Recent researches show that machine learning has the potential to learn better heuristics than the one designed by human for solving combinatorial optimization problems. The deep neural network is used to characterize the input instance for constructing a feasible solution incrementally. Recently, an attention model is proposed to solve routing problems. In this model, the state of an instance is represented by node features that are fixed over time. However, the fact is, the state of an instance is changed according to the decision that the model made at different construction steps, and the node features should be updated correspondingly. Therefore, this paper presents a dynamic attention model with dynamic encoder-decoder architecture, which enables the model to explore node features dynamically and exploit hidden structure information effectively at different construction steps. This paper focuses on a challenging NP-hard problem, vehicle routing problem. The experiments indicate that our model outperforms the previous methods and also shows a good generalization performance.

The goalof online optimization is to find an approximatemaximizer of a given function f: D R d R with as little evaluations off as possible. In this paper we assumethat the only accessto the function f is through an oracle returning the (possibly) perturbed values of the function at the queried points. Perturbations can be deterministic or stochastic. No analytical expression of f or any of its derivatives is available. At each round k the learner picks a new point x k D and the value f(x k) is revealed by the oracle, up to an additive perturbation ξ k . After each evaluation, the learner can return a point x k D, which may differ from the last queried point x k .

There is increasing demand for automated systems that can fabricate 3D structures. Robotic spatial extrusion has become an attractive alternative to traditional layer-based 3D printing due to a manipulator's flexibility to print large, directionally-dependent structures. However, existing extrusion planning algorithms require a substantial amount of human input, do not scale to large instances, and lack theoretical guarantees. In this work, we present a rigorous formalization of robotic spatial extrusion planning and provide several efficient and probabilistically complete planning algorithms. The key planning challenge is, throughout the printing process, satisfying both stiffness constraints that limit the deformation of the structure and geometric constraints that ensure the robot does not collide with the structure. We show that, although these constraints often conflict with each other, a greedy backward state-space search guided by a stiffness-aware heuristic is able to successfully balance both constraints. We empirically compare our methods on a benchmark of over 40 simulated extrusion problems. Finally, we apply our approach to 3 real-world extrusion problems.

Current stateof-the-art first-order algorithms find an approximate Nash equilibrium using Õ(κ x κ y) [Tseng, 1995] or Õ(min{κ x κy, κ x κ y }) [Alkousa et al., 2019] gradient evaluations, where κ x and κ y are the condition numbers for the strong-convexity and strong-concavity assumptions. A gap remains between these results and the best existing lower bound Ω( κ x κ y) due to Zhang et al. [2019]. This paper presents the first algorithm with Õ( κ x κ y) gradient complexity, matching the lower bound up to logarithmic factors. Our new algorithm is designed based on an accelerated proximal point method and an accelerated solver for minimax proximal steps. It can be easily extended to the settings of strongly-convex-concave, convex-concave, nonconvex-strongly-concave, and nonconvexconcave functions. This paper also presents algorithms that match or outperform all existing methods in these settings in terms of gradient complexity, up to logarithmic factors.

State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based adversarial attacks to generate adversarially perturbed images. We pose the question whether another type of optimization could give neural network classifiers an edge. Here, we introduce a novel approach that uses minimax optimization to foil gradient-based adversarial attacks. Our minimax classifier is the discriminator of a generative adversarial network (GAN) that plays a minimax game with the GAN generator. In addition, our GAN generator projects all points onto a manifold that is different from the original manifold since the original manifold might be the cause of adversarial attacks. To measure the performance of our minimax defense, we use adversarial attacks - Carlini Wagner (CW), DeepFool, Fast Gradient Sign Method (FGSM) - on three datasets: MNIST, CIFAR-10 and German Traffic Sign (TRAFFIC). Against CW attacks, our minimax defense achieves 98.07% (MNIST-default 98.93%), 73.90% (CIFAR-10-default 83.14%) and 94.54% (TRAFFIC-default 96.97%). Against DeepFool attacks, our minimax defense achieves 98.87% (MNIST), 76.61% (CIFAR-10) and 94.57% (TRAFFIC). Against FGSM attacks, we achieve 97.01% (MNIST), 76.79% (CIFAR-10) and 81.41% (TRAFFIC). Our Minimax adversarial approach presents a significant shift in defense strategy for neural network classifiers.

