convergence for non-Markovian simulated AAs

Mathieu Gerber (formerly CREST) and Luke Bornn have arXived a paper on the almost sure convergence of simulated annealing algorithms when using a non-Markovian sequence that can be in the limiting case completely deterministic and hence use quasi-Monte Carlo sequences. The paper extends the earlier Gerber and Bornn (2015) that I missed. While the paper is highly technical, it shows that under some conditions a sequence of time-varying kernels can be used to reach the maximum of an objective function. With my limited experience with simulated annealing I find this notion of non-iid or even non-random both worth investigating and somewhat unsurprising from a practitioner’s view in that modifying a standard simulated annealing algorithm with steps depending on the entire past of the sequence usually produces better performances.