论文检索

Nikita Kotelevskii, Samuel Horváth, Karthik Nandakumar, Martin Takac, Maxim Panov

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.

Margot Herin, Patrice Perny, Nataliya Sokolovska

In multicriteria decision making, sophisticated decision models often involve a non-additive set function (named capacity) to define the weights of all subsets of criteria. This makes it possible to model criteria interactions, leaving room for a diversity of attitudes in criteria aggregation. Fitting a capacity-based decision model to a given Decision Maker is a challenging problem and several batch learning methods have been proposed in the literature to derive the capacity from a database of preference examples. In this paper, we introduce an online algorithm for learning a sparse representation of the capacity, designed for decision contexts where preference examples become available sequentially. Our method based on regularized dual averaging is also well fitted to decision contexts involving a large number of preference examples or a large number of criteria. Moreover, we propose a variant making it possible to include normative constraints on the capacity (e.g., monotonicity, supermodularity) while preserving scalability, based on the alternating direction method of multipliers.

Wei Chen, Xiaokai Huang, Zijian Li, Ruichu Cai, Zhiyi Huang, Zhifeng Hao

Learning the causal structure of each individual plays a crucial role in neuroscience, biology, and so on. Existing methods consider data from each individual separately, which may yield inaccurate causal structure estimations in limited samples. To leverage more samples, we consider incorporating data from all individuals as population data. We observe that the variables of all individuals are influenced by the common environment variables they share. These shared environment variables can be modeled as latent variables and serve as a bridge connecting data from different individuals. In particular, we propose an Individual Linear Acyclic Model (ILAM) for each individual from population data, which models the individual's variables as being linearly influenced by their parents, in addition to environment variables and noise terms. Theoretical analysis shows that the model is identifiable when all environment variables are non-Gaussian, or even if some are Gaussian with an adequate diversity in the variance of noises for each individual. We then develop an individual causal structures learning method based on the Share Independence Component Analysis technique. Experimental results on synthetic and real-world data demonstrate the correctness of the method even when the sample size of each individual's data is small.

Emma Caizergues, François Durand, Fabien Mathieu

This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates estimation accuracy. We propose a general approach for making any sorting algorithm anytime and introduce two new algorithms: multizip sort and Corsort. Simulations showcase the superior performance of both algorithms compared to existing methods. Multizip sort keeps a low global complexity, while Corsort produces intermediate estimates surpassing previous algorithms.

Lucius E.J. Bynum, Joshua R. Loftus, Julia Stoyanovich

Counterfactuals underpin numerous techniques for auditing and understanding artificial intelligence (AI) systems. The traditional paradigm for counterfactual reasoning in this literature is the interventional counterfactual, where hypothetical interventions are imagined and simulated. For this reason, the starting point for causal reasoning about legal protections and demographic data in AI is an imagined intervention on a legally-protected characteristic, such as ethnicity, race, gender, disability, age, etc. We ask, for example, what would have happened had your race been different? An inherent limitation of this paradigm is that some demographic interventions — like interventions on race — may not be well-defined or translate into the formalisms of interventional counterfactuals. In this work, we explore a new paradigm based instead on the backtracking counterfactual, where rather than imagine hypothetical interventions on legally-protected characteristics, we imagine alternate initial conditions while holding these characteristics fixed. We ask instead, what would explain a counterfactual outcome for you as you actually are or could be? This alternate framework allows us to address many of the same social concerns, but to do so while asking fundamentally different questions that do not rely on demographic interventions.

Yanhui Zhu, Samik Basu, A. Pavan

We present an evolutionary algorithm evo-SMC for the problem of Submodular Maximization under Cost constraints (SMC). Our algorithm achieves 1/2-approximation with a high probability 1-1/n within O(n2 K) iterations, where K denotes the maximum size of a feasible solution set with cost constraint B. To the best of our knowledge, this is the best approximation guarantee offered by evolutionary algorithms for this problem. We further refine evo-SMC and develop st-evo-SMC. This stochastic version yields a significantly faster algorithm while maintaining the approximation ratio of 1/2, with probability 1-epsilon. The required number of iterations reduces to O(nK log(1/epsilon)/p), where the user defined parameters p represents the stochasticity probability, and epsilon denotes the error threshold. Finally, the empirical evaluations carried out through extensive experimentation substantiate the efficiency and effectiveness of our proposed algorithms. Our algorithms consistently outperform existing methods, producing higher-quality solutions.

