Minimax Optimization Research Articles

Low-complexity reconfigurable FIR lowpass equalizers for polynomial channel models

This paper introduces realizations of a reconfigurable finite-impulse-response (FIR) filter for simultaneous equalization and lowpass filtering. The main advantage of the proposed solutions is computational complexity reduction compared to existing solutions for a given performance, which leads to reduced hardware complexity. The proposed structures employ properties of both a variable bandwidth (VBW) filter and a variable equalizer (VE) with variable coefficients. The overall transfer function of the proposed reconfigurable lowpass equalizer (RLPE) is a weighted linear combination of fixed subfilters where the weights are directly determined by the bandwidth and one or several parameters of the channel needed to be equalized. The paper provides design procedures based on minimax optimization and introduces a fast design method for the filter with several variable parameters that can substantially decrease the design time. Filter order estimation expressions as well as complexity expressions are presented for all proposed realizations. Design examples include comparison of the RLPE structures and a common approach of using a regular FIR equalization filter requiring online redesign when the bandwidth or channel characteristics are changed. It is shown that the number of general multiplications can be reduced up to 91% using the proposed RLPE.

CARE: Large Precision Matrix Estimation for Compositional Data

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Robust predictive minmax fault‐tolerant control for multi‐phase batch processes under partial actuator faults and asynchronous switching

AbstractIn view of the uncertainties, partial actuator faults, asynchronous switching as well as unknown external interference in multi‐phase batch processes, a robust predictive minmax fault‐tolerant control approach is presented. First, considering that a controller and a system state cannot switch synchronously during switching, a match‐and‐mismatch switching model is constructed. Then, an output tracking error is introduced to establish an equivalent extended switching model. In this extended model, the robust control issue is transformed into the minmax optimization issue by establishing the minmax performance index. On this basis, the control laws with control input and interference input are designed. Second, sufficient conditions are given to assure the system separately has asymptotic and exponential stabilities in each phase and batch. By calculating the given sufficient conditions online, the gains of the control laws, and the minimum and maximum operating time under match and mismatch cases are obtained. With the maximum operating time, the controller receives the switching signal beforehand to eliminate the mismatch case of switching. Additionally, a robust criterion is supplied to confirm the system's robustness. Finally, a simulation study of an injection molding process shows that the approach is valid and feasible.

Boosting generalization of fine-tuning BERT for fake news detection

Using deep neural networks to detect fake news has gradually become an extremely important field of research. Recent studies, which adopt fine-tuning BERT to detect fake news, have yielded promising results. Unfortunately, fine-tuning BERT is prone to overfitting the training data, which may reduce its generalization ability. The problem remains challenging when one tries to generalize the detector to unseen fake news. First, we investigate the effects of several fine-tuning strategies on the generalization of BERT models used in fake news detection. Specifically, we explore three fine-tuning strategies, which include initialization of model parameters, freezing of model parameters, and training iterations for fine-tuning. Besides, we propose an adversarial fine-tuning strategy to boost the generalization of fine-tuning BERT for fake news detection. In detail, we define the BERT fine-tuning procedure as a mini-max optimization problem. We also propose a novel adversarial fine-tuning training strategy based on feature regularization, called FGM-FRAT, to further improve the generalization. Specifically, we propose to adopt the model representation to guide the generation of adversarial examples during adversarial training on the word vector space. The proposed method outperforms state-of-the-art fake news detection methods. Extensive experiments on several benchmark databases, which include FakeNewsNet, BuzzFeedNews, LIAR, WELFake, and KaggleFakeNews, show that using the proposed method improves the generalization accuracy from 61% to 73% for BERT. It indicates that our FGM-FRAT can greatly improve the generalization of fine-tuning BERT for fake news detection. Moreover, the proposed method also can be extended to other pre-trained language models and other text classification tasks.

