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On the Applicability of Inverse Optimization for Policy Identification


L. Giger

Master Thesis, FS16

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agentís objective function that best explains a historical sequence of signals and corresponding optimal actions. In [4], this inverse optimization problem is formalized as a distributionally robust program minimizing the worst-case risk that the estimated decision (i.e., the decision implied by a particular quadratic candidate objective) differs from the agentís actual response to a random signal. The paper provides theoretical bounds on the performance of the method, but these bounds are too loose to be helpful in practise. In this work we present a detailed evaluation of the method, applying it to a wide range of test cases including identifying controller behavior, distribution estimation, classification problems and visual search problems, in which we aim to replicate and explain the behavior of a human agent. These test cases are chosen so as to cover a wide range of target optimization problems. These include quadratic problems that perfectly match the prior assumptions, convex problems with objective functions that are not contained in the parametrical prior set and problems with nonconvex objectives for which any quadratic approximation can only be valid locally. The main finding of this thesis is that inverse optimization allows to incorporate prior knowledge about the problem structure efficiently, in particular knowledge about the constraints of the original, parametric problem.

Supervisors: Chithrupa Ramesh, Marius Schmitt, Peyman Mohajerin Esfahani, John Lygeros


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2017:IFA_5620
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