Yumeng Zhang, Max Ward, Hung Nguyen

Given a directed graph, a set of source nodes, a target node and a budget, we study the problem of maximizing the number of source nodes disconnected from the target node by removing edges not exceeding the budget. Our model is mainly motivated by a cyber security use case where we need to minimize the attack surface of a Windows Active Directory system. In these high-profile attacks, the attackers first compromise a source (i.e., a compromised user node) and then laterally move to a destination (i.e., a high-privileged admin node). Our aim is to minimize the number of users with a path to the admin. We first prove that the problem is NP-hard. Algorithms for exact optimality usually struggle to converge on graphs that approach real-world network scales and therefore are not practical for usage. In light of this, we study anytime algorithms that return an acceptable result whenever the algorithm is terminated, and can improve optimality by allowing longer computational time. We observe the source connectivity of directed graphs, based on which we propose a novel anytime algorithm---the spiral algorithm. We also develop two Monte Carlo Tree Search (MCTS) algorithms as a baseline to study the performance of typical anytime algorithms for our problem, and show that the spiral algorithm improves the optimality at a significantly faster speed and therefore exhibits better anytime behavior compared with MCTS.

Zhengchen Yang, Jiping Zheng

Submodular function maximization has been studied extensively in recent years due to its numerous applications in machine learning and artificial intelligence. We study a natural online variant of this problem on massive streaming data in which elements arrive one-by-one and the algorithm has to maintain a solution under cardinality constraint, i.e., k. Upon arrival of an element, the algorithm to maximize a monotone submodular function has to decide whether to accept the element and may replace a previously chosen element. Existing algorithms cannot simultaneously achieve optimal performance in terms of competitive ratio, memory complexity and running time. Also, the algorithm with best competitive ratio performs poorly in practice. In this paper, we propose a new algorithm OnlineAdaptive with optimal performance by exploiting adaptive thresholds to decide the acceptance of arriving elements by replacement. We prove that the competitive ratio of OnlineAdaptive is at least 1/4, and the ratio is about 0.2959 when k>=4 and approaches 0.3178 when k tends to infinity. In addition, OnlineAdaptive only needs O(k) memory and just performs one oracle per element. Experiments on diverse datasets confirm that OnlineAdaptive outperforms existing algorithms in both quality and efficiency.

Ziliang Xiong, Mingyu Xiao

The Minimum Dominating Set Problem (MDSP) is an important NP-Hard optimization problem with many applications in various domains. This paper designs two exact algorithms for MDSP that use the same Branch-and-Bound framework. However, one uses LP relaxations as lower bounds for pruning the search space, and the other one is a pure combinatorial algorithm. The two algorithms possess a distinct advantage. Performance experiments on standard test datasets reveal that our combinatorial algorithm is over 1000 times faster than the previous state-of-the-art exact algorithm presented in IJCAI 2023, and our LP Relaxation algorithm can even enhance the speed of our combinatorial algorithm by over 100 times. However, our combinatorial algorithm still outperform the LP Relaxation algorithm on very dense graphs.

Zhenxuan Xie, Zhipeng Lü, Zhouxing Su, Chu-Min Li, Junwen Ding, Yuxuan Wang

The Latin square completion (LSC) problem aims to assign n symbols to the empty cells of a partially filled Latin square such that in each row and each column, each symbol appears exactly once. In this paper, we propose a swap relaxation-based fast local search algorithm called SRLS for solving the LSC problem. First, it introduces a novel search space definition, which forbids row conflicts based on which a swap-based neighborhood is defined. Second, a color domain relaxation technique is employed in the swap-based neighborhood by temporarily accepting the violation of some constraints to connect high-quality solutions. Third, two effective scoring functions are adopted to select neighborhood moves minimizing the number of conflicting edges as well as the number of color domain violations. Finally, SRLS employs an adaptive restart mechanism to balance the exploitation and exploration of the search. Extensive experiments on 1819 public benchmark instances demonstrate that SRLS outperforms the state-of-the-art algorithms in the literature in terms of both success rate and computational efficiency.

