Rafael Monteiro

Rafael Monteiro, Kartik Sau

In this paper, we introduce a new heuristics for global optimization in scenarios where extensive evaluations of the cost function are expensive, inaccessible, or even prohibitive. The method, which we call Landscape-Sketch-and-Step (LSS), combines Machine Learning, Stochastic Optimization, and Reinforcement Learning techniques, relying on historical information from previously sampled points to make judicious choices of parameter values where the cost function should be evaluated at. Unlike optimization by Replica Exchange Monte Carlo methods, the number of evaluations of the cost function required in this approach is comparable to that used by Simulated Annealing, quality that is especially important in contexts like high-throughput computing or high-performance computing tasks, where evaluations are either computationally expensive or take a long time to be performed. The method also differs from standard Surrogate Optimization techniques, for it does not construct a surrogate model that aims at approximating or reconstructing the objective function. We illustrate our method by applying it to low dimensional optimization problems (dimensions 1, 2, 4, and 8) that mimick known difficulties of minimization on rugged energy landscapes often seen in Condensed Matter Physics, where cost functions are rugged and plagued with local minima. When compared to classical Simulated Annealing, the LSS shows an effective acceleration of the optimization process.

Rafael Monteiro

We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by fluids behavior, namely, on how binary fluids phase separate. Thus, parameters and hyperparameters have physical meaning, whose effects are studied in several different scenarios. PSBC's equations can be seen as a dynamical system whose coefficients are trainable weights, with a similar architecture to that of a Recurrent Neural Network. As such, forward propagation amounts to an initial value problem. Boundary conditions are also present, bearing similarity with figure padding techniques in Computer Vision. Model compression is exploited in several ways, with weight sharing taking place both across and within layers. The model is tested on pairs of digits of the classical MNIST database. An associated multiclass classifier is also constructed using a combination of Ensemble Learning and one versus one techniques. It is also shown how the PSBC can be combined with other methods - like aggregation and PCA - in order to construct better binary classifiers. The role of boundary conditions and viscosity is thoroughly studied in the case of digits ``0'' and ``1''.