20874 - ALGORITHMS FOR OPTIMIZATION AND INFERENCE

The course will teach the students the fundamentals of designing and analyzing algorithms for optimization and inference problems. The students will be able to estimate the computational complexity and the resource requirements of the algorithms they encounter, and to use them as building blocks in their own work. They will be familiarized with fundamental algorithmic theory and optimization techniques, and their interplay with inference and learning methods.

Basic Notions and Algorithmic Background

Algorithmic efficiency

Complexity classes and reductions

Graph and Combinatorial Optimization

Fundamental graph optimization problems

Matroids and Matroid intersection, Submodularity

Approximation algorithms for hard combinatorial optimization problems

Mathematical Optimization techniques

Linear Programming models and algorithms

Duality and Sensitivity analysis

Integer Programming models and algorithms

Non-linear Programming models and algorithms

Stochastic and Robust Optimization

Large-scale optimization

Inference and Learning

Submodular optimization and its applications in ML and AI

Mathematics of Neural Networks

Optimization algorithms for Deep Learning

• Understand the Recognize the efficiency of algorithms
• Estimate the computational and resource requirements of algorithms 
• Classify optimization problems according to their computational complexity
• Formulate optimization problems as Linear/Integer/Non-linear programming models, including stochastic and robust aspects 
• Understand the mathematics behind neural networks and inference algorithms

• Design and analyze efficient algorithms
• Estimate the computational and resource requirements of algorithms 
• Classify optimization problems according to their computational complexity 
• Formulate optimization problems as Linear/Integer/Non-linear programming models
• Solve stochastic, robust, and large-scale optimization problems using the appropriate techniques
• Apply inference algorithms

• Face-to-face lectures

The teaching method is face-to-face lectures. Several lectures will include exercises to be done in class.

There will be a written exam and two homework assignments. The homework assignments are not mandatory.

The final grade will be calculated by taking for each student the best outcome out of the following two ones:

(a) Final written test contributes 70% of the final grade, and homework assignments contribute 30%.

(b) Final written test contributes 100% of the final grade.

The exam will test the students' ability to explain and reproduce the concepts learned in class, and connect these concepts to specific problem instances. There will be no difference between attending and non-attending students.

• Lecture slides and notes provided by the instructor
• T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, (The MIT press), 3rd/4th edition
• W. Cook, W. Cunningham, W. Pulleyblank and A. Schrijver. Combinatorial Optimization. Wiley-Interscience, 1997
• B. Guenin, J. Könemann, L. Tuncel, A Gentle Introduction to Optimization, Cambridge University Press, 2014
• Computer and Intractability. A Guide to NP-Completeness. M. R. Garey and D. S. Johnson. Publisher W. H. Freeman, 1979
• Information Theory, Inference, and Learning Algorithms, D. J. C. MacKay, Cambridge University Press, 2003