Slide 18 of 19
Notes:
My experiments to date indicate that global information-based approaches layered atop an appropriate constrained local minimization are best for searching minima at corners and edges of a search space. To this end, I’m seeking to make more efficient approximations to global optimal decision procedures.
Other existing approaches can also benefit. For instance, higher dimensional problems can be approached with direction set methods, which minimize along sequentially along each of an orthogonal set of vectors. At this time, I’m refining an information-based approach to the line searching component of this method.
In addition, we have more information at our disposal than just function evaluations. The number of distinct minima and the distance traversed in local optimization give us probabilistic information about the number of local minima and the size of their basins of attraction. Such information can be used to adjust one's search radius. More significantly, such information can be used to direct one’s search strategy. Imagine a number of search strategies run in parallel, each making use of all information gained thus far, with more runtime being given to those strategies which are probabilistically best-suited to the function given the information gained. I envision a sort of expert system which uses information gained not merely to direct optimization, but to guide emphasis of optimization strategies as well.