We introduce pattern injection local search (PILS), an optimization strategy that uses pattern mining to explore high-order local-search neighborhoods, and illustrate its application on the vehicle routing problem. PILS operates by storing a limited number of frequent patterns from elite solutions. During the local search, each pattern is used to define one move in which 1) incompatible edges are disconnected, 2) the edges defined by the pattern are reconnected, and 3) the remaining solution fragments are optimally reconnected. Each such move is accepted only in case of solution improvement. As visible in our experiments, this strategy results in a new paradigm of local search, which complements and enhances classical search approaches in a controllable amount of computational time. We demonstrate that PILS identifies useful high-order moves (e.g., 9-opt and 10-opt) which would otherwise not be found by enumeration, and that it significantly improves the performance of state-of-the-art population-based and neighborhood-centered metaheuristics.

Gradient-based methods are often used for policy optimization in deep reinforcement learning, despite being vulnerable to local optima and saddle points. Although gradient-free methods (e.g., genetic algorithms or evolution strategies) help mitigate these issues, poor initialization and local optima are still concerns in highly nonconvex spaces. This paper presents a method for policy optimization based on Monte-Carlo tree search and gradient-free optimization. Our method, called Monte-Carlo tree search for policy optimization (MCTSPO), provides a better exploration-exploitation trade-off through the use of the upper confidence bound heuristic. We demonstrate improved performance on reinforcement learning tasks with deceptive or sparse reward functions compared to popular gradient-based and deep genetic algorithm baselines.

The first part of this paper is devoted to the decision-theoretic analysis of random-design linear prediction with square loss. It is known that, under boundedness constraints on the response (and thus regression coefficients), the minimax excess risk scales as $C\sigma^2d/n$ up to constants, where $d$ is the model dimension, $n$ the sample size, and $\sigma^2$ the noise parameter. Here, we study the expected excess risk with respect to the full linear class. We show that the ordinary least squares (OLS) estimator is minimax optimal in the well-specified case, for every distribution of covariates and noise level. Further, we express the minimax risk in terms of the distribution of statistical leverage scores of individual samples. We deduce a precise minimax lower bound of $\sigma^2d/(n-d+1)$, valid for any distribution of covariates, which nearly matches the risk of OLS for Gaussian covariates. We then obtain nonasymptotic upper bounds on the minimax risk for covariates that satisfy a "small ball"-type regularity condition, which scale as $(1+o(1))\sigma^2d/n$ as $d=o(n)$, both in the well-specified and misspecified cases. Our main technical contribution is the study of the lower tail of the smallest singular value of empirical covariance matrices around $0$. We establish a general lower bound on this lower tail, together with a matching upper bound under a necessary regularity condition. Our proof relies on the PAC-Bayesian technique for controlling empirical processes, and extends an analysis of Oliveira (2016) devoted to a different part of the lower tail. Equivalently, our upper bound shows that the operator norm of the inverse sample covariance matrix has bounded $L^q$ norm up to $q\asymp n$, and this exponent is unimprovable. Finally, we show that the regularity condition on the design naturally holds for independent coordinates.

Learning text representation is crucial for text classification and other language related tasks. There are a diverse set of text representation networks in the literature, and how to find the optimal one is a non-trivial problem. Recently, the emerging Neural Architecture Search (NAS) techniques have demonstrated good potential to solve the problem. Nevertheless, most of the existing works of NAS focus on the search algorithms and pay little attention to the search space. In this paper, we argue that the search space is also an important human prior to the success of NAS in different applications. Thus, we propose a novel search space tailored for text representation. Through automatic search, the discovered network architecture outperforms state-of-the-art models on various public datasets on text classification and natural language inference tasks. Furthermore, some of the design principles found in the automatic network agree well with human intuition.

