Jump functions are the most studied non-unimodal benchmark in the theory of randomized search heuristics, in particular, evolutionary algorithms (EAs). They have significantly improved our understanding of how EAs escape from local optima. However, their particular structure -- to leave the local optimum one can only jump directly to the global optimum -- raises the question of how representative such results are. For this reason, we propose an extended class $\textsc{Jump}_{k,\delta}$ of jump functions that contain a valley of low fitness of width $\delta$ starting at distance $k$ from the global optimum. We prove that several previous results extend to this more general class: for all $k = o(n^{1/3})$ and $\delta < k$, the optimal mutation rate for the $(1+1)$~EA is $\frac{\delta}{n}$, and the fast $(1+1)$~EA runs faster than the classical $(1+1)$~EA by a factor super-exponential in $\delta$. However, we also observe that some known results do not generalize: the randomized local search algorithm with stagnation detection, which is faster than the fast $(1+1)$~EA by a factor polynomial in $k$ on $\textsc{Jump}_k$, is slower by a factor polynomial in $n$ on some $\textsc{Jump}_{k,\delta}$ instances. Computationally, the new class allows experiments with wider fitness valleys, especially when they lie further away from the global optimum.

In some puzzles, the strategy we need to use near the goal can be quite different from the strategy that is effective earlier on, e.g. due to a smaller branching factor near the exit state in a maze. A common approach in these cases is to apply both a forward and a backward search, and to try and align the two. In this work we propose an approach that takes this idea a step forward, within a reinforcement learning (RL) framework. Training a traditional forward-looking agent using RL can be difficult because rewards are often sparse, e.g. given only at the goal. Instead, we first train a backward-looking agent with a simple relaxed goal. We then augment the state representation of the puzzle with straightforward hint features that are extracted from the behavior of that agent. Finally, we train a forward looking agent with this informed augmented state. We demonstrate that this simple "access" to partial backward plans leads to a substantial performance boost. On the challenging domain of the Sokoban puzzle, our RL approach substantially surpasses the best learned solvers that generalize over levels, and is competitive with SOTA performance of the best highly-crafted solution. Impressively, we achieve these results while learning from only a small number of practice levels and using simple RL techniques.

In this work, we presented a study regarding two important aspects of evolving feature-based game evaluation functions: the choice of genome representation and the choice of opponent used to test the model. We compared three representations. One simpler and more limited, based on a vector of weights that are used in a linear combination of predefined game features. And two more complex, based on binary and n-ary trees. On top of this test, we also investigated the influence of fitness defined as a simulation-based function that: plays against a fixed weak opponent, plays against a fixed strong opponent, and plays against the best individual from the previous population. For a testbed, we have chosen a recently popular domain of digital collectible card games. We encoded our experiments in a programming game, Legends of Code and Magic, used in Strategy Card Game AI Competition. However, as the problems stated are of general nature we are convinced that our observations are applicable in the other domains as well.

Unlike DFS, which goes deep in a certain direction first before considering another direction, BFS will analyze the next node in each possible direction first and then repeat the process for the next node in each direction. So instead of working on one path/direction all the way, it is analyzing all the possible paths at the same time, node to node. It will analyze the first node in each direction, and then analyze the second node each direction, and repeat the process until the target node is found. Once the target node or solution is found, it stops looking. This algorithm is guaranteed to find the optimum solution as it will be going over all the paths at the same time and which ever reaches the goal first will be the optimum path/solution.

A Graph is a data structure consisting of finite number of nodes (or vertices) and edges that connect them. The numbered circles are nodes with the lines connecting them being the edges. A pair (0,1) represents an edge that connects the nodes or vertices 0 and 1. Graphs are used to represent and solve many real life problems. For example, they can represent any network which could be social media like Facebook, LinkedIn etc. or Google maps. In graph search, we traverse or search the graph data structure from node to node. The easiest to understand example would be that of navigation maps like Google Maps.