Tao Wu, Huachao Cui, Tao Guan, Yuesong Wang, Yan Jin

The Traveling Thief Problem (TTP) is a challenging combinatorial optimization problem with broad practical applications. TTP combines two NP-hard problems: the Traveling Salesman Problem (TSP) and Knapsack Problem (KP). While a number of machine learning and deep learning based algorithms have been developed for TSP and KP, there is limited research dedicated to TTP. In this paper, we present the first reinforcement learning based multi-start neighborhood search algorithm, denoted by ReinforceNS, for solving TTP. To accelerate the search, we employ a pre-processing procedure for neighborhood reduction. A TSP routing and an iterated greedy packing are independently utilized to construct a high-quality initial solution, further improved by a reinforcement learning based neighborhood search. Additionally, a post-optimization procedure is devised for continued solution improvement. We conduct extensive experiments on 60 commonly used benchmark instances with 76 to 33810 cities in the literature. The experimental results demonstrate that our proposed ReinforceNS algorithm outperforms three state-of-the-art algorithms in terms of solution quality with the same time limit. In particular, ReinforceNS achieves 12 new results for 18 instances publicly reported in a recent TTP competition. We also perform an additional experiment to validate the effectiveness of the reinforcement learning strategy.

Rui Sun, Yiyuan Wang, Shimao Wang, Hui Li, Ximing Li, Minghao Yin

The maximum k-plex problem (MKPP) is an significant relaxation version of the maximum clique problem with extensive applications. Recently, lots of researchers have proposed many heuristic algorithms based on various methods to solve the MKPP. In this work, to further improve the performance of solving the MKPP, we propose an efficient local search algorithm based on three main ideas. First, we propose a relaxed bounded configuration checking strategy that considers two kinds of historical searching information to relax the restricted strength of configuration checking and the forbidden condition of candidate vertices for the operation Add, respectively. Second, we present a novel solution information-based vertex selection strategy based on two kinds of solution information to select high-quality candidate vertices. Third, we define the solution core and then introduce a core-based perturbation strategy to help the algorithm jump out of local optima. The experimental results show that the proposed algorithm significantly outperforms the state-of-the-art MKPP algorithms in almost all the instances.

Shawn Skyler, Shahaf Shperberg, Dor Atzmon, Ariel Felner, Oren Salzman, Shao-Hung Chan, Han Zhang, Sven Koenig, William Yeoh, Carlos Hernandez Ulloa

This paper provides a theoretical study on Multi-Objective Heuristic Search. We first classify states in the state space into must-expand, maybe-expand, and never-expand states and then transfer these definitions to nodes in the search tree. We then formalize a framework that generalizes A* to Multi-Objective Search. We study different ways to order nodes under this framework and their relation to traditional tie-breaking policies and provide theoretical findings. Finally, we study and empirically compare different ordering functions.

Shengjie Ren, Zhijia Qiu, Chao Bian, Miqing Li, Chao Qian

In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to polynomial or even exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including (mu+1)-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.

Owen Randall, Martin Müller, Ting-Han Wei, Ryan Hayward

We propose Expected Work Search (EWS), a new game solving algorithm. EWS combines win rate estimation, as used in Monte Carlo Tree Search, with proof size estimation, as used in Proof Number Search. The search efficiency of EWS stems from minimizing a novel notion of Expected Work, which predicts the expected computation required to solve a position. EWS outperforms traditional solving algorithms on the games of Go and Hex. For Go, we present the first solution to the empty 5x5 board with the commonly used positional superko ruleset. For Hex, our algorithm solves the empty 8x8 board in under 4 minutes. Experiments show that EWS succeeds both with and without extensive domain-specific knowledge.

Chao Qian, Ke Xue, Ren-Jian Wang

Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have found many successful applications in reinforcement learning and robotics, helping improve the robustness in complex environments. Furthermore, they often empirically find a better overall solution than traditional search algorithms which explicitly search for a single highest-performing solution. However, their theoretical analysis is far behind, leaving many fundamental questions unexplored. In this paper, we try to shed some light on the optimization ability of QD algorithms via rigorous runtime analysis. By comparing the popular QD algorithm MAP-Elites with (\mu+1)-EA (a typical EA focusing on finding better objective values only), we prove that on two NP-hard problem classes with wide applications, i.e., monotone approximately submodular maximization with a size constraint, and set cover, MAP-Elites can achieve the (asymptotically) optimal polynomial-time approximation ratio, while (\mu+1)-EA requires exponential expected time on some instances. This provides theoretical justification for that QD algorithms can be helpful for optimization, and discloses that the simultaneous search for high-performing solutions with diverse behaviors can provide stepping stones to good overall solutions and help avoid local optima.

