Min-max routing problems aim to minimize the maximum tour length among agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes a new deep-learning framework to solve large-scale min-max routing problems. We model the simultaneous decision-making of multiple agents as a sequential generation process, allowing the utilization of scalable deep-learning models for sequential decision-making. In the sequentially approximated problem, we propose a scalable contextual Transformer model, Equity-Transformer, which generates sequential actions considering an equitable workload among other agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multiple traveling salesman problem (min-max mTSP) and the min-max multiple pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: //github.com/kaist-silab/equity-transformer
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Bayesian state and parameter estimation have been automated effectively in a variety of probabilistic programming languages. The process of model comparison on the other hand, which still requires error-prone and time-consuming manual derivations, is often overlooked despite its importance. This paper efficiently automates Bayesian model averaging, selection, and combination by message passing on a Forney-style factor graph with a custom mixture node. Parameter and state inference, and model comparison can then be executed simultaneously using message passing with scale factors. This approach shortens the model design cycle and allows for the straightforward extension to hierarchical and temporal model priors to accommodate for modeling complicated time-varying processes.
Periodically occurring accumulations of events or measured values are present in many time-dependent datasets and can be of interest for analyses. The frequency of such periodic behavior is often not known in advance, making it difficult to detect and tedious to explore. Automated analysis methods exist, but can be too costly for smooth, interactive analysis. We propose a compact visual representation that reveals periodicity by showing a phase histogram for a given period length that can be used standalone or in combination with other linked visualizations. Our approach supports guided, interactive analyses by suggesting other period lengths to explore, which are ranked based on two quality measures. We further describe how the phase can be mapped to visual representations in other views to reveal periodicity there.
The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a one-dimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schr\"odinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase.
Considering the infrastructure deployment cost and energy consumption, it is unrealistic to provide seamless coverage of the vehicular network. The presence of uncovered areas tends to hinder the prevalence of the in-vehicle services with large data volume. To this end, we propose a predictive cooperative multi-relay transmission strategy (PreCMTS) for the intermittently connected vehicular networks, fulfilling the 6G vision of semantic and green communications. Specifically, we introduce a task-driven knowledge graph (KG)-assisted semantic communication system, and model the KG into a weighted directed graph from the viewpoint of transmission. Meanwhile, we identify three predictable parameters about the individual vehicles to perform the following anticipatory analysis. Firstly, to facilitate semantic extraction, we derive the closed-form expression of the achievable throughput within the delay requirement. Then, for the extracted semantic representation, we formulate the mutually coupled problems of semantic unit assignment and predictive relay selection as a combinatorial optimization problem, to jointly optimize the energy efficiency and semantic transmission reliability. To find a favorable solution within limited time, we proposed a low-complexity algorithm based on Markov approximation. The promising performance gains of the PreCMTS are demonstrated by the simulations with realistic vehicle traces generated by the SUMO traffic simulator.
Data profiling is an essential process in modern data-driven industries. One of its critical components is the discovery and validation of complex statistics, including functional dependencies, data constraints, association rules, and others. However, most existing data profiling systems that focus on complex statistics do not provide proper integration with the tools used by contemporary data scientists. This creates a significant barrier to the adoption of these tools in the industry. Moreover, existing systems were not created with industrial-grade workloads in mind. Finally, they do not aim to provide descriptive explanations, i.e. why a given pattern is not found. It is a significant issue as it is essential to understand the underlying reasons for a specific pattern's absence to make informed decisions based on the data. Because of that, these patterns are effectively rest in thin air: their application scope is rather limited, they are rarely used by the broader public. At the same time, as we are going to demonstrate in this presentation, complex statistics can be efficiently used to solve many classic data quality problems. Desbordante is an open-source data profiler that aims to close this gap. It is built with emphasis on industrial application: it is efficient, scalable, resilient to crashes, and provides explanations. Furthermore, it provides seamless Python integration by offloading various costly operations to the C++ core, not only mining. In this demonstration, we show several scenarios that allow end users to solve different data quality problems. Namely, we showcase typo detection, data deduplication, and data anomaly detection scenarios.
Vehicle light detection is required for important downstream safe autonomous driving tasks, such as predicting a vehicle's light state to determine if the vehicle is making a lane change or turning. Currently, many vehicle light detectors use single-stage detectors which predict bounding boxes to identify a vehicle light, in a manner decoupled from vehicle instances. In this paper, we present a method for detecting a vehicle light given an upstream vehicle detection and approximation of a visible light's center. Our method predicts four approximate corners associated with each vehicle light. We experiment with CNN architectures, data augmentation, and contextual preprocessing methods designed to reduce surrounding-vehicle confusion. We achieve an average distance error from the ground truth corner of 5.09 pixels, about 17.24% of the size of the vehicle light on average. We train and evaluate our model on the LISA Lights dataset, allowing us to thoroughly evaluate our vehicle light corner detection model on a large variety of vehicle light shapes and lighting conditions. We propose that this model can be integrated into a pipeline with vehicle detection and vehicle light center detection to make a fully-formed vehicle light detection network, valuable to identifying trajectory-informative signals in driving scenes.
The dynamic vehicle routing problem with time windows (DVRPTW) is a generalization of the classical VRPTW to an online setting, where customer data arrives in batches and real-time routing solutions are required. In this paper we adapt the Hybrid Genetic Search (HGS) algorithm, a successful heuristic for VRPTW, to the dynamic variant. We discuss the affected components of the HGS algorithm including giant-tour representation, cost computation, initial population, crossover, and local search. Our approach modifies these components for DVRPTW, attempting to balance solution quality and constraints on future customer arrivals. To this end, we devise methods for comparing different-sized solutions, normalizing costs, and accounting for future epochs that do not require any prior training. Despite this limitation, computational results on data from the EURO meets NeurIPS Vehicle Routing Competition 2022 demonstrate significantly improved solution quality over the best-performing baseline algorithm.
Direct policy optimization in reinforcement learning is usually solved with policy-gradient algorithms, which optimize policy parameters via stochastic gradient ascent. This paper provides a new theoretical interpretation and justification of these algorithms. First, we formulate direct policy optimization in the optimization by continuation framework. The latter is a framework for optimizing nonconvex functions where a sequence of surrogate objective functions, called continuations, are locally optimized. Second, we show that optimizing affine Gaussian policies and performing entropy regularization can be interpreted as implicitly optimizing deterministic policies by continuation. Based on these theoretical results, we argue that exploration in policy-gradient algorithms consists in computing a continuation of the return of the policy at hand, and that the variance of policies should be history-dependent functions adapted to avoid local extrema rather than to maximize the return of the policy.
The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.
Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.
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