Quantum computing is a promising new paradigm for computer science. Quantum algorithms have proven themselves superior to classical ones in some classes of problems. The major examples are Shor's algorithm for solving the hidden subgroup problem and Grover's algorithm for the unstructured search problem, but quantum computing is not limited to them[18]. Simulating complex atomic systems using a quantum computer[8] could profoundly impact physics research since a quantum computer can naturally simulate the effects of quantum mechanics. Quantum Computing has also been impactful in the machine learning field. Basic linear algebra subroutines, such as Fourier transform, finding eigenvectors and eigenvalues, and solving linear equations, for example, exhibit exponential quantum speedups over their best known classical counterparts[4] Also, quantum machine learning aims to implement machine learning algorithms in quantum systems, by using the quantum properties such as superposition and entanglement to solve these problems efficiently[17]. However, practical limitations still hinder the development of a universal quantum computer that could use such algorithms. Current quantum computers are referred to as NISQ (Noisy Intermediate-Scale Quantum) computers [22] because of qubits imperfections and their available limited number, currently between 50 and 100. These numbers are not sufficient to execute error-correcting codes once 9 qubits are necessary to make 1 qubit fault-tolerant [7].

Artificial intelligence (AI) is becoming increasingly more popular and can be found in workplaces and homes around the world. However, how do we ensure trust in these systems? Regulation changes such as the GDPR mean that users have a right to understand how their data has been processed as well as saved. Therefore if, for example, you are denied a loan you have the right to ask why. This can be hard if the method for working this out uses "black box" machine learning techniques such as neural networks. TrustyAI is a new initiative which looks into explainable artificial intelligence (XAI) solutions to address trustworthiness in ML as well as decision services landscapes. In this paper we will look at how TrustyAI can support trust in decision services and predictive models. We investigate techniques such as LIME, SHAP and counterfactuals, benchmarking both LIME and counterfactual techniques against existing implementations. We also look into an extended version of SHAP, which supports background data selection to be evaluated based on quantitative data and allows for error bounds.

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in 2016 to solve dynamic programs to optimality. In particular, our paper presents and evaluates the effectiveness of the local-bound (LocB) and rough upper-bound pruning (RUB). LocB is a new and effective rule that leverages the approximate MDD structure to avoid the exploration of non-interesting nodes. RUB is a rule to reduce the search space during the development of bounded-width-MDDs. The experimental study we conducted on the Maximum Independent Set Problem (MISP), Maximum Cut Problem (MCP), Maximum 2 Satisfiability (MAX2SAT) and the Traveling Salesman Problem with Time Windows (TSPTW) shows evidence indicating that rough-upper-bound and local-bound pruning have a high impact on optimization solvers based on branch-and-bound with MDDs. In particular, it shows that RUB delivers excellent results but requires some effort when defining the model. Also, it shows that LocB provides a significant improvement automatically; without necessitating any user-supplied information. Finally, it also shows that rough-upper-bound and local-bound pruning are not mutually exclusive, and their combined benefit supersedes the individual benefit of using each technique.

We study the problem of performing automated experiment design for drug screening through Bayesian inference and optimisation. In particular, we compare and contrast the behaviour of linear-Gaussian models and Gaussian processes, when used in conjunction with upper confidence bound algorithms, Thompson sampling, or bounded horizon tree search. We show that non-myopic sophisticated exploration techniques using sparse tree search have a distinct advantage over methods such as Thompson sampling or upper confidence bounds in this setting. We demonstrate the significant superiority of the approach over existing and synthetic datasets of drug toxicity.

Best group subset selection aims to choose a small part of non-overlapping groups to achieve the best interpretability on the response variable. It is practically attractive for group variable selection; however, due to the computational intractability in high dimensionality setting, it doesn't catch enough attention. To fill the blank of efficient algorithms for best group subset selection, in this paper, we propose a group-splicing algorithm that iteratively detects effective groups and excludes the helpless ones. Moreover, coupled with a novel Bayesian group information criterion, an adaptive algorithm is developed to determine the true group subset size. It is certifiable that our algorithms enable identifying the optimal group subset in polynomial time under mild conditions. We demonstrate the efficiency and accuracy of our proposal by comparing state-of-the-art algorithms on both synthetic and real-world datasets.