arXiv subjects

Chao Qian

Publications and source records attributed to Chao Qian.

At least 109 records · Page 6Linked to original sources

arXiv2022

On the Robustness of Median Sampling in Noisy Evolutionary Optimization

Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect caused by noise. Sampling is a popular strategy, which evaluates the objective a couple of times, and employs the mean of these evaluation results as an estimate of the objective value. In this work, we introduce a novel sampling method, median sampling, into EAs, and illustrate its properties and usefulness theoretically by solving OneMax, the problem of maximizing the number of 1s in a bit string. Instead of the mean, median sampling employs the median of the evaluation results as an estimate. Through rigorous theoretical analysis on OneMax under the commonly used onebit noise, we show that median sampling reduces the expected runtime exponentially. Next, through two special noise models, we show that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be better than mean sampling; otherwise, it may fail and mean sampling can be better. The results may guide us to employ median sampling properly in practical applications.

cs.NE↗

arXiv2022

Multi-objective Evolutionary Algorithms are Still Good: Maximizing Monotone Approximately Submodular Minus Modular Functions

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multi-objective EA, i.e., GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties but without explicit formulation. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this paper studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., $f=g-c$) with a size constraint, where $g$ is a non-negative monotone approximately submodular function and $c$ is a non-negative modular function, resulting in the objective function $f$ being non-monotone non-submodular. We prove that the GSEMO can achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.

cs.NE↗

arXiv2022

Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization

Bayesian optimization (BO) is a class of popular methods for expensive black-box optimization, and has been widely applied to many scenarios. However, BO suffers from the curse of dimensionality, and scaling it to high-dimensional problems is still a challenge. In this paper, we propose a variable selection method MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select and optimize a subset of variables. That is, MCTS-VS constructs a low-dimensional subspace via MCTS and optimizes in the subspace with any BO algorithm. We give a theoretical analysis of the general variable selection method to reveal how it can work. Experiments on high-dimensional synthetic functions and real-world problems (i.e., NAS-bench problems and MuJoCo locomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can achieve state-of-the-art performance.

cs.LG↗

arXiv2022

Multi-agent Dynamic Algorithm Configuration

Automated algorithm configuration relieves users from tedious, trial-and-error tuning tasks. A popular algorithm configuration tuning paradigm is dynamic algorithm configuration (DAC), in which an agent learns dynamic configuration policies across instances by reinforcement learning (RL). However, in many complex algorithms, there may exist different types of configuration hyperparameters, and such heterogeneity may bring difficulties for classic DAC which uses a single-agent RL policy. In this paper, we aim to address this issue and propose multi-agent DAC (MA-DAC), with one agent working for one type of configuration hyperparameter. MA-DAC formulates the dynamic configuration of a complex algorithm with multiple types of hyperparameters as a contextual multi-agent Markov decision process and solves it by a cooperative multi-agent RL (MARL) algorithm. To instantiate, we apply MA-DAC to a well-known optimization algorithm for multi-objective optimization problems. Experimental results show the effectiveness of MA-DAC in not only achieving superior performance compared with other configuration tuning approaches based on heuristic rules, multi-armed bandits, and single-agent RL, but also being capable of generalizing to different problem classes. Furthermore, we release the environments in this paper as a benchmark for testing MARL algorithms, with the hope of facilitating the application of MARL.

cs.LG↗

arXiv2022

Clifford systems, harmonic maps and metrics with non-negative curvature

Associated with a symmetric Clifford system $\{P_0, P_1,\cdots, P_{m}\}$ on $\mathbb{R}^{2l}$, there is a canonical vector bundle $η$ over $S^{l-1}$. For $m=4$ and $8$, we construct explicitly its characteristic map, and determine completely when the sphere bundle $S(η)$ associated to $η$ admits a cross-section. These generalize the results in \cite{St51} and \cite{Ja58}. As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (cf. \cite{PT97} \cite{PT98}). By a suitable choice of Clifford system, we construct a metric of non-negative curvature on $S(η)$ which is diffeomorphic to the inhomogeneous focal submanifold $M_+$ of OT-FKM type isoparametric hypersurfaces with $m=3$.

math.DG↗

arXiv2022

ZOOpt: Toolbox for Derivative-Free Optimization

Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (Zeroth Order Optimization) toolbox that provides efficient derivative-free solvers and is designed easy to use. ZOOpt provides single-machine parallel optimization on the basis of python core and multi-machine distributed optimization for time-consuming tasks by incorporating with the Ray framework -- a famous platform for building distributed applications. ZOOpt particularly focuses on optimization problems in machine learning, addressing high-dimensional and noisy problems such as hyper-parameter tuning and direct policy search. The toolbox is maintained toward a ready-to-use tool in real-world machine learning tasks.

