arXiv subjects

Chao Qian

Publications and source records attributed to Chao Qian.

At least 91 records · Page 5Linked to original sources

arXiv2023

Symmetry of hypersurfaces with symmetric boundary

Let $G$ be a compact connected subgroup of $SO(n+1)$. In $\mathbb{R}^{n+1}$, we gain interior $G$-symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (CMC) which have $G$-invariant boundaries and $G$-invariant contact angles along boundaries. The main ingredients of the proof are to build an associated Cauchy problem based on infinitesimal Lie group actions, and to apply Morrey's regularity theory and the Cauchy-Kovalevskaya Theorem. Moreover, we also investigate the same kind of symmetry inheritance from boundaries for hypersurfaces of constant higher order mean curvature and Helfrich-type hypersurfaces in $\mathbb{R}^{n+1}$.

math.DG↗

arXiv2023

Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.

cs.LG↗

arXiv2023

Effective and Imperceptible Adversarial Textual Attack via Multi-objectivization

The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.

cs.CL↗

arXiv2023

Enhancing Energy-efficiency by Solving the Throughput Bottleneck of LSTM Cells for Embedded FPGAs

To process sensor data in the Internet of Things(IoTs), embedded deep learning for 1-dimensional data is an important technique. In the past, CNNs were frequently used because they are simple to optimise for special embedded hardware such as FPGAs. This work proposes a novel LSTM cell optimisation aimed at energy-efficient inference on end devices. Using the traffic speed prediction as a case study, a vanilla LSTM model with the optimised LSTM cell achieves 17534 inferences per second while consuming only 3.8 $μ$J per inference on the FPGA XC7S15 from Spartan-7 family. It achieves at least 5.4$\times$ faster throughput and 1.37$\times$ more energy efficient than existing approaches.

cs.AR↗

arXiv2023

Macro Placement by Wire-Mask-Guided Black-Box Optimization

The development of very large-scale integration (VLSI) technology has posed new challenges for electronic design automation (EDA) techniques in chip floorplanning. During this process, macro placement is an important subproblem, which tries to determine the positions of all macros with the aim of minimizing half-perimeter wirelength (HPWL) and avoiding overlapping. Previous methods include packing-based, analytical and reinforcement learning methods. In this paper, we propose a new black-box optimization (BBO) framework (called WireMask-BBO) for macro placement, by using a wire-mask-guided greedy procedure for objective evaluation. Equipped with different BBO algorithms, WireMask-BBO empirically achieves significant improvements over previous methods, i.e., achieves significantly shorter HPWL by using much less time. Furthermore, it can fine-tune existing placements by treating them as initial solutions, which can bring up to 50% improvement in HPWL. WireMask-BBO has the potential to significantly improve the quality and efficiency of chip floorplanning, which makes it appealing to researchers and practitioners in EDA and will also promote the application of BBO. Our code is available at https://github.com/lamda-bbo/WireMask-BBO.

cs.LG↗

arXiv2023

Towards Running Time Analysis of Interactive Multi-objective Evolutionary Algorithms

Evolutionary algorithms (EAs) are widely used for multi-objective optimization due to their population-based nature. Traditional multi-objective EAs (MOEAs) generate a large set of solutions to approximate the Pareto front, leaving a decision maker (DM) with the task of selecting a preferred solution. However, this process can be inefficient and time-consuming, especially when there are many objectives or the subjective preferences of DM is known. To address this issue, interactive MOEAs (iMOEAs) combine decision making into the optimization process, i.e., update the population with the help of the DM. In contrast to their wide applications, there has existed only two pieces of theoretical works on iMOEAs, which only considered interactive variants of the two simple single-objective algorithms, RLS and (1+1)-EA. This paper provides the first running time analysis (the essential theoretical aspect of EAs) for practical iMOEAs. Specifically, we prove that the expected running time of the well-developed interactive NSGA-II (called R-NSGA-II) for solving the OneMinMax and OneJumpZeroJump problems is $O(n \log n)$ and $O(n^k)$, respectively, which are all asymptotically faster than the traditional NSGA-II. Meanwhile, we present a variant of OneMinMax, and prove that R-NSGA-II can be exponentially slower than NSGA-II. These results provide theoretical justification for the effectiveness of iMOEAs while identifying situations where they may fail. Experiments are also conducted to validate the theoretical results.

cs.NE↗

arXiv2023

A Study of Quantisation-aware Training on Time Series Transformer Models for Resource-constrained FPGAs

This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our approach demonstrates that matching the quantisation scheme to the real data distribution can reduce computational overhead while maintaining acceptable precision. Moreover, our approach is robust when applied to real-world data and mixed-precision quantisation, where most objects are quantised to 4 bits. Our findings inform model quantisation and deployment decisions while providing a foundation for advancing quantisation techniques.

cs.LG↗

arXiv2023

Neural Network Driven, Interactive Design for Nonlinear Optical Molecules Based on Group Contribution Method

A Lewis-mode group contribution method (LGC) -- multi-stage Bayesian neural network (msBNN) -- evolutionary algorithm (EA) framework is reported for rational design of D-Pi-A type organic small-molecule nonlinear optical materials is presented. Upon combination of msBNN and corrected Lewis-mode group contribution method (cLGC), different optical properties of molecules are afforded accurately and efficiently - by using only a small data set for training. Moreover, by employing the EA model designed specifically for LGC, structural search is well achievable. The logical origins of the well performance of the framework are discussed in detail. Considering that such a theory guided, machine learning framework combines chemical principles and data-driven tools, most likely, it will be proven efficient to solve molecular design related problems in wider fields.

stat.ML↗

arXiv2023

Can Evolutionary Clustering Have Theoretical Guarantees?

Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar. Due to its importance and NP-hardness, a lot of methods have been proposed, among which evolutionary algorithms are a class of popular ones. Evolutionary clustering has found many successful applications, but all the results are empirical, lacking theoretical support. This paper fills this gap by proving that the approximation performance of the GSEMO (a simple multi-objective evolutionary algorithm) for solving four formulations of clustering, i.e., $k$-tMM, $k$-center, discrete $k$-median and $k$-means, can be theoretically guaranteed. Furthermore, we consider clustering under fairness, which tries to avoid algorithmic bias, and has recently been an important research topic in machine learning. We prove that for discrete $k$-median clustering under individual fairness, the approximation performance of the GSEMO can be theoretically guaranteed with respect to both the objective function and the fairness constraint.

cs.NE↗

arXiv2023

Submodular Maximization under the Intersection of Matroid and Knapsack Constraints

Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of constraint, while many real-world problems often involve several constraints. In this paper, we consider the problem of submodular maximization under the intersection of two commonly used constraints, i.e., $k$-matroid constraint and $m$-knapsack constraint, and propose a new algorithm SPROUT by incorporating partial enumeration into the simultaneous greedy framework. We prove that SPROUT can achieve a polynomial-time approximation guarantee better than the state-of-the-art algorithms. Then, we introduce the random enumeration and smooth techniques into SPROUT to improve its efficiency, resulting in the SPROUT++ algorithm, which can keep a similar approximation guarantee. Experiments on the applications of movie recommendation and weighted max-cut demonstrate the superiority of SPROUT++ in practice.

cs.DS↗

arXiv2023

Robust multi-agent coordination via evolutionary generation of auxiliary adversarial attackers

Cooperative multi-agent reinforcement learning (CMARL) has shown to be promising for many real-world applications. Previous works mainly focus on improving coordination ability via solving MARL-specific challenges (e.g., non-stationarity, credit assignment, scalability), but ignore the policy perturbation issue when testing in a different environment. This issue hasn't been considered in problem formulation or efficient algorithm design. To address this issue, we firstly model the problem as a limited policy adversary Dec-POMDP (LPA-Dec-POMDP), where some coordinators from a team might accidentally and unpredictably encounter a limited number of malicious action attacks, but the regular coordinators still strive for the intended goal. Then, we propose Robust Multi-Agent Coordination via Evolutionary Generation of Auxiliary Adversarial Attackers (ROMANCE), which enables the trained policy to encounter diversified and strong auxiliary adversarial attacks during training, thus achieving high robustness under various policy perturbations. Concretely, to avoid the ego-system overfitting to a specific attacker, we maintain a set of attackers, which is optimized to guarantee the attackers high attacking quality and behavior diversity. The goal of quality is to minimize the ego-system coordination effect, and a novel diversity regularizer based on sparse action is applied to diversify the behaviors among attackers. The ego-system is then paired with a population of attackers selected from the maintained attacker set, and alternately trained against the constantly evolving attackers. Extensive experiments on multiple scenarios from SMAC indicate our ROMANCE provides comparable or better robustness and generalization ability than other baselines.

cs.MA↗

arXiv2023

Fast Teammate Adaptation in the Presence of Sudden Policy Change

In cooperative multi-agent reinforcement learning (MARL), where an agent coordinates with teammate(s) for a shared goal, it may sustain non-stationary caused by the policy change of teammates. Prior works mainly concentrate on the policy change during the training phase or teammates altering cross episodes, ignoring the fact that teammates may suffer from policy change suddenly within an episode, which might lead to miscoordination and poor performance as a result. We formulate the problem as an open Dec-POMDP, where we control some agents to coordinate with uncontrolled teammates, whose policies could be changed within one episode. Then we develop a new framework, fast teammates adaptation (Fastap), to address the problem. Concretely, we first train versatile teammates' policies and assign them to different clusters via the Chinese Restaurant Process (CRP). Then, we train the controlled agent(s) to coordinate with the sampled uncontrolled teammates by capturing their identifications as context for fast adaptation. Finally, each agent applies its local information to anticipate the teammates' context for decision-making accordingly. This process proceeds alternately, leading to a robust policy that can adapt to any teammates during the decentralized execution phase. We show in multiple multi-agent benchmarks that Fastap can achieve superior performance than multiple baselines in stationary and non-stationary scenarios.

