Seminar: Pedro Zattoni Scroccaro (TU Delft) and Luis Vargas (CWI), 2 PhD-talks

 
Zoom link: 
https://cwi-nl.zoom.us/j/84909645595?pwd=b1M4QnNKVzNMdmNSVFNaZUJmR1kvUT09 
(Meeting ID: 849 0964 5595, Passcode: 772448)

Speaker: Pedro Zattoni Scroccaro (TU Delft) 

Title: Learning Drivers’ Preferences: an Inverse Optimization Approach

Abstract:
In Inverse Optimization problems, a learning agent aims to learn how to mimic the behavior of an expert agent, which given an exogenous signal, returns an action. The underlying assumption is that in order to compute its action, the expert agent solves an optimization problem parametric in the exogenous signal. Therefore, given examples of exogenous signals and corresponding expert actions, the goal of the learner is to learn the cost function being optimized by the expert. In this talk, we will present fundamental concepts of Inverse Optimization, novel results, as well as an application on learning to route vehicles like expert human drivers (Amazon Last Mile Routing Research Challenge). Accompanying papers: https://arxiv.org/abs/2305.07730 and https://arxiv.org/abs/2307.07357.

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Speaker: Luis Vargas (CWI)

Title: Complexity Results About the Exactness of Sum-of-Squares Approximations for Polynomial Optimization

Abstract:
A polynomial optimization problem (PoP) asks for minimizing a polynomial function over a semialgebraic set i.e., a set defined by
polynomial inequalities and equations. Polynomial optimization captures many hard problems and it is difficult to solve as expected. The Lasserre sum-of-squares hierarchy is a sequence of tractable approximations for (PoP). Under mild assumptions, this hierarchy is shown to converge asymptotically to the optimal value of (PoP). In this talk, we study the question of whether the Lasserre sum-of-squares hierarchy has finite convergence to the optimal value.  Nie (2012) shows that if the problem has finitely many minimizers and they satisfy the classical optimality conditions, then finite convergence holds. Using this, he shows that finite convergence holds generically. In this talk, we show that 1) testing whether a standard quadratic program has finitely many minimizers is NP-hard. Moreover, 2) testing whether the Lasserre hierarchy of a polynomial optimization problem has finite convergence is NP-hard.

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