learning-to-optimize

A Generalization Result for Convergence in Learning-to-Optimize

  • Michael Sucker
  • Peter Ochs
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , ,

    Convergence in learning-to-optimize is hardly studied, because conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied easily to learned algorithms. Thus, we develop a probabilistic framework that resembles deterministic optimization and allows for transferring geometric arguments into learning-to-optimize. Our main theorem is a generalization result for parametric classes of potentially … Read more

    A Markovian Model for Learning-to-Optimize

  • Michael Sucker
  • Peter Ochs
    • Categories Optimization in Data Science, Stochastic Approaches, Stochastic Programming Tags , , , ,

    We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. … Read more

    Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation

  • Michael Sucker
  • Jalal Fadili
  • Peter Ochs
    • Categories Optimization in Data Science, Other Topics Tags ,

    We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones … Read more