Sorted Table Search Procedures are the quintessential query-answering tool, with widespread usage that now includes also Web Applications, e.g, Search Engines (Google Chrome) and ad Bidding Systems (AppNexus). Speeding them up, at very little cost in space, is still a quite significant achievement. Here we study to what extend Machine Learning Techniques can contribute to obtain such a speed-up via a systematic experimental comparison of known efficient implementations of Sorted Table Search procedures, with different Data Layouts, and their Learned counterparts developed here. We characterize the scenarios in which those latter can be profitably used with respect to the former, accounting for both CPU and GPU computing. Our approach contributes also to the study of Learned Data Structures, a recent proposal to improve the time/space performance of fundamental Data Structures, e.g., B-trees, Hash Tables, Bloom Filters. Indeed, we also formalize an Algorithmic Paradigm of Learned Dichotomic Sorted Table Search procedures that naturally complements the Learned one proposed here and that characterizes most of the known Sorted Table Search Procedures as having a "learning phase" that approximates Simple Linear Regression.

The Boolean Satisfiability problem (SAT) is important on artificial intelligence community and the impact of its solving on complex problems. Recently, great breakthroughs have been made respectively on stochastic local search (SLS) algorithms for uniform random k-SAT resulting in several state-of-the-art SLS algorithms Score2SAT, YalSAT, ProbSAT, CScoreSAT and on a hybrid algorithm for hard random SAT (HRS) resulting in one state-of-the-art hybrid algorithm SparrowToRiss. However, there is no an algorithm which can effectively solve both uniform random k-SAT and HRS. In this paper, we present a new SLS algorithm named SelectNTS for uniform random k-SAT and HRS. SelectNTS is an improved probability selecting based local search algorithm for SAT problem. The core of SelectNTS relies on new clause and variable selection heuristics. The new clause selection heuristic uses a new clause weighting scheme and a biased random walk. The new variable selection heuristic uses a probability selecting strategy with the variation of CC strategy based on a new variable weighting scheme. Extensive experimental results on the well-known random benchmarks instances from the SAT Competitions in 2017 and 2018, and on randomly generated problems, show that our algorithm outperforms state-of-the-art random SAT algorithms, and our SelectNTS can effectively solve both uniform random k-SAT and HRS.

This paper introduces an enhanced meta-heuristic (ML-ACO) that combines machine learning (ML) and ant colony optimization (ACO) to solve combinatorial optimization problems. To illustrate the underlying mechanism of our enhanced algorithm, we start by describing a test problem -- the orienteering problem -- used to demonstrate the efficacy of ML-ACO. In this problem, the objective is to find a route that visits a subset of vertices in a graph within a time budget to maximize the collected score. In the first phase of our ML-ACO algorithm, an ML model is trained using a set of small problem instances where the optimal solution is known. Specifically, classification models are used to classify an edge as being part of the optimal route, or not, using problem-specific features and statistical measures. We have tested several classification models including graph neural networks, logistic regression and support vector machines. The trained model is then used to predict the probability that an edge in the graph of a test problem instance belongs to the corresponding optimal route. In the second phase, we incorporate the predicted probabilities into the ACO component of our algorithm. Here, the probability values bias sampling towards favoring those predicted high-quality edges when constructing feasible routes. We empirically show that ML-ACO generates results that are significantly better than the standard ACO algorithm, especially when the computational budget is limited. Furthermore, we show our algorithm is robust in the sense that (a) its overall performance is not sensitive to any particular classification model, and (b) it generalizes well to large and real-world problem instances. Our approach integrating ML with a meta-heuristic is generic and can be applied to a wide range of combinatorial optimization problems.

Code generation, defined as automatically writing a piece of code to solve a given problem for which an evaluation function exists, is a classic hard AI problem. Its general form, writing code using a general language used by human programmers from scratch is thought to be impractical. Adding constraints to the code grammar, implementing domain specific concepts as primitives and providing examples for the algorithm to learn, makes it practical. Formal fields is a framework to do code generation across domains using the same algorithms and language structure. Its ultimate goal is not just solving different narrow problems, but providing necessary abstractions to integrate many working solutions as a single lifelong reasoning system. It provides a common grammar to define: a domain language, a problem and its evaluation. The framework learns from examples of code snippets about the structure of the domain language and searches completely new code snippets to solve unseen problems in the same field. Formal fields abstract the search algorithm away from the problem. The search algorithm is taken from existing reinforcement learning algorithms. In our implementation it is an apropos Monte-Carlo Tree Search (MCTS). We have implemented formal fields as a fully documented open source project applied to the Abstract Reasoning Challenge (ARC). The implementation found code snippets solving twenty two previously unsolved ARC problems.