cs.LG↗

arXiv2022

Topology and curvature of isoparametric families in spheres

An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds. The present paper has two parts. The first part investigates topology of the isoparametric families, namely the homotopy, homeomorphism, or diffeomorphism types, parallelizability, as well as the Lusternik-Schnirelmann category. This part extends substantially the results of Q.M.Wang in \cite{Wa88}. The second part is concerned with their curvatures, more precisely, we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.

math.DG↗

arXiv2022

Neural Network Pruning by Cooperative Coevolution

Neural network pruning is a popular model compression method which can significantly reduce the computing cost with negligible loss of accuracy. Recently, filters are often pruned directly by designing proper criteria or using auxiliary modules to measure their importance, which, however, requires expertise and trial-and-error. Due to the advantage of automation, pruning by evolutionary algorithms (EAs) has attracted much attention, but the performance is limited for deep neural networks as the search space can be quite large. In this paper, we propose a new filter pruning algorithm CCEP by cooperative coevolution, which prunes the filters in each layer by EAs separately. That is, CCEP reduces the pruning space by a divide-and-conquer strategy. The experiments show that CCEP can achieve a competitive performance with the state-of-the-art pruning methods, e.g., prune ResNet56 for $63.42\%$ FLOPs on CIFAR10 with $-0.24\%$ accuracy drop, and ResNet50 for $44.56\%$ FLOPs on ImageNet with $0.07\%$ accuracy drop.

cs.NE↗

arXiv2022

Robust Subset Selection by Greedy and Evolutionary Pareto Optimization

Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to find a subset which is robust against (i.e., is good over) a number of possible objective functions due to uncertainty, resulting in the problem of robust subset selection. This paper considers robust subset selection with monotone objective functions, relaxing the submodular property required by previous studies. We first show that the greedy algorithm can obtain an approximation ratio of $1-e^{-βγ}$, where $β$ and $γ$ are the correlation and submodularity ratios of the objective functions, respectively; and then propose EPORSS, an evolutionary Pareto optimization algorithm that can utilize more time to find better subsets. We prove that EPORSS can also be theoretically grounded, achieving a similar approximation guarantee to the greedy algorithm. In addition, we derive the lower bound of $β$ for the application of robust influence maximization, and further conduct experiments to validate the performance of the greedy algorithm and EPORSS.

cs.NE↗

arXiv2022

Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees

Given a ground set of items, the result diversification problem aims to select a subset with high "quality" and "diversity" while satisfying some constraints. It arises in various real-world artificial intelligence applications, such as web-based search, document summarization and feature selection, and also has applications in other areas, e.g., computational geometry, databases, finance and operations research. Previous algorithms are mainly based on greedy or local search. In this paper, we propose to reformulate the result diversification problem as a bi-objective maximization problem, and solve it by a multi-objective evolutionary algorithm (EA), i.e., the GSEMO. We theoretically prove that the GSEMO can achieve the (asymptotically) optimal theoretical guarantees under both static and dynamic environments. For cardinality constraints, the GSEMO can achieve the optimal polynomial-time approximation ratio, $1/2$. For more general matroid constraints, the GSEMO can achieve an asymptotically optimal polynomial-time approximation ratio, $1/2-ε/(4n)$, where $ε>0$ and $n$ is the size of the ground set of items. Furthermore, when the objective function (i.e., a linear combination of quality and diversity) changes dynamically, the GSEMO can maintain this approximation ratio in polynomial running time, addressing the open question proposed by Borodin. This also theoretically shows the superiority of EAs over local search for solving dynamic optimization problems for the first time, and discloses the robustness of the mutation operator of EAs against dynamic changes. Experiments on the applications of web-based search, multi-label feature selection and document summarization show the superior performance of the GSEMO over the state-of-the-art algorithms (i.e., the greedy algorithm and local search) under both static and dynamic environments.

cs.NE↗

arXiv2022

Running Time Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) using Binary or Stochastic Tournament Selection

