normal approximation

PUBLIC R&D PROJECT PORTFOLIO SELECTION UNDER EXPENDITURE UNCERTAINTY AND POLICY CONSTRAINTS

  • Musa Caglar
  • Sinan Gurel
    • Categories Applications - OR and Management Sciences Tags , , , ,

    We consider a project portfolio selection problem faced by research councils in project and call-based R&D grant programs. In such programs, typically, each applicant project receives a score value during specially-designed peer review processes. Each project also has a certain budget, estimated by its principle investigator. The problem is to select an optimal (maximum total … Read more

    Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT

  • Andreas Anastasiou
  • Krishnakumar Balasubramanian
  • Murat A. Erdogdu
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i.e., establishing the rates of convergence of a multivariate martingale difference sequence to a normal random vector, … Read more