Abstract--Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are handcrafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances. We show that directly optimizing the search cost is hard for bootstrapping, and propose to optimize the expected cost of reaching a leaf node in the search tree. T o capture the complex relations among the variables and constraints, we design a representation scheme based on Graph Neural Network that can process CSP instances with different sizes and constraint arities. Experimental results on random CSP instances show that the learned policies outperform classical handcrafted heuristics in terms of minimizing the search tree size, and can effectively generalize to instances that are larger than those used in training. Constraint Satisfaction Problem (CSP) is one of the most widely studied problems in computer science and artificial intelligence. It provides a common framework for modeling and solving combinatorial problems in many application domains, such as planning and scheduling [1], [2], vehicle routing [3], [4], graph problems [5], [6], and computational biology [7], [8]. A CSP instance involves a set of variables and constraints. T o solve it, one needs to find a value assignment for all variables such that all constraints are satisfied, or prove such assignment does not exist. Despite its ubiquitous applications, unfortunately, CSP is well known to be NPcomplete in general [9]. T o solve CSP efficiently, backtracking search algorithms are often employed, which are exact algorithms with the guarantee that a solution will be found if one exists.

Originally published in 1968 by Hart, Nilsson, and Raphael,2 the well-known A* search algorithm is a foundational pathfinding algorithm in computer science and artificial intelligence (AI) for traversing trees and graphs. The method provides the optimal path from the initial state to the target goal state, given the use of an admissible heuristic (must not overestimate the remaining distance to the goal). The A* algorithm is included in nearly all AI textbooks and courses worldwide. Given its widespread fame, however, there is no reliably documented evidence as to the origin of the name "A*": What does it really stand for and what does it mean? This Communications Viewpoint answers the question.

We propose a reinforcement learning framework for discrete environments in which an agent makes both strategic and tactical decisions. The former manifests itself through the use of value function, while the latter is powered by a tree search planner. These tools complement each other. The planning module performs a local \textit{what-if} analysis, which allows to avoid tactical pitfalls and boost backups of the value function. The value function, being global in nature, compensates for inherent locality of the planner. In order to further solidify this synergy, we introduce an exploration mechanism with two distinctive components: uncertainty modelling and risk measurement. To model the uncertainty we use value function ensembles, and to reflect risk we use propose several functionals that summarize the implied by the ensemble. We show that our method performs well on hard exploration environments: Deep-sea, toy Montezuma's Revenge, and Sokoban. In all the cases, we obtain speed-up in learning and boost in performance.

A classic graph coloring problem is to assign colors to vertices of any graph so that distinct colors are assigned to adjacent vertices. Optimal graph coloring colors a graph with a minimum number of colors, which is its chromatic number . Finding out the chromatic number is a combinatorial optimization problem proven to be computationally intractable, which implies that no algorithm that computes large instances of the problem in a reasonable time is known. F or this reason, approximate methods and metaheuristics form a set of techniques that do not guarantee optimality, but obtain good solutions in a reasonable time. This paper reports a comparative study of the Hill-Climbing, Simulated Annealing, T abu Search, and Iterated Local Search metaheuristics for the classic graph coloring problem considering its time efficiency for processing the DSJC125 and DSJC250 instances of the DIMACS benchmark.

Was investigated in this paper the use of a search strategy in the problem of finding the best path among multiple origins and multiple destinations. In this kind of problem, it must be decided within a lot of combinations which is the best origin and the best destination, and also the best path between these two regions. One remarkable difficulty to answer this sort of problem is to perform the search in a reduced time. This monography is a extension of previous research in which the problem described here was studied only in a bus network in the city of Fortaleza. This extension consisted of an exploration of the search strategy in graphs that represent public ways in cities like Fortaleza, Mumbai and Tokyo. Using this strategy with a heuristic algorithm, Haversine distance, was noticed that is possible to reduce substantially the time of the search, but introducing an error because of the loss of the admissible characteristic of the heuristic function applied.

Computational intelligence is a well-established paradigm, where new theories with a sound biological understanding have been evolving. The current experimental systems have many of the characteristics of biological computers (brains in other words) and are beginning to be built to perform a variety of tasks that are difficult or impossible to do with conventional computers. As evident, the ultimate achievement in this field would be to mimic or exceed human cognitive capabilities including reasoning, recognition, creativity, emotions, understanding, learning and so on. This book comprising of 17 chapters offers a step-by-step introduction (in a chronological order) to the various modern computational intelligence tools used in practical problem solving. Staring with different search techniques including informed and uninformed search, heuristic search, minmax, alpha-beta pruning methods, evolutionary algorithms and swarm intelligent techniques; the authors illustrate the design of knowledge-based systems and advanced expert systems, which incorporate uncertainty and fuzziness.