Deep Learning for Explicitly Modeling Optimization Landscapes
This work addresses optimization problems with complex interdependencies for researchers and practitioners in fields such as graphics and job scheduling, presenting a novel but incremental approach.
The paper tackles the challenge of modeling complex optimization landscapes by introducing a deep learning method that encodes parameter interactions to predict high-performance solutions, which are then used to initialize local search algorithms, demonstrating applicability across diverse real-world domains like packing and scheduling.
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly modeling the interactions between sets of parameters and the overall quality of the solutions discovered. We demonstrate a novel method, based on learning deep networks, to model the global landscapes of optimization problems. To represent the search space concisely and accurately, the deep networks must encode information about the underlying parameter interactions and their contributions to the quality of the solution. Once the networks are trained, the networks are probed to reveal parameter combinations with high expected performance with respect to the optimization task. These estimates are used to initialize fast, randomized, local search algorithms, which in turn expose more information about the search space that is subsequently used to refine the models. We demonstrate the technique on multiple optimization problems that have arisen in a variety of real-world domains, including: packing, graphics, job scheduling, layout and compression. The problems include combinatoric search spaces, discontinuous and highly non-linear spaces, and span binary, higher-cardinality discrete, as well as continuous parameters. Strengths, limitations, and extensions of the approach are extensively discussed and demonstrated.