In this paper, we study the problem of k-center clustering with outliers. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez's algorithm, that was developed for solving the ordinary k-center clustering problem. Based on some novel observations, we show that a simple randomized version of this greedy strategy actually can handle outliers efficiently. We further show that this randomized greedy approach also yields small coreset for the problem in doubling metrics (even if the doubling dimension is not given), which can greatly reduce the computational complexity. Moreover, together with the partial clustering framework proposed by Guha et al. (2019), we prove that our coreset method can be applied to distributed data with a low communication complexity. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower complexities comparing with the existing methods.

Abstract: In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method recently developed in [26] by the authors. Abstract: Nonconvex-nonconcave minimax optimization has been the focus of intense research over the last decade due to its broad applications in machine learning and operation research. Unfortunately, most existing algorithms cannot be guaranteed to converge and always suffer from limit cycles. Their global convergence relies on certain conditions that are difficult to check, including but not limited to the global Polyak-Łojasiewicz condition, the existence of a solution satisfying the weak Minty variational inequality and α-interaction dominant condition.

Combinatorial problems are ubiquitous in the world around us. Actually, they are found in all fields of human activity. As illustrations, it may be a question of scheduling the operations to be carried out within an industrial process (production line of a vehicle, an airplane or a satellite), of extracting the recurring patterns in a transaction database (data mining), of organizing the roster of a service (in a hospital, university or industrial environment), of generating molecular structures with good properties (in chemistry or bioinformatics), etc. Solving optimization problems remains a difficult task, especially when the size of the instances of the problems to be solved is large and/or when optimality is desired. In reality, the difficulty is twofold: being able to appropriately write models for encountered problems and being able to effectively solve the different instances of these problems. The main paradigms for optimization, namely mathematical programming, metaheuristics and Constraint Programming (CP), including the Boolean SAT framework, offer varied and interesting tools (languages, libraries, software), and are in a way, quite complementary; each paradigm having its own success stories.

Fifteen Puzzle problem is one of the most classical problems that have captivated mathematical enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 1013 states that have to be explored and several algorithms have been applied to solve the Fifteen Puzzle instances. In this paper, to deal with this large state space, Bidirectional A* (BA*) search algorithm with three heuristics, such as Manhattan distance (MD), linear conflict (LC), and walking distance (WD) has been used to solve the Fifteen Puzzle problems. The three mentioned heuristics will be hybridized in a way that can dramatically reduce the number of generated states by the algorithm. Moreover, all those heuristics require only 25KB of storage but help the algorithm effectively reduce the number of generated states and expand fewer nodes. Our implementation of BA* search can significantly reduce the space complexity, and guarantee either optimal or near-optimal solutions.1

Networks found with Neural Architecture Search (NAS) achieve state-of-the-art performance in a variety of tasks, out-performing human-designed networks. However, most NAS methods heavily rely on human-defined assumptions that constrain the search: architecture's outer-skeletons, number of layers, parameter heuristics and search spaces. Additionally, common search spaces consist of repeatable modules (cells) instead of fully exploring the architecture's search space by designing entire architectures (macro-search). Imposing such constraints requires deep human expertise and restricts the search to pre-defined settings. In this paper, we propose LCMNAS, a method that pushes NAS to less constrained search spaces by performing macro-search without relying on pre-defined heuristics or bounded search spaces. LCMNAS introduces three components for the NAS pipeline: i) a method that leverages information about well-known architectures to autonomously generate complex search spaces based on Weighted Directed Graphs with hidden properties, ii) an evolutionary search strategy that generates complete architectures from scratch, and iii) a mixed-performance estimation approach that combines information about architectures at initialization stage and lower fidelity estimates to infer their trainability and capacity to model complex functions. We present experiments in 13 different data sets showing that LCMNAS is capable of generating both cell and macro-based architectures with minimal GPU computation and state-of-the-art results. More, we conduct extensive studies on the importance of different NAS components in both cell and macro-based settings. Code for reproducibility is public at https://github.com/VascoLopes/LCMNAS.

