We propose a novel surrogate-assisted Evolutionary Algorithm for solving expensive combinatorial optimization problems. We integrate a surrogate model, which is used for fitness value estimation, into a state-of-the-art P3-like variant of the Gene-Pool Optimal Mixing Algorithm (GOMEA) and adapt the resulting algorithm for solving non-binary combinatorial problems. We test the proposed algorithm on an ensemble learning problem. Ensembling several models is a common Machine Learning technique to achieve better performance. We consider ensembles of several models trained on disjoint subsets of a dataset. Finding the best dataset partitioning is naturally a combinatorial non-binary optimization problem. Fitness function evaluations can be extremely expensive if complex models, such as Deep Neural Networks, are used as learners in an ensemble. Therefore, the number of fitness function evaluations is typically limited, necessitating expensive optimization techniques. In our experiments we use five classification datasets from the OpenML-CC18 benchmark and Support-vector Machines as learners in an ensemble. The proposed algorithm demonstrates better performance than alternative approaches, including Bayesian optimization algorithms. It manages to find better solutions using just several thousand fitness function evaluations for an ensemble learning problem with up to 500 variables.

We propose the first general-purpose gradient-based attack against transformer models. Instead of searching for a single adversarial example, we search for a distribution of adversarial examples parameterized by a continuous-valued matrix, hence enabling gradient-based optimization. We empirically demonstrate that our white-box attack attains state-of-the-art attack performance on a variety of natural language tasks. Furthermore, we show that a powerful black-box transfer attack, enabled by sampling from the adversarial distribution, matches or exceeds existing methods, while only requiring hard-label outputs.

We propose an effective consistency training framework that enforces a training model's predictions given original and perturbed inputs to be similar by adding a discrete noise that would incur the highest divergence between predictions. This virtual adversarial discrete noise obtained by replacing a small portion of tokens while keeping original semantics as much as possible efficiently pushes a training model's decision boundary. Moreover, we perform an iterative refinement process to alleviate the degraded fluency of the perturbed sentence due to the conditional independence assumption. Experimental results show that our proposed method outperforms other consistency training baselines with text editing, paraphrasing, or a continuous noise on semi-supervised text classification tasks and a robustness benchmark.

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the $\ell_0$-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with smooth components. Our algorithmic framework consists of approximate and exact algorithms. The approximate algorithms are based on coordinate descent and local search, with runtimes comparable to popular sparse learning algorithms. Our exact algorithm is based on a standalone branch-and-bound (BnB) framework, which can solve the associated mixed integer programming (MIP) problem to certified optimality. By exploiting the problem structure, our custom BnB algorithm can solve to optimality problem instances with $5 \times 10^6$ features in minutes to hours -- over $1000$ times larger than what is currently possible using state-of-the-art commercial MIP solvers. We also explore statistical properties of the $\ell_0$-based estimators. We demonstrate, theoretically and empirically, that our proposed estimators have an edge over popular group-sparse estimators in terms of statistical performance in various regimes.

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with $10^{12}$ trees to $10^{15}$ trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than $10^{1000}$ trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering.

We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. First, we propose novel bounding algorithms based on Lagrangian Decomposition. Previous works have used off-the-shelf solvers to solve relaxations at each node of the BaB tree, or constructed weaker relaxations that can be solved efficiently, but lead to unnecessarily weak bounds. Our formulation restricts the optimization to a subspace of the dual domain that is guaranteed to contain the optimum, resulting in accelerated convergence