Approximate Bilevel Programming via Pareto Optimization for Imputation and Control of Optimization and Equilibrium Models
Jerome Thai

Citation
Jerome Thai. "Approximate Bilevel Programming via Pareto Optimization for Imputation and Control of Optimization and Equilibrium Models". Talk or presentation, 28, May, 2015.

Abstract
We consider the problem of imputing the function that describes an optimization or equilibrium process from noisy partial observations of nearly optimal (possibly non-cooperative) decisions. We generalize existing inverse optimization and variational inequality problems to construct a novel class of multi-objective optimization problems: approximate bilevel programs. In this class, the “ill” nature of the complementary condition prevalent in bilevel programming is avoided, and residual functions commonly used for the design and analysis of iterative procedures, are a powerful tool to study approximate solutions to optimization and equilibrium problems. In particular, we show that duality gaps provide stronger bounds than lp norms of KKT residuals. The weighted criterion method is in some sense equivalent to existing formulations in the case of full observations. Our novel approach allows us to solve bilevel and inverse problems under a unifying framework, via block coordinate descent, and is demonstrated on 1) consumer utility estimation and pricing and 2) latency inference in the road network of Los Angeles.

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Citation formats

• HTML

  Jerome Thai. <a
  href="http://www.cps-forces.org/pubs/69.html"
  ><i>Approximate Bilevel Programming via Pareto
  Optimization for Imputation and Control of Optimization and
  Equilibrium Models</i></a>, Talk or
  presentation,  28, May, 2015.

• Plain text

  Jerome Thai. "Approximate Bilevel Programming via
  Pareto Optimization for Imputation and Control of
  Optimization and Equilibrium Models". Talk or
  presentation,  28, May, 2015.

• BibTeX

  @presentation{Thai15_ApproximateBilevelProgrammingViaParetoOptimizationFor,
      author = {Jerome Thai},
      title = {Approximate Bilevel Programming via Pareto
                Optimization for Imputation and Control of
                Optimization and Equilibrium Models},
      day = {28},
      month = {May},
      year = {2015},
      abstract = {We consider the problem of imputing the function
                that describes an optimization or equilibrium
                process from noisy partial observations of nearly
                optimal (possibly non-cooperative) decisions. We
                generalize existing inverse optimization and
                variational inequality problems to construct a
                novel class of multi-objective optimization
                problems: approximate bilevel programs. In this
                class, the �ill� nature of the complementary
                condition prevalent in bilevel programming is
                avoided, and residual functions commonly used for
                the design and analysis of iterative procedures,
                are a powerful tool to study approximate solutions
                to optimization and equilibrium problems. In
                particular, we show that duality gaps provide
                stronger bounds than lp norms of KKT residuals.
                The weighted criterion method is in some sense
                equivalent to existing formulations in the case of
                full observations. Our novel approach allows us to
                solve bilevel and inverse problems under a
                unifying framework, via block coordinate descent,
                and is demonstrated on 1) consumer utility
                estimation and pricing and 2) latency inference in
                the road network of Los Angeles.},
      URL = {http://cps-forces.org/pubs/69.html}
  }
  

Posted by Carolyn Winter on 10 Jun 2015.
Groups: forces
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