It might seem counter-intuitive at first: We find that, in expectation, the proportion of data points in an unknown population-that belong to classes that do not appear in the training data-is almost entirely determined by the number $f_k$ of classes that do appear in the training data the same number of times. While in theory we show that the difference of the induced estimator decays exponentially in the size of the sample, in practice the high variance prevents us from using it directly for an estimator of the sample coverage. However, our precise characterization of the dependency between $f_k$'s induces a large search space of different representations of the expected value, which can be deterministically instantiated as estimators. Hence, we turn to optimization and develop a genetic algorithm that, given only the sample, searches for an estimator with minimal mean-squared error (MSE). In our experiments, our genetic algorithm discovers estimators that have a substantially smaller MSE than the state-of-the-art Good-Turing estimator. This holds for over 96% of runs when there are at least as many samples as classes. Our estimators' MSE is roughly 80% of the Good-Turing estimator's.

Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving MILPs, and many commercial and academic software packages exist. Nevertheless, the availability of data, both from problem instances and from solvers, and the desire to solve new problems and larger (real-life) instances, trigger the need for continuing algorithmic development. MILP solvers use branch and bound as their main component. In recent years, there has been an explosive development in the use of machine learning algorithms for enhancing all main tasks involved in the branch-and-bound algorithm, such as primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This paper presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address how to represent MILPs in the context of applying learning algorithms, MILP benchmarks and software.

This paper formulates model selection as an infinite-armed bandit problem. The models are arms, and picking an arm corresponds to a partial training of the model (resource allocation). The reward is the accuracy of the selected model after its partial training. In this best arm identification problem, regret is the gap between the expected accuracy of the optimal model and that of the model finally chosen. We first consider a straightforward generalization of UCB-E to the stochastic infinite-armed bandit problem and show that, under basic assumptions, the expected regret order is $T^{-\alpha}$ for some $\alpha \in (0,1/5)$ and $T$ the number of resources to allocate. From this vanilla algorithm, we introduce the algorithm Mutant-UCB that incorporates operators from evolutionary algorithms. Tests carried out on three open source image classification data sets attest to the relevance of this novel combining approach, which outperforms the state-of-the-art for a fixed budget.

Artificial intelligence (AI) has driven many information and communication technology (ICT) breakthroughs. Nonetheless, the scope of ICT systems has expanded far beyond AI since the Turing test proposal. Critically, recent AI regulation proposals adopt AI definitions affecting ICT techniques, approaches, and systems that are not AI. In some cases, even works from mathematics, statistics, and engineering would be affected. Worryingly, AI misdefinitions are observed from Western societies to the Global South. In this paper, we propose a framework to score how \textit{validated as appropriately-defined for regulation} (VADER) an AI definition is. Our online, publicly-available VADER framework scores the coverage of premises that should underlie AI definitions for regulation, which aim to (i) reproduce principles observed in other successful technology regulations, and (ii) include all AI techniques and approaches while excluding non-AI works. Regarding the latter, our score is based on a dataset of representative AI, non-AI ICT, and non-ICT examples. We demonstrate our contribution by reviewing the AI regulation proposals of key players, namely the United States, United Kingdom, European Union, and Brazil. Importantly, none of the proposals assessed achieve the appropriateness score, ranging from a revision need to a concrete risk to ICT systems and works from other fields.

Bayesian optimization (BO) offers an elegant approach for efficiently optimizing black-box functions. However, acquisition criteria demand their own challenging inner-optimization, which can induce significant overhead. Many practical BO methods, particularly in high dimension, eschew a formal, continuous optimization of the acquisition function and instead search discretely over a finite set of space-filling candidates. Here, we propose to use candidates which lie on the boundary of the Voronoi tessellation of the current design points, so they are equidistant to two or more of them. We discuss strategies for efficient implementation by directly sampling the Voronoi boundary without explicitly generating the tessellation, thus accommodating large designs in high dimension. On a battery of test problems optimized via Gaussian processes with expected improvement, our proposed approach significantly improves the execution time of a multi-start continuous search without a loss in accuracy.

