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A Solution to the Inverse Optimization Problem Using Convex Decomposition


A.B. Hempel

UC San Diego, Caltech, and UC Berkeley

Inverse optimization is used in many different fields such as expert learning and economic policy analysis. The main assumption in these applications is that a given function is the solution to an unknown optimization problem. The goal is then to identify this generating optimization problem to, for example, reproduce an expertís actions in an autonomous system or gain a better understanding of policies.

We consider the case of piecewise affine functions, which are of particular interest because the explicit solutions to parametric linear and quadratic programs have this structure. In this talk, we show that every piecewise affine function can be obtained by a simple linear transformation of the solution to a linear or quadratic program and further show how the generating problem data can be constructed. The main step in the construction is the decomposition of the given piecewise affine function into a convex and a concave part. We show how these results can be used to model hybrid dynamical systems as optimizing processes. This alternative interpretation has implications on control strategies for these systems. As an example, model predictive control problems are bilevel (instead of mixed integer) optimization problems, which can have computational benefits.


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