CORE Seminar: Katya Scheinberg

Derivative free optimization (DFO) is the field that addresses optimization of black-box functions – that is functions whose value can be computed (possibly approximately) but whose derivatives cannot be approximated directly. The applications of DFO range from aircraft engineering to hyperparameter tuning in machine learning. All derivative free methods rely on sampling the objective function at one or more points at each iteration. Constructing and maintaining these sample sets has been one of the most essential issues in DFO. Majority of the existing results rely on deterministic sampling techniques.

We will discuss the new developments for using randomized sampled sets within the DFO framework. Randomized sample sets have many advantages over the deterministic sets. In particular, it is often easier to enforce “good” properties of the models with high probability, rather than in the worst case. In addition, randomized sample sets can help automatically discover a good local low dimensional approximation to the high dimensional objective function. We will demonstrate how compressed sensing results can be used to show that reduced size random sample sets can provide full second order information under the assumption of the sparsity of the Hessian.