Large language models are increasingly solving tasks that are commonly believed to require human-level reasoning ability. However, these models still perform very poorly on benchmarks of general intelligence such as the Abstraction and Reasoning Corpus (ARC). In this paper, we approach ARC as a programming-by-examples problem, and introduce a novel and scalable method for language model self-improvement called Code Iteration (CodeIt). Our method iterates between 1) program sampling and hindsight relabeling, and 2) learning from prioritized experience replay. By relabeling the goal of an episode (i.e., the target program output given input) to the realized output produced by the sampled program, our method effectively deals with the extreme sparsity of rewards in program synthesis. Applying CodeIt to the ARC dataset, we demonstrate that prioritized hindsight replay, along with pre-training and data-augmentation, leads to successful inter-task generalization. CodeIt is the first neuro-symbolic approach that scales to the full ARC evaluation dataset. Our method solves 15% of ARC evaluation tasks, achieving state-of-the-art performance and outperforming existing neural and symbolic baselines.

Learning rewards from human behaviour or feedback is a promising approach to aligning AI systems with human values but fails to consistently extract correct reward functions. Interpretability tools could enable users to understand and evaluate possible flaws in learned reward functions. We propose Counterfactual Trajectory Explanations (CTEs) to interpret reward functions in reinforcement learning by contrasting an original with a counterfactual partial trajectory and the rewards they each receive. We derive six quality criteria for CTEs and propose a novel Monte-Carlo-based algorithm for generating CTEs that optimises these quality criteria. Finally, we measure how informative the generated explanations are to a proxy-human model by training it on CTEs. CTEs are demonstrably informative for the proxy-human model, increasing the similarity between its predictions and the reward function on unseen trajectories. Further, it learns to accurately judge differences in rewards between trajectories and generalises to out-of-distribution examples. Although CTEs do not lead to a perfect understanding of the reward, our method, and more generally the adaptation of XAI methods, are presented as a fruitful approach for interpreting learned reward functions.

Causal discovery is an essential part of causal inference (Spirtes et al., 2000; Peters et al., 2017), but estimating causal effects is extremely challenging if the underlying causal graph is unknown. Algorithms for learning causal graphs are many and varied, using different parametric structure, classes of graphical models, and assumptions about whether all relevant variables are measured (Spirtes et al., 2000; Kaltenpoth and Vreeken, 2023; Claassen and Bucur, 2022; Nowzohour et al., 2017; Zhang and Hyvarinen, 2009; Peters et al., 2017). In this paper, we consider only nonparametric assumptions, i.e. conditional independences in distributions that are represented by graphs. The primary graphical model used in causal inference is the directed acyclic graph, also known as a DAG. These offer a clear interpretation and are straightforward to conduct inference with, and are associated with probabilistic distributions by encoding conditional independence constraints.

Adversarial examples arose as a challenge for machine learning. To hinder them, most defenses alter how models are trained (e.g., adversarial training) or inference is made (e.g., randomized smoothing). Still, while these approaches markedly improve models' adversarial robustness, models remain highly susceptible to adversarial examples. Identifying that, in certain domains such as traffic-sign recognition, objects are implemented per standards specifying how artifacts (e.g., signs) should be designed, we propose a novel approach for improving adversarial robustness. Specifically, we offer a method to redefine standards, making minor changes to existing ones, to defend against adversarial examples. We formulate the problem of artifact design as a robust optimization problem, and propose gradient-based and greedy search methods to solve it. We evaluated our approach in the domain of traffic-sign recognition, allowing it to alter traffic-sign pictograms (i.e., symbols within the signs) and their colors. We found that, combined with adversarial training, our approach led to up to 25.18\% higher robust accuracy compared to state-of-the-art methods against two adversary types, while further increasing accuracy on benign inputs.

In Software Product Lines (SPLs) it may be difficult or even impossible to test all the products of the family because of the large number of valid feature combinations that may exist. Thus, we want to find a minimal subset of the product family that allows us to test all these possible combinations (pairwise). Furthermore, when testing a single product is a great effort, it is desirable to first test products composed of a set of priority features. This problem is called Prioritized Pairwise Test Data Generation Problem. State-of-the-art algorithms based on Integer Linear Programming for this problema are faster enough for small and medium instances. However, there exists some real instances that are too large to be computed with these algorithms in a reasonable time because of the exponential growth of the number of candidate solutions. Also, these heuristics not always lead us to the best solutions. In this work we propose a new approach based on a hybrid metaheuristic algorithm called Construct, Merge, Solve & Adapt. We compare this matheuristic with four algorithms: a Hybrid algorithm based on Integer Linear Programming ((HILP), a Hybrid algorithm based on Integer Nonlinear Programming (HINLP), the Parallel Prioritized Genetic Solver (PPGS), and a greedy algorithm called prioritized-ICPL. The analysis reveals that CMSA results in statistically significantly better quality solutions in most instances and for most levels of weighted coverage, although it requires more execution time.