cs.MA↗

arXiv2023

Benchmarking Algorithms for Submodular Optimization Problems Using IOHProfiler

Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for a wide class of submodular problems under various types of constraints while clearly outperforming standard greedy approximation algorithms. This paper introduces a setup for benchmarking algorithms for submodular optimization problems with the aim to provide researchers with a framework to enhance and compare the performance of new algorithms for submodular problems. The focus is on the development of iterative search algorithms such as evolutionary algorithms with the implementation provided and integrated into IOHprofiler which allows for tracking and comparing the progress and performance of iterative search algorithms. We present a range of submodular optimization problems that have been integrated into IOHprofiler and show how the setup can be used for analyzing and comparing iterative search algorithms in various settings.

cs.AI↗

arXiv2022

Multi-objective Evolutionary Algorithms are Generally Good: Maximizing Monotone Submodular Functions over Sequences

Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular optimization, which have a wide range of applications, such as maximum coverage, sparse regression, influence maximization, document summarization and sensor placement, just to name a few. Though they have provided some theoretical explanation for the general-purpose nature of EAs, the considered submodular objective functions are defined only over sets or multisets. To complement this line of research, this paper studies the problem class of maximizing monotone submodular functions over sequences, where the objective function depends on the order of items. We prove that for each kind of previously studied monotone submodular objective functions over sequences, i.e., prefix monotone submodular functions, weakly monotone and strongly submodular functions, and DAG monotone submodular functions, a simple multi-objective EA, i.e., GSEMO, can always reach or improve the best known approximation guarantee after running polynomial time in expectation. Note that these best-known approximation guarantees can be obtained only by different greedy-style algorithms before. Empirical studies on various applications, e.g., accomplishing tasks, maximizing information gain, search-and-tracking and recommender systems, show the excellent performance of the GSEMO.

cs.NE↗

arXiv2022

Running Time Analysis of the (1+1)-EA for Robust Linear Optimization

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint $k$. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter $d$ or budget $k$ allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

cs.CC↗

arXiv2022

Running Time Analysis of the (1+1)-EA for OneMax and LeadingOnes under Bit-wise Noise

In many real-world optimization problems, the objective function evaluation is subject to noise, and we cannot obtain the exact objective value. Evolutionary algorithms (EAs), a type of general-purpose randomized optimization algorithm, have been shown to be able to solve noisy optimization problems well. However, previous theoretical analyses of EAs mainly focused on noise-free optimization, which makes the theoretical understanding largely insufficient for the noisy case. Meanwhile, the few existing theoretical studies under noise often considered the one-bit noise model, which flips a randomly chosen bit of a solution before evaluation; while in many realistic applications, several bits of a solution can be changed simultaneously. In this paper, we study a natural extension of one-bit noise, the bit-wise noise model, which independently flips each bit of a solution with some probability. We analyze the running time of the (1+1)-EA solving OneMax and LeadingOnes under bit-wise noise for the first time, and derive the ranges of the noise level for polynomial and super-polynomial running time bounds. The analysis on LeadingOnes under bit-wise noise can be easily transferred to one-bit noise, and improves the previously known results. Since our analysis discloses that the (1+1)-EA can be efficient only under low noise levels, we also study whether the sampling strategy can bring robustness to noise. We prove that using sampling can significantly increase the largest noise level allowing a polynomial running time, that is, sampling is robust to noise.

cs.NE↗

arXiv2022

Maximizing Submodular or Monotone Approximately Submodular Functions by Multi-objective Evolutionary Algorithms

Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising results on the running time analysis (one essential theoretical aspect) of EAs have been obtained, while most of them focused on isolated combinatorial optimization problems, which do not reflect the general-purpose nature of EAs. To provide a general theoretical explanation of the behavior of EAs, it is desirable to study their performance on general classes of combinatorial optimization problems. To the best of our knowledge, the only result towards this direction is the provably good approximation guarantees of EAs for the problem class of maximizing monotone submodular functions with matroid constraints. The aim of this work is to contribute to this line of research. Considering that many combinatorial optimization problems involve non-monotone or non-submodular objective functions, we study the general problem classes, maximizing submodular functions with/without a size constraint and maximizing monotone approximately submodular functions with a size constraint. We prove that a simple multi-objective EA called GSEMO-C can generally achieve good approximation guarantees in polynomial expected running time.

cs.NE↗

arXiv2022

Analysis of Noisy Evolutionary Optimization When Sampling Fails

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Most previous studies on sampling are empirical, and the few theoretical studies mainly showed the effectiveness of sampling with a sufficiently large sample size. In this paper, we theoretically examine what strategies can work when sampling with any fixed sample size fails. By constructing a family of artificial noisy examples, we prove that sampling is always ineffective, while using parent or offspring populations can be helpful on some examples. We also construct an artificial noisy example to show that when using neither sampling nor populations is effective, a tailored adaptive sampling (i.e., sampling with an adaptive sample size) strategy can work. These findings may enhance our understanding of sampling to some extent, but future work is required to validate them in natural situations.

cs.NE↗