We consider the problem of recovering a complex vector $\mathbf{x}\in \mathbb{C}^n$ from $m$ quadratic measurements $\{\langle A_i\mathbf{x}, \mathbf{x}\rangle\}_{i=1}^m$. This problem, known as quadratic feasibility, encompasses the well known phase retrieval problem and has applications in a wide range of important areas including power system state estimation and x-ray crystallography. In general, not only is the the quadratic feasibility problem NP-hard to solve, but it may in fact be unidentifiable. In this paper, we establish conditions under which this problem becomes {identifiable}, and further prove isometry properties in the case when the matrices $\{A_i\}_{i=1}^m$ are Hermitian matrices sampled from a complex Gaussian distribution. Moreover, we explore a nonconvex {optimization} formulation of this problem, and establish salient features of the associated optimization landscape that enables gradient algorithms with an arbitrary initialization to converge to a \emph{globally optimal} point with a high probability. Our results also reveal sample complexity requirements for successfully identifying a feasible solution in these contexts.

Dubins tours represent a solution of the Dubins Traveling Salesman Problem (DTSP) that is a variant of the optimization routing problem to determine a curvature-constrained shortest path to visit a set of locations such that the path is feasible for Dubins vehicle, which moves only forward and has a limited turning radius. The DTSP combines the NP-hard combinatorial optimization to determine the optimal sequence of visits to the locations, as in the regular TSP, with the continuous optimization of the heading angles at the locations, where the optimal heading values depend on the sequence of visits and vice versa. We address the computationally challenging DTSP by fast evaluation of the sequence of visits by the proposed Windowing Surrogate Model (WiSM) which estimates the length of the optimal Dubins path connecting a sequence of locations in a Dubins tour. The estimation is sped up by a regression model trained using close to optimum solutions of small Dubins tours that are generalized for large-scale instances of the addressed DTSP utilizing the sliding window technique and a cache for already computed results. The reported results support that the proposed WiSM enables a fast convergence of a relatively simple evolutionary algorithm to high-quality solutions of the DTSP. We show that with an increasing number of locations, our algorithm scales significantly better than other state-of-the-art DTSP solvers.

NeuroEvolution is one of the most competitive evolutionary learning frameworks for designing novel neural networks for use in specific tasks, such as logic circuit design and digital gaming. However, the application of benchmark methods such as the NeuroEvolution of Augmenting Topologies (NEAT) remains a challenge, in terms of their computational cost and search time inefficiency. This paper advances a method which incorporates a type of topological edge coding, named Reverse Encoding Tree (RET), for evolving scalable neural networks efficiently. Using RET, two types of approaches -- NEAT with Binary search encoding (Bi-NEAT) and NEAT with Golden-Section search encoding (GS-NEAT) -- have been designed to solve problems in benchmark continuous learning environments such as logic gates, Cartpole, and Lunar Lander, and tested against classical NEAT and FS-NEAT as baselines. Additionally, we conduct a robustness test to evaluate the resilience of the proposed NEAT algorithms. The results show that the two proposed strategies deliver an improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps; (2) using fewer episodes to solve problems in targeted environments, and (3) maintaining adaptive robustness under noisy perturbations, which outperform the baselines in all tested cases. Our analysis also demonstrates that RET expends potential future research directions in dynamic environments. Code is available from https://github.com/HaolingZHANG/ReverseEncodingTree.

-- Efficient driving in urban traffic scenarios requires foresight. The observation of other traffic participants, and the inference of their possible next actions depending on the own action is considered cooperative prediction and planning. Humans are well equipped with the capability to predict the actions of multiple interacting traffic participants and plan accordingly, without the need to directly communicate with others. Prior work has shown that it is possible to achieve effective cooperative planning without the need for explicit communication. However, the search space for cooperative plans is so large that the vast amount of the computational budget is spent on exploring the search space in unpromising regions that are far away from the solution. T o accelerate the planning process, we combined learned heuristics with a cooperative planning method in order to guide the search towards regions with promising actions, yielding better results at lower computational costs. Cooperative planning methods consider the mutual dependence of actions in multi-agent environments, opposed to methods that reduce multi-agent environments to single-agent environments, with other agents' action being independent of one another.

The identification of relevant features, i.e., the driving variables that determine a process or the property of a system, is an essential part of the analysis of data sets whose entries are described by a large number of variables. The preferred measure for quantifying the relevance of nonlinear statistical dependencies is mutual information, which requires as input probability distributions. Probability distributions cannot be reliably sampled and estimated from limited data, especially for real-valued data samples such as lengths or energies. Here, we introduce total cumulative mutual information (TCMI), a measure of the relevance of mutual dependencies based on cumulative probability distributions. TCMI can be estimated directly from sample data and is a non-parametric, robust and deterministic measure that facilitates comparisons and rankings between feature sets with different cardinality. The ranking induced by TCMI allows for feature selection, i.e., the identification of the set of relevant features that are statistical related to the process or the property of a system, while taking into account the number of data samples as well as the cardinality of the feature subsets. We evaluate the performance of our measure with simulated data, compare its performance with similar multivariate dependence measures, and demonstrate the effectiveness of our feature selection method on a set of standard data sets and a typical scenario in materials science.