Collaborative control of path tracking and roll stability in intelligent commercial vehicle: A minimax robust regulator based on Nash game

—Currently, most vehicles are generally equipped with roll stability control system or electronic stability control system to improve stability. However, when encountering emergency obstacle avoidance and similar conditions, roll stability control system may compete with path tracking control system for vehicle control, resulting in the inability to balance path tracking and roll stability. Therefore, a closed-loop feedback Nash game collaborative control method is proposed to solve the collaborative problem between the two control systems. Firstly, a fifth-order vehicle model with coupled yaw-roll dynamics is presented, which was extended to a vehicle-road closed-loop model based on lateral position, yaw angle and road preview information. Secondly, the path tracking control system and roll stability control system are regarded as two agents in the dynamic game control process. On this basis, a Nash game collaborative control strategy is designed by fully considering the control interaction between two game agents. Finally, considering the influence of uncertain disturbances, a finite-time minimax robust control strategy is proposed by using minimax optimization theory. Simulation and hardware in loop experiments show that the minimax robust regulator based on Nash game controller can effectively improve the path tracking and roll stability performance of vehicles. Moreover, the regulator improves the robustness of the system when it is subjected to bounded uncertain lateral disturbances.

Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games

This paper makes progress toward learning Nash equilibria in two-player, zero-sum Markov games from offline data. Despite a large number of prior works tackling this problem, the state-of-the-art results suffer from the curse of multiple agents in the sense that their sample complexity bounds scale linearly with the total number of joint actions. The current paper proposes a new model-based algorithm, which provably finds an approximate Nash equilibrium with a sample complexity that scales linearly with the total number of individual actions. This work also develops a matching minimax lower bound, demonstrating the minimax optimality of the proposed algorithm for a broad regime of interest. An appealing feature of the result lies in algorithmic simplicity, which reveals the unnecessity of sophisticated variance reduction and sample splitting in achieving sample optimality.

Minimax Optimal Bandits for Heavy Tail Rewards.

Stochastic multiarmed bandits (stochastic MABs) are a problem of sequential decision-making with noisy rewards, where an agent sequentially chooses actions under unknown reward distributions to minimize cumulative regret. The majority of prior works on stochastic MABs assume that the reward distribution of each action has bounded supports or follows light-tailed distribution, i.e., sub-Gaussian distribution. However, in a variety of decision-making problems, the reward distributions follow a heavy-tailed distribution. In this regard, we consider stochastic MABs with heavy-tailed rewards, whose p th moment is bounded by a constant νp for . First, we provide theoretical analysis on sub-optimality of the existing exploration methods for heavy-tailed rewards where it has been proven that existing exploration methods do not guarantee a minimax optimal regret bound. Second, to achieve the minimax optimality under heavy-tailed rewards, we propose a minimax optimal robust upper confidence bound (MR-UCB) by providing tight confidence bound of a p -robust estimator. Furthermore, we also propose a minimax optimal robust adaptively perturbed exploration (MR-APE) which is a randomized version of MR-UCB. In particular, unlike the existing robust exploration methods, both proposed methods have no dependence on νp . Third, we provide the gap-dependent and independent regret bounds of proposed methods and prove that both methods guarantee the minimax optimal regret bound for a heavy-tailed stochastic MAB problem. The proposed methods are the first algorithm that theoretically guarantees the minimax optimality under heavy-tailed reward settings to the best of our knowledge. Finally, we demonstrate the superiority of the proposed methods in simulation with Pareto and Fréchet noises with respect to regrets.

Closed-form solutions of consistency ratio in best worst method minmax optimization model: max of edge error matrix and minmax edge error determinant methods