Evolutionary algorithms (EAs) have been widely used to solve multi-objective optimization problems, and have become the most popular tool. However, the theoretical foundation of multi-objective EAs (MOEAs), especially the essential theoretical aspect, i.e., running time analysis, has been still largely underdeveloped. The few existing theoretical works mainly considered simple MOEAs, while the non-dominated sorting genetic algorithm II (NSGA-II), probably the most influential MOEA, has not been analyzed except for a very recent work considering a simplified variant without crossover. In this paper, we present a running time analysis of the standard NSGA-II for solving LOTZ, OneMinMax and COCZ, the three commonly used bi-objective optimization problems. Specifically, we prove that the expected running time (i.e., number of fitness evaluations) is $O(n^3)$ for LOTZ, and $O(n^2\log n)$ for OneMinMax and COCZ, which is surprisingly as same as that of the previously analyzed simple MOEAs, GSEMO and SEMO. Next, we introduce a new parent selection strategy, stochastic tournament selection (i.e., $k$ tournament selection where $k$ is uniformly sampled at random), to replace the binary tournament selection strategy of NSGA-II, decreasing the required expected running time to $O(n^2)$ for all the three problems. Experiments are also conducted, suggesting that the derived running time upper bounds are tight for LOTZ, and almost tight for OneMinMax and COCZ.

cs.NE↗

arXiv2022

An Adaptive and Scalable ANN-based Model-Order-Reduction Method for Large-Scale TO Designs

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which is computational expensive especially for large-scale design. Deep learning-based models have been developed to accelerate the process either by acting as surrogate models replacing the simulation process, or completely replacing the optimization process. However, most of them require a large set of labelled training data, which are generated mostly through simulations. The data generation time scales rapidly with the design domain size, decreasing the efficiency of the method itself. Another major issue is the weak generalizability of most deep learning models. Most models are trained to work with the design problem similar to that used for data generation and require retraining if the design problem changes. In this work a scalable deep learning-based model-order-reduction method is proposed to accelerate large-scale TO process, by utilizing MapNet, a neural network which maps the field of interest from coarse-scale to fine-scale. The proposed method allows for each simulation of the TO process to be performed at a coarser mesh, thereby greatly reducing the total computational time. Moreover, by using domain fragmentation, the transferability of the MapNet is largely improved. Specifically, it has been demonstrated that the MapNet trained using data from one cantilever beam design with a specific loading condition can be directly applied to other structure design problems with different domain shapes, sizes, boundary and loading conditions.

cs.LG↗

arXiv2022

On two questions of James

64 years ago, I. M. James raised two fundamental questions about octonionic Stiefel spaces. The prime objective of this paper is to figure out partial answers to both of them.

math.DG↗

arXiv2021

An adaptive artificial neural network-based generative design method for layout designs

Layout designs are encountered in a variety of fields. For problems with many design degrees of freedom, efficiency of design methods becomes a major concern. In recent years, machine learning methods such as artificial neural networks have been used increasingly to speed up the design process. A main issue of many such approaches is the need for a large corpus of training data that are generated using high-dimensional simulations. The high computational cost associated with training data generation largely diminishes the efficiency gained by using machine learning methods. In this work, an adaptive artificial neural network-based generative design approach is proposed and developed. This method uses a generative adversarial network to generate design candidates and thus the number of design variables is greatly reduced. To speed up the evaluation of the objective function, a convolutional neural network is constructed as the surrogate model for function evaluation. The inverse design is carried out using the genetic algorithm in conjunction with two neural networks. A novel adaptive learning and optimization strategy is proposed, which allows the design space to be effectively explored for the search for optimal solutions. As such the number of training data needed is greatly reduced. The performance of the proposed design method is demonstrated on two heat source layout design problems. In both problems, optimal designs have been obtained. Compared with several existing approaches, the proposed approach has the best performance in terms of accuracy and efficiency.

cs.LG↗

arXiv2020

Accelerating gradient-based topology optimization design with dual-model neural networks

Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as Finite Element Analysis (FEA). In this work, neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64x64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data.

cs.AI↗

arXiv2020

Extrinsic geometry of the Gromoll-Meyer sphere

Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Furthermore, on the quotiente $\widetilde{N}^{11}/S^3$, we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere $Σ^7$. Moreover, the induced metric on each hypersurface has positive Ricci curvature and quasi-positive sectional curvature simultaneously.

math.DG↗

arXiv2020

Bayesian Optimization using Pseudo-Points

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

stat.ML↗

arXiv2019

Maximizing Monotone DR-submodular Continuous Functions by Derivative-free Optimization

In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $β$ and $α$ to characterize how close a function is to continuous DR-submodulr and submodular, respectively. Under a convex polytope constraint, we prove that LDGM can achieve a $(1-e^{-β}-ε)$-approximation guarantee after $O(1/ε)$ iterations, which is the same as the best previous gradient-based algorithm. Moreover, in some special cases, a variant of LDGM can achieve a $((α/2)(1-e^{-α})-ε)$-approximation guarantee for (weakly) submodular functions. We also compare LDGM with the gradient-based algorithm Frank-Wolfe under noise, and show that LDGM can be more robust. Empirical results on budget allocation verify the effectiveness of LDGM.

cs.LG↗