Abbas Mehrabian, Ankit Anand, Hyunjik Kim, Nicolas Sonnerat, Matej Balog, Gheorghe Comanici, Tudor Berariu, Andrew Lee, Anian Ruoss, Anna Bulanova 等

This work proposes a new learning-to-search benchmark and uses AI to discover new mathematical knowledge related to an open conjecture of Erdos (1975) in extremal graph theory. The problem is to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum---jump-starting the search for larger graphs using good graphs found at smaller sizes---we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Fei Liu, Xi Lin, Weiduo Liao, Zhenkun Wang, Qingfu Zhang, Xialiang Tong, Mingxuan Yuan

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution performance, while the real-world problem instances usually come from different distributions. A costly fine-tuning approach or generalized model retraining from scratch could be needed to tackle the out-of-distribution instances. Unlike the existing methods, this work investigates an efficient prompt learning approach in NCO for cross-distribution adaptation. To be concrete, we propose a novel prompt learning method to facilitate fast zero-shot adaptation of a pre-trained model to solve routing problem instances from different distributions. The proposed model learns a set of prompts among various distributions and then selects the best-matched one to prompt a pre-trained attention model for each problem instance. Extensive experiments show that the proposed prompt learning approach facilitates the fast adaptation of pre-trained routing models. It also outperforms existing generalized models on both in-distribution prediction and zero-shot generalization to a diverse set of new tasks. Our code implementation is available online at https://github.com/FeiLiu36/PromptVRP.

Dan-Xuan Liu, Yi-Heng Xu, Chao Qian

Peptide vaccines are growing in significance for fighting diverse diseases. Machine learning has improved the identification of peptides that can trigger immune responses, and the main challenge of peptide vaccine design now lies in selecting an effective subset of peptides due to the allelic diversity among individuals. Previous works mainly formulated this task as a constrained optimization problem, aiming to maximize the expected number of peptide-Major Histocompatibility Complex (peptide-MHC) bindings across a broad range of populations by selecting a subset of diverse peptides with limited size; and employed a greedy algorithm, whose performance, however, may be limited due to the greedy nature. In this paper, we propose a new framework PVD-EMO based on Evolutionary Multi-objective Optimization, which reformulates Peptide Vaccine Design as a bi-objective optimization problem that maximizes the expected number of peptide-MHC bindings and minimizes the number of selected peptides simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve it. We also incorporate warm-start and repair strategies into MOEAs to improve efficiency and performance. We prove that the warm-start strategy ensures that PVD-EMO maintains the same worst-case approximation guarantee as the previous greedy algorithm, and meanwhile, the EMO framework can help avoid local optima. Experiments on a peptide vaccine design for COVID-19, caused by the SARS-CoV-2 virus, demonstrate the superiority of PVD-EMO.

Zhuoyi Lin, Yaoxin Wu, Bangjian Zhou, Zhiguang Cao, Wen Song, Yingqian Zhang, Senthilnath Jayavelu

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to assist heuristics training for different downstream VRP variants. Particularly, we modularize neural architectures for complex VRPs into 1) the backbone Transformer for tackling the travelling salesman problem (TSP), and 2) the additional lightweight modules for processing problem-specific features in complex VRPs. Accordingly, we propose to pre-train the backbone Transformer for TSP, and then apply it in the process of fine-tuning the Transformer models for each target VRP variant. On the one hand, we fully fine-tune the trained backbone Transformer and problem-specific modules simultaneously. On the other hand, we only fine-tune small adapter networks along with the modules, keeping the backbone Transformer still. Extensive experiments on typical VRPs substantiate that 1) the full fine-tuning achieves significantly better performance than the one trained from scratch, and 2) the adapter-based fine-tuning also delivers comparable performance while being notably parameter-efficient. Furthermore, we empirically demonstrate the favorable effect of our method in terms of cross-distribution application and versatility.