The Best Worst Method (BWM), a reduced version of the AHP, is a recent multi-criteria decision-making tool based on pairwise comparisons with reference to the best and worst criteria. Consistency Ratio (CR) measurement for the rating quality and prioritizations is still a controversial topic. Firstly, the computation for the current CR of BWM must rely on a software optimization solver to find the optimal values, and the solver may not always guarantee the exact optimal solutions, especially if the computational cost settings are not large enough for higher number of criteria. Secondly, much effort to evaluate optimization algorithms is needed to find the best solutions with the least computational resources due to diverse solvers possibly leading to different results with different performances. Thirdly, optimization programming code is not trivial to be implemented for general BWM users. To address these issues, this paper presents the closed-form solutions, Max of Edge Error Matrix (MEEM) (Eq. (44) of Theorem 4) and Minmax Edge Error Determinant (MEED) (Algorithm 1), to replace the BWM optimization models to directly calculate the CR values. Two simulations have been performed with a basic laptop using a single process. One simulation of twenty thousand random pairs of vectors took 26.34 h to perform to verify that the approximate results are higher than or very close to the exact closed-form values of both methods when high computational cost is allocated for the solver to increase the precision. Another simulation of one million random pairs of vectors only took 1.27 h to perform to verify that the MEED and MEEM methods always produce the same results for the number of criteria up to nine. The computational time for the exact results is dramatically reduced when the solver is not needed. The advantages of the proposed solutions include the following: the software to solve the optimization model to obtain CR is unnecessary, and the proposed calculation is extremely efficient to obtain the exact accuracy. The two-step optimization model can preserve the fixed Minmax Edge Error to find the weights which add up to one, which is the condition to determine if the model reaches exact optimal solutions. As the CR optimization model produces multiple versions of weights, which are recommended not to be used, the new method does not need to compute the unnecessary weight values to get the Minmax Edge Error. With the provision of equations leading to closed forms, users can understand the properties of CR in much clearer perspectives. Due to the computational efficiency and explainability, the proposed closed forms can replace the CR optimization model to compute CR efficiently and accurately for all diverse applications using BWM.

Domain Invariant Learning for Gaussian Processes and Bayesian Exploration

Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD generalization abilities. Surprisingly, their OOD generalization abilities have been under-explored before compared with other lines of GP research. In this paper, we identify that GP is not free from the problem and propose a domain invariant learning algorithm for Gaussian processes (DIL-GP) with a min-max optimization on the likelihood. DIL-GP discovers the heterogeneity in the data and forces invariance across partitioned subsets of data. We further extend the DIL-GP to improve Bayesian optimization's adaptability on changing environments. Numerical experiments demonstrate the superiority of DIL-GP for predictions on several synthetic and real-world datasets. We further demonstrate the effectiveness of the DIL-GP Bayesian optimization method on a PID parameters tuning experiment for a quadrotor. The full version and source code are available at: https://github.com/Billzxl/DIL-GP.

Faster Stochastic Variance Reduction Methods for Compositional MiniMax Optimization

This paper delves into the realm of stochastic optimization for compositional minimax optimization—a pivotal challenge across various machine learning domains, including deep AUC and reinforcement learning policy evaluation. Despite its significance, the problem of compositional minimax optimization is still under-explored. Adding to the complexity, current methods of compositional minimax optimization are plagued by sub-optimal complexities or heavy reliance on sizable batch sizes. To respond to these constraints, this paper introduces a novel method, called Nested STOchastic Recursive Momentum (NSTORM), which can achieve the optimal sample complexity and obtain the nearly accuracy solution, matching the existing minimax methods. We also demonstrate that NSTORM can achieve the same sample complexity under the Polyak-Lojasiewicz (PL)-condition—an insightful extension of its capabilities. Yet, NSTORM encounters an issue with its requirement for low learning rates, potentially constraining its real-world applicability in machine learning. To overcome this hurdle, we present ADAptive NSTORM (ADA-NSTORM) with adaptive learning rates. We demonstrate that ADA-NSTORM can achieve the same sample complexity but the experimental results show its more effectiveness. All the proposed complexities indicate that our proposed methods can match lower bounds to existing minimax optimizations, without requiring a large batch size in each iteration. Extensive experiments support the efficiency of our proposed methods.

