Multi-Objective Population Based Training

Population Based Training (PBT) is an efficient hyperparameter optimization algorithm. PBT is a single-objective algorithm, but many real-world hyperparameter optimization problems involve two or more conflicting objectives. In this work, we therefore introduce a multi-objective version of PBT, MO-PBT. Our experiments on diverse multi-objective hyperparameter optimization problems (Precision/Recall, Accuracy/Fairness, Accuracy/Adversarial Robustness) show that MO-PBT outperforms random search, single-objective PBT, and the state-of-the-art multi-objective hyperparameter optimization algorithm MO-ASHA

Application of quantum-inspired generative models to small molecular datasets

Quantum and quantum-inspired machine learning has emerged as a promising and challenging research field due to the increased popularity of quantum computing, especially with near-term devices. Theoretical contributions point toward generative modeling as a promising direction to realize the first examples of real-world quantum advantages from these technologies. A few empirical studies also demonstrate such potential, especially when considering quantum-inspired models based on tensor networks. In this work, we apply tensor-network-based generative models to the problem of molecular discovery. In our approach, we utilize two small molecular datasets: a subset of $4989$ molecules from the QM9 dataset and a small in-house dataset of $516$ validated antioxidants from TotalEnergies. We compare several tensor network models against a generative adversarial network using different sample-based metrics, which reflect their learning performances on each task, and multiobjective performances using $3$ relevant molecular metrics per task. We also combined the output of the models and demonstrate empirically that such a combination can be beneficial, advocating for the unification of classical and quantum(-inspired) generative learning.Comment: First versio

Otimização multi-objetivo envolvendo aproximadores de função via processos gaussianos e algoritmos híbridos que empregam otimização direta do hipervolume

Orientador: Fernando José Von ZubenTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: O principal propósito desta tese é reduzir a lacuna entre otimização mono-objetivo e multiobjetivo e mostrar que conectar técnicas de lados opostos pode gerar melhores resultados. Para atingir esta meta, nós fornecemos contribuições em três direções. Primeiro, mostra-se a conexão entre otimalidade da perda média e do hipervolume quando avaliando uma única solução, provando limites de otimalidade quando a solução de um é aplicada ao outro. Ademais, uma avaliação do gradiente do hipervolume mostra que ele pode ser interpretado como um caso particular da perda média ponderada, onde os pesos aumentam conforme as perdas associadas aumentam. Levantou-se a hipótese de que isto pode ajudar a treinar modelos de aprendizado de máquina, uma vez que amostras com erro alto também terão peso alto. Um experimento com uma rede neural valida a hipótese, mostrando melhor desempenho. Segundo, avaliaram-se tentativas anteriores de usar otimização do hipervolume baseada em gradiente para resolver problemas multi-objetivo e por que elas falharam. Baseado na análise, foi proposto um algoritmo híbrido que combina otimização evolutiva e baseada em gradiente. Experimentos nas funções de benchmark ZDT mostram melhor desempenho e convergência mais rápida comparado a algoritmos evolutivos de referência. Finalmente, foram apresentadas condições necessárias e suficientes para que uma função descreva uma fronteira de Pareto válida. Com base nestes resultados, adaptou-se um processo Gaussiano para penalizar violações das condições e mostrou-se que ele fornece melhores estimativas do que outros algoritmos de aproximação. Em particular, ele cria uma curva que não viola as restrições tanto quanto algoritmos que não consideram as condições, sendo mais confiável como um indicador de performance. Foi também demonstrado que uma métrica de otimização comum, quando aproximando funções com processos Gaussianos, é uma boa indicadora das regiões que um algoritmo deveria explorar para encontrar a fronteira de ParetoAbstract: The main purpose of this thesis is to bridge the gap between single-objective and multi- objective optimization and to show that connecting techniques from both ends can lead to improved results. To reach this goal, we provide contributions in three directions. First, we show the connection between optimality of a mean loss and the hypervolume when evaluating a single solution, proving optimality bounds when the solution from one is applied to the other. Furthermore, an evaluation of the gradient of the hypervolume shows that it can be interpreted as a particular case of the weighted mean loss, where the weights increase as their associated losses increases. We hypothesize that this can help to train a machine learning model, since samples with high error will also have high weight. An experiment with a neural network validates the hypothesis, showing improved performance. Second, we evaluate previous attempts at using gradient-based hypervolume optimization to solve multi-objective problems and why they have failed. Based on the analysis, we propose a hybrid algorithm that combines gradient-based and evolutionary optimization. Experiments on the benchmark functions ZDT show improved performance and faster convergence compared with reference evolutionary algorithms. Finally, we prove necessary and sufficient conditions for a function to describe a valid Pareto frontier. Based on this result, we adapt a Gaussian process to penalize violation of the conditions and show that it provides better estimates than other approximation algorithms. In particular, it creates a curve that does not violate the constraints as much as done by algorithms that do not consider the restrictions, being a more reliable performance indicator. We also show that a common optimization metric when approximating functions with Gaussian processes is a good indicator of the regions an algorithm should explore to find the Pareto frontierDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétrica2015/09199-0CAPESFAPES

Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement

Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond decomposition, we propose a novel neural heuristic with diversity enhancement (NHDE) to produce more Pareto solutions from two perspectives. On the one hand, to hinder duplicated solutions for different subproblems, we propose an indicator-enhanced deep reinforcement learning method to guide the model, and design a heterogeneous graph attention mechanism to capture the relations between the instance graph and the Pareto front graph. On the other hand, to excavate more solutions in the neighborhood of each subproblem, we present a multiple Pareto optima strategy to sample and preserve desirable solutions. Experimental results on classic MOCO problems show that our NHDE is able to generate a Pareto front with higher diversity, thereby achieving superior overall performance. Moreover, our NHDE is generic and can be applied to different neural methods for MOCO.Comment: Accepted at NeurIPS 202

A comparative study of multi objective optimization algorithms for a cellular automata model

Cellular Automata (CA) models can represent dynamic systems which are discrete in space and time that reflects the effect of intrinsic parameters where individual events are considered to occur from randomness. A CA model of two agents' chemical kinetics has been optimized earlier using NSGA-II based on Evolutionary Algorithm (EA). But the stochastic nature of the CA model along with its high sensitivity on the model parameters requires extensive investigation using different optimization algorithms. For this purpose, in the current study, four more recently developed and popular optimization algorithms based on EA, called NSGA-IIr, NSGA-IIa, AbYSS and MOEA/D, have been considered for investigation based on various performance measuring parameters. The study also compares the performances of the algorithms for different computational efforts with an objective to minimize the required number of objective function evaluations. Simulation results and Friedman rank statistical test show NSGA-IIa and NSGA-IIr as the best choices to optimize the CA stochastic model across any number of objective function evaluations. Though the choice of optimization algorithm does not change with function evaluations, higher function evaluations improve the pseudo-pareto front for the CA optimization problem. Such results will facilitate the use of stochastic CA models to represent complex (bio)-chemical networks

Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set

Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on the set of (often infinite number of) models that cannot be strictly improved. But it does not provide an actionable procedure for picking one or a few special models to return to practical users. In this paper, we consider \emph{optimization in Pareto set (OPT-in-Pareto)}, the problem of finding Pareto models that optimize an extra reference criterion function within the Pareto set. This function can either encode a specific preference from the users, or represent a generic diversity measure for obtaining a set of diversified Pareto models that are representative of the whole Pareto set. Unfortunately, despite being a highly useful framework, efficient algorithms for OPT-in-Pareto have been largely missing, especially for large-scale, non-convex, and non-linear objectives in deep learning. A naive approach is to apply Riemannian manifold gradient descent on the Pareto set, which yields a high computational cost due to the need for eigen-calculation of Hessian matrices. We propose a first-order algorithm that approximately solves OPT-in-Pareto using only gradient information, with both high practical efficiency and theoretically guaranteed convergence property. Empirically, we demonstrate that our method works efficiently for a variety of challenging multi-task-related problems