To automate the generation of interactive features, recent methods are proposed to either explicitly traverse the interactive feature space or implicitly express the interactions via intermediate activations of some designed models. These two kinds of methods show that there is essentially a trade-off between feature interpretability and efficient search. To possess both of their merits, we propose a novel method named Feature Interaction Via Edge Search (FIVES), which formulates the task of interactive feature generation as searching for edges on the defined feature graph. We first present our theoretical evidence that motivates us to search for interactive features in an inductive manner. Then we instantiate this search strategy by alternatively updating the edge structure and the predictive model of a graph neural network (GNN) associated with the defined feature graph. In this way, the proposed FIVES method traverses a trimmed search space and enables explicit feature generation according to the learned adjacency tensor of the GNN. Experimental results on both benchmark and real-world datasets demonstrate the advantages of FIVES over several state-of-the-art methods.

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The greedy techniques are low computational cost algorithms, which have also been modified to incorporate the non-negativity of the representations. One such modification has been proposed for Matching Pursuit (MP) based algorithms, which first chooses positive coefficients and uses a non-negative optimisation technique that guarantees the non-negativity of the coefficients. The performance of greedy algorithms, like all non-exhaustive search methods, suffer from high coherence with the linear generative model, called the dictionary. We here first reformulate the non-negative matching pursuit algorithm in the form of a deep neural network. We then show that the proposed model after training yields a significant improvement in terms of exact recovery performance, compared to other non-trained greedy algorithms, while keeping the complexity low.

People often plan hierarchically. That is, rather than planning over a monolithic representation of a task, they decompose the task into simpler subtasks and then plan to accomplish those. Although much work explores how people decompose tasks, there is less analysis of why people decompose tasks in the way they do. Here, we address this question by formalizing task decomposition as a resource-rational representation problem. Specifically, we propose that people decompose tasks in a manner that facilitates efficient use of limited cognitive resources given the structure of the environment and their own planning algorithms. Using this model, we replicate several existing findings. Our account provides a normative explanation for how people identify subtasks as well as a framework for studying how people reason, plan, and act using resource-rational representations.

One of the primary goals of the mathematical analysis of algorithms is to provide guidance about which algorithm is the "best" for solving a given computational problem. Worst-case analysis summarizes the performance profile of an algorithm by its worst performance on any input of a given size, implicitly advocating for the algorithm with the best-possible worst-case performance. Strong worst-case guarantees are the holy grail of algorithm design, providing an application-agnostic certification of an algorithm's robustly good performance. However, for many fundamental problems and performance measures, such guarantees are impossible and a more nuanced analysis approach is called for. This chapter surveys several alternatives to worst-case analysis that are discussed in detail later in the book.

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

We consider the problem of dynamically allocating tasks to multiple agents under time window constraints and task completion uncertainty. Our objective is to minimize the number of unsuccessful tasks at the end of the operation horizon. We present a multi-robot allocation algorithm that decouples the key computational challenges of sequential decision-making under uncertainty and multi-agent coordination and addresses them in a hierarchical manner. The lower layer computes policies for individual agents using dynamic programming with tree search, and the upper layer resolves conflicts in individual plans to obtain a valid multi-agent allocation. Our algorithm, Stochastic Conflict-Based Allocation (SCoBA), is optimal in expectation and complete under some reasonable assumptions. In practice, SCoBA is computationally efficient enough to interleave planning and execution online. On the metric of successful task completion, SCoBA consistently outperforms a number of baseline methods and shows strong competitive performance against an oracle with complete lookahead. It also scales well with the number of tasks and agents. We validate our results over a wide range of simulations on two distinct domains: multi-arm conveyor belt pick-and-place and multi-drone delivery dispatch in a city.