Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \geq 1$. This generalizes linear regression and (real) phase retrieval, and is closely related to convex regression. Working within a non-asymptotic framework, we study this problem in the high-dimensional setting assuming that $k$ is a fixed constant, and focus on estimation of the unknown coefficients of the affine functions underlying the model. We analyze a natural alternating minimization (AM) algorithm for the non-convex least squares objective when the design is random. We show that the AM algorithm, when initialized suitably, converges with high probability and at a geometric rate to a small ball around the optimal coefficients. In order to initialize the algorithm, we propose and analyze a combination of a spectral method and a random search scheme in a low-dimensional space, which may be of independent interest. The final rate that we obtain is near-parametric and minimax optimal (up to a poly-logarithmic factor) as a function of the dimension, sample size, and noise variance. In that sense, our approach should be viewed as a direct and implementable method of enforcing regularization to alleviate the curse of dimensionality in problems of the convex regression type. As a by-product of our analysis, we also obtain guarantees on a classical algorithm for the phase retrieval problem under considerably weaker assumptions on the design distribution than was previously known. Numerical experiments illustrate the sharpness of our bounds in the various problem parameters.

Sequential decision problems in applications such as manipulation in warehouses, multi-step meal preparation, and routing in autonomous vehicle networks often involve reasoning about uncertainty, planning over discrete modes as well as continuous states, and reacting to dynamic updates. To formalize such problems generally, we introduce a class of Markov Decision Processes (MDPs) called Dynamic Multimodal Stochastic Shortest Paths (DMSSPs). Much of the work in these domains solves deterministic variants, which can yield poor results when the uncertainty has downstream effects. We develop a Hybrid Stochastic Planning (HSP) algorithm, which uses domain-agnostic abstractions to efficiently unify heuristic search for planning over discrete modes, approximate dynamic programming for stochastic planning over continuous states, and hierarchical interleaved planning and execution.

Abstract-- For planning rearrangements of objects in a clutter, it is required to know the goal configuration of the objects. The intermediate local search relies I. INTRODUCTION For instance, typical human environments, object movements. RELATED WORK are usually cluttered; and manipulating the environment to deal with such clutter is integral to performing everyday Related work in robotics Rearrangement of multiple movable chores in social environments, whether that means rearranging objects, a challenging problem that involves planning, objects upon a surface or across multiple surfaces. In particular, planning for geometric a surface is a difficult problem, because it requires the rearrangement with multiple movable objects and its variations, manipulation of existing objects on the surface, as well as such as navigation among movable obstacles [1], [2], the placement of new objects to be put on the surface. To have been studied using various approaches. Since even a solve such a problem, in general, task planning is required simplified variant the rearrangement problem with only one to decide for the order of manipulation actions (e.g., when to movable obstacle has been proved to be NPhard [3], [4], pick, place, move objects), and feasibility checks are required most studies introduce several important restrictions to the to check the execution of each manipulation action against problem, like monotonicity of plans [5]-[9], where each geometric/kinematic constraints (e.g., to avoid collisions).

Recent advances in Neural Architecture Search (NAS) have produced state-of-the-art architectures on several tasks. NAS shifts the efforts of human experts from developing novel architectures directly to designing architecture search spaces and methods to explore them efficiently. The search space definition captures prior knowledge about the properties of the architectures and it is crucial for the complexity and the performance of the search algorithm. However, different search space definitions require restarting the learning process from scratch. We propose a novel agent based on the Transformer that supports joint training and efficient transfer of prior knowledge between multiple search spaces and tasks.

While recent NAS algorithms are thousands of times faster than the pioneering works, it is often overlooked that they use fewer candidate operations, resulting in a significantly smaller search space. We present PR-DARTS, a NAS algorithm that discovers strong network configurations in a much larger search space and a single day. A small candidate operation pool is used, from which candidates are progressively pruned and replaced with better performing ones. Experiments on CIFAR-10 and CIFAR-100 achieve 2.51% and 15.53% test error, respectively, despite searching in a space where each cell has 150 times as many possible configurations than in the DARTS baseline.

Comprehensive quality-aware automated semantic web service composition is an NP-hard problem, where service composition workflows are unknown, and comprehensive quality, i.e., Quality of services (QoS) and Quality of semantic matchmaking (QoSM) are simultaneously optimized. The objective of this problem is to find a solution with optimized or near-optimized overall QoS and QoSM within polynomial time over a service request. In this paper, we proposed novel memetic EDA-based approaches to tackle this problem. The proposed method investigates the effectiveness of several neighborhood structures of composite services by proposing domain-dependent local search operators. Apart from that, a joint strategy of the local search procedure is proposed to integrate with a modified EDA to reduce the overall computation time of our memetic approach. To better demonstrate the effectiveness and scalability of our approach, we create a more challenging, augmented version of the service composition benchmark based on WSC-08 \cite{bansal2008wsc} and WSC-09 \cite{kona2009wsc}. Experimental results on this benchmark show that one of our proposed memetic EDA-based approach (i.e., MEEDA-LOP) significantly outperforms existing state-of-the-art algorithms.

Most structure inference methods either rely on exhaustive search or are purely data-driven. Exhaustive search robustly infers the structure of arbitrarily complex data, but it is slow. Data-driven methods allow efficient inference, but do not generalize when test data have more complex structures than training data. In this paper, we propose a hybrid inference algorithm, the Neurally-Guided Structure Inference (NG-SI), keeping the advantages of both search-based and data-driven methods. The key idea of NG-SI is to use a neural network to guide the hierarchical, layer-wise search over the compositional space of structures. We evaluate our algorithm on two representative structure inference tasks: probabilistic matrix decomposition and symbolic program parsing. It outperforms data-driven and search-based alternatives on both tasks.

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a brief survey of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges.

Neural Architecture Search (NAS) has emerged as a promising technique for automatic neural network design. However, existing NAS approaches often utilize manually designed action space, which is not directly related to the performance metric to be optimized (e.g., accuracy). As a result, using manually designed action space to perform NAS often leads to sample-inefficient explorations of architectures and thus can be sub-optimal. In order to improve sample efficiency, this paper proposes Latent Action Neural Architecture Search (LaNAS) that learns the action space to recursively partition the architecture search space into regions, each with concentrated performance metrics (\emph{i.e.}, low variance). During the search phase, as different architecture search action sequences lead to regions of different performance, the search efficiency can be significantly improved by biasing towards the regions with good performance. On the largest NAS dataset NasBench-101, our experimental results demonstrated that LaNAS is 22x, 14.6x and 12.4x more sample-efficient than random search, regularized evolution, and Monte Carlo Tree Search (MCTS) respectively. When applied to the open domain, LaNAS finds an architecture that achieves SoTA 98.0% accuracy on CIFAR-10 and 75.0% top1 accuracy on ImageNet (mobile setting), after exploring only 6,000 architectures.

In this article we demonstrate how to solve a variety of problems and puzzles using the built-in SAT solver of the computer algebra system Maple. Once the problems have been encoded into Boolean logic, solutions can be found (or shown to not exist) automatically, without the need to implement any search algorithm. In particular, we describe how to solve the $n$-queens problem, how to generate and solve Sudoku puzzles, how to solve logic puzzles like the Einstein riddle, how to solve the 15-puzzle, how to solve the maximum clique problem, and finding Graeco-Latin squares.