Advanced Optimization Algorithms in the Era of Machine Learning

Dear Colleagues, 

We are witnessing the rapid advance of Machine Learning and its application in various domains. We would like to provide the opportunity to explore related areas that focus on the development of alternative optimization algorithms that provide a different perspective on machine learning.

We would like to explore the extensions of optimization algorithms that improve the efficiency of the learning, the modelling of Bayesian systems, that reveal the connection with computational physics, that allow to integrate discrete variables, that allow to integrate the solution of a bilevel or multilevel optimization problems. In addition, we would like to consider discrete and continuous integration as, for example, where cost function and constrains of optimization problems are estimated on data either in two-step or end-to-end training. We would like to give the opportunity to explore the use of Hessian-free optimization method for bilevel problems and the exploration of efficient optimal transport, variational optimization, equilibrium problems, normalizing flows, and generative diffusion systems.

In the scope of the Special Issue are methods for lower bound approximations and stochastic relaxations of discrete problems; adjoint methods of optimization problems; solver free learning of optimization problems; optimization free gradient estimation methods; continuous relaxations of discrete operations and algorithms (e.g., sorting, ranking, argmax, shortest-path, if-else constructs, loops, top-k, logic operators, indexing, etc.); Smoothing or variational for the optimization of discrete structures (e.g., graphs, tree, sequences); Semi-definitive optimization relaxation of discrete or logical optimization (e.g., SAT solver, MaxSAT), Optimization and integration of numerical simulators (e.g., field equations, fluid dynamics, differentiable molecular dynamics, differentiable particle simulators,  differentiable protein binding, differentiable protein-folding).

Dr. Francesco Alesiani
Guest Editor

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• optimization for machine learning
• gradient estimation for continuous–discrete programming
• efficient algorithms for optimal transport optimization, diffusion models and normalizing flows
• optimization algorithms for discrete and combinatorial optimization
• optimization algorithms for bilevel optimization
• optimization algorithms of Bayesian learning
• physic inspired optimization and learning methods