We do not assign textbooks.

Reference books, course materials, etc.

We will upload course materials. Reference books will be introduced in classes.

Assessment criteria and methods

Students are assessed by the midterm and final reports.

Related courses

  • MCS.T302 : Mathematical Optimization
  • MCS.T322 : Combinatorial Algorithms
  • MCS.T405 : Theory of Algorithms

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is desirable to have basic knowledge of mathematics and undergraduate level of optimization theory.

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