When considering post-training quantization, prior work has typically focused on developing a mixed precision scheme or learning the best way to partition a network for quantization. In our work, CPT-V, we look at a general way to improve the accuracy of networks that have already been quantized, simply by perturbing the quantization scales. Borrowing the idea of contrastive loss from self-supervised learning, we find a robust way to jointly minimize a loss function using just 1,000 calibration images. In order to determine the best performing quantization scale, CPT-V contrasts the features of quantized and full precision models in a self-supervised fashion. Unlike traditional reconstruction-based loss functions, the use of a contrastive loss function not only rewards similarity between the quantized and full precision outputs but also helps in distinguishing the quantized output from other outputs within a given batch. In addition, in contrast to prior works, CPT-V proposes a block-wise evolutionary search to minimize a global contrastive loss objective, allowing for accuracy improvement of existing vision transformer (ViT) quantization schemes. For example, CPT-V improves the top-1 accuracy of a fully quantized ViT-Base by 10.30%, 0.78%, and 0.15% for 3-bit, 4-bit, and 8-bit weight quantization levels. Extensive experiments on a variety of other ViT architectures further demonstrate its robustness in extreme quantization scenarios. Our code is available at .

This has raised concerns about the possibility that algorithms may produce unfair and discriminatory decisions for specific population groups, particularly in sensitive socio-computational domains such as voting, hiring, banking, education, and criminal justice [12, 25]. To alleviate such concerns, there has been a lot of research devoted to incorporating fairness into the algorithms for automated decision tasks, including classification [14], clustering [10], ranking [24, 32], matching [28], and data summarization [8, 20]. This paper considers the diversity maximization problem and addresses its fairness-aware variant. The problem consists in selecting a diverse subset of items from a given dataset and is encountered in data summarization [8, 23], web search [2], recommendation [21], feature selection [31], and elsewhere [34]. Existing literature on the problem of diversity maximization primarily focuses on two objectives, namely max-min diversification (MMD), which aims to maximize the minimum distance between any pair of selected items, and max-sum diversification (MSD), which seeks to maximize the sum of pairwise distances between selected items. As shown in Figure 1, MMD tends to cover the data range uniformly, while MSD tends to pick "outliers" and may include highly similar items in the solution. Since the notion of diversity captured by MMD better represents the property that data summarization, feature selection, and many other tasks target with their solutions, we will only consider MMD in this paper. To be precise, given a set V of n items in a metric space and a positive integer k n, MMD asks for a size-k subset S of V to maximize the minimum pairwise distance within S. In particular, we study the fair max-min diversification (FMMD) problem, a variant of MMD that aims not only to maximize the diversity measure defined above but also to guarantee the satisfaction of group fairness constraints as described below.

Deploying TinyML models on low-cost IoT hardware is very challenging, due to limited device memory capacity. Neural processing unit (NPU) hardware address the memory challenge by using model compression to exploit weight quantization and sparsity to fit more parameters in the same footprint. However, designing compressible neural networks (NNs) is challenging, as it expands the design space across which we must make balanced trade-offs. This paper demonstrates Unified DNAS for Compressible (UDC) NNs, which explores a large search space to generate state-of-the-art compressible NNs for NPU. ImageNet results show UDC networks are up to $3.35\times$ smaller (iso-accuracy) or 6.25% more accurate (iso-model size) than previous work.

Domain-specific heuristics are an essential technique for solving combinatorial problems efficiently. Current approaches to integrate domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory when dealing with heuristics that are specified non-monotonically on the basis of partial assignments. Such heuristics frequently occur in practice, for example, when picking an item that has not yet been placed in bin packing. Therefore, we present novel syntax and semantics for declarative specifications of domain-specific heuristics in ASP. Our approach supports heuristic statements that depend on the partial assignment maintained during solving, which has not been possible before. We provide an implementation in Alpha that makes Alpha the first lazy-grounding ASP system to support declaratively specified domain-specific heuristics. Two practical example domains are used to demonstrate the benefits of our proposal. Additionally, we use our approach to implement informed search with A*, which is tackled within ASP for the first time. A* is applied to two further search problems. The experiments confirm that combining lazy-grounding ASP solving and our novel heuristics can be vital for solving industrial-size problems.

Abstract: Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known applications of quantum computing, enabling quantum computers to perform a database search (unsorted array) and quadratically outperform their classical counterparts in terms of time. Given the restricted access to database search for an oracle model (black-box), researchers have demonstrated various implementations of Grover's circuit for two to four qubits on various platforms. However, larger search spaces have not yet been explored. In this paper, a scalable Quantum Grover Search algorithm is introduced and implemented using 5-qubit and 6-qubit quantum circuits, along with a design pattern for ease of building an Oracle for a higher order of qubits.