Related papers: An Efficient Mean Field Approach to the Set Coveri…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
A novel artificial neural network approach to constraint satisfaction problems is presented. Based on information-theoretical considerations, it differs from a conventional mean-field approach in the form of the resulting free energy. The…
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…
The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem…
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…
The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
A novel approach is presented for the solution of instantaneous chemical equilibrium problems. The chemical equilibrium can be considered, due to its intrinsically local character, as a mapping of the three-dimensional parameter space…
The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…
The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…