Jointly Improving the Sample and Communication Complexities in Decentralized Stochastic Minimax Optimization

We propose a novel single-loop decentralized algorithm, DGDA-VR, for solving the stochastic nonconvex strongly-concave minimax problems over a connected network of agents, which are equipped with stochastic first-order oracles to estimate their local gradients. DGDA-VR, incorporating variance reduction, achieves O(ε^−3) oracle complexity and O(ε^−2) communication complexity without resorting to multi-communication rounds – both are optimal, i.e., matching the lower bounds for this class of problems. Since DGDA-VR does not require multiple communication rounds, it is applicable to a broader range of decentralized computational environments. To the best of our knowledge, this is the first distributed method using a single communication round in each iteration to jointly optimize the oracle and communication complexities for the problem considered here.

Solving Maxmin Optimization Problems via Population Games

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

Generalized variational framework with minimax optimization for parametric blind deconvolution

Blind deconvolution (BD), which aims to separate unknown convolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

Independence-Encouraging Subsampling for Nonparametric Additive Models

The additive model is a popular nonparametric regression method due to its ability to retain modeling flexibility while avoiding the curse of dimensionality. The backfitting algorithm is an intuitive and widely used numerical approach for fitting additive models. However, its application to large datasets may incur a high computational cost and is thus infeasible in practice. To address this problem, we propose a novel approach called independence-encouraging subsampling (IES) to select a subsample from big data for training additive models. Inspired by the minimax optimality of an orthogonal array (OA) due to its pairwise independent predictors and uniform coverage for the range of each predictor, the IES approach selects a subsample that approximates an OA to achieve the minimax optimality. Our asymptotic analyses demonstrate that an IES subsample converges to an OA and that the backfitting algorithm over the subsample converges to a unique solution even if the predictors are highly dependent in the full data. The proposed IES method is shown to be numerically appealing via simulations and a real data application. Theoretical proofs, R codes, and supplementary numerical results are accessible online as supplementary materials.

False Data Injection Attack with Max-Min Optimization in Smart Grid

With the proliferation of information and communication technology (ICT), the smart grid is critically vulnerable to cyber-attacks such as false data injection (FDI), denial-of-service, and data spoofing. The cyber-attackers defunctionalize critical operations of the smart grid by compromising the ICT. The decisions for the critical operation of the smart grid are processed with a state estimator, and ICT makes the state estimator vulnerable to FDI attacks. Hence, vulnerability analysis of the state estimator needs to be investigated for potential FDI attacks to protect it from future cyber-attacks. This work proposes the FDI attack vector construction without the knowledge of bad data detection (BDD) threshold on linear and non-linear state estimators using max-min optimization considering the partial network information. The optimization problem is formulated from the attacker's perspective to target the manipulation of measurements in the attack zone so as to increase the generation cost. The equivalent power injection model is developed for the attack zone to construct the deceptive attacks using DC and AC power flow models. The effectiveness of the proposed framework has been tested on 5 bus PJM network, modified IEEE 30 bus, IEEE 57 bus, and IEEE 118 bus system. The proposed framework is compared with existing state-of-art methods (viz., linear attack policy, non-linear attack policy, load redistribution attack, and line flow attack) to assess its efficacy. It is observed that the developed FDI attack vector successfully bypasses the bad data detectors such as the chi-square test, largest normalized residue, and l2 detector that is normally used by the system operator. Moreover, the study compares and discusses the impact of FDI attacks on the estimated state variables obtained with state estimators and, thereby, the generation cost calculated with the DC & AC optimal power flow tool.

Efficient Approximation Methods for Lexicographic Max-Min Optimization

Lexicographic max-min (LMM) optimization is of considerable importance in many fairness-oriented applications. LMM problems can be reformulated in a way that allows to solve them by applying the standard lexicographic maximization algorithm. However, the reformulation introduces a large number of auxiliary variables and linear constraints, making the process computationally complex. In this paper, two approximation schemes for such a reformulation are presented, resulting in problem size reduction and significant performance gains. Their influence on the quality of the solution is shown in a series of computational experiments concerned with the fair network dimensioning and bandwidth allocation problem.

A Heuristic Cutting Plane Algorithm For Budget Allocation of Large-scale Domestic Airport Network Protection

Abstract It is well known that airport security is an important component of homeland security, since airports are highly vulnerable to terrorist attacks. In order to improve the overall security of the domestic airport network, some work studied the budget allocation of domestic airport network protection. They established a minimax optimization model and designed an exact cutting plane algorithm to solve the problem. However, the exact algorithm can not solve large-scale problems in an acceptable time. Hence, this paper designs a heuristic cutting plane algorithm for solving budget allocation of large-scale domestic airport network protection. Finally, numerical experiments are carried out to demonstrate the feasibility and effectiveness of the new algorithm.

Research on Real-Time Detection of Maize Seedling Navigation Line Based on Improved YOLOv5s Lightweighting Technology

This study focuses on real-time detection of maize crop rows using deep learning technology to meet the needs of autonomous navigation for weed removal during the maize seedling stage. Crop row recognition is affected by natural factors such as soil exposure, soil straw residue, mutual shading of plant leaves, and light conditions. To address this issue, the YOLOv5s network model is improved by replacing the backbone network with the improved MobileNetv3, establishing a combination network model YOLOv5-M3 and using the convolutional block attention module (CBAM) to enhance detection accuracy. Distance-IoU Non-Maximum Suppression (DIoU-NMS) is used to improve the identification degree of the occluded targets, and knowledge distillation is used to increase the recall rate and accuracy of the model. The improved YOLOv5s target detection model is applied to the recognition and positioning of maize seedlings, and the optimal target position for weeding is obtained by max-min optimization. Experimental results show that the YOLOv5-M3 network model achieves 92.2% mean average precision (mAP) for crop targets and the recognition speed is 39 frames per second (FPS). This method has the advantages of high detection accuracy, fast speed, and is light weight and has strong adaptability and anti-interference ability. It determines the relative position of maize seedlings and the weeding machine in real time, avoiding squeezing or damaging the seedlings.

Nrat: towards adversarial training with inherent label noise

AbstractAdversarial training (AT) has been widely recognized as the most effective defense approach against adversarial attacks on deep neural networks and it is formulated as a min-max optimization. Most AT algorithms are geared towards research-oriented datasets such as MNIST, CIFAR10, etc., where the labels are generally correct. However, noisy labels, e.g., mislabelling, are inevitable in real-world datasets. In this paper, we investigate AT with inherent label noise, where the training dataset itself contains mislabeled samples. We first empirically show that the performance of AT typically degrades as the label noise rate increases. Then, we propose a Noisy-Robust Adversarial Training (NRAT) algorithm, which leverages the recent advancements in learning with noisy labels to enhance the performance of AT in the presence of label noise. For experimental comparison, we consider two essential metrics in AT: (i) trade-off between natural and robust accuracy; (ii) robust overfitting. Our experiments show that NRAT’s performance is on par with, or better than, the state-of-the-art AT methods on both evaluation metrics. Our code is publicly available at: https://github.com/TrustAI/NRAT.

Implementation of artificial intelligence in "ToqyzQumalaq" mobile logic game

This research paper delves into the implementation of artificial intelligence (AI) in the mobile logic game "ToqyzQumalaq," focusing on incorporating advanced algorithmic strategies to improve gameplay. The game's complexity and strategic depth present unique challenges in AI development, addressed through the integration of algorithms like Minimax, Alpha-Beta Pruning, Greedy, and Particle Swarm Optimization (PSO). The study emphasizes the creation of evaluation functions for these algorithms, ensuring AI efficiency and human-like decision-making. This aspect is vital for maintaining the strategic unpredictability essential to "ToqyzQumalaq." Extensive experimental testing against human players of various skill levels demonstrates the algorithms' effectiveness. These tests reveal the strengths and limitations of each algorithm, providing insights into their application in the game. This paper contributes to AI in gaming, highlighting the challenges and opportunities in developing AI for complex games. Its findings are relevant not only to game developers but also serve as an educational tool, showcasing the practical application of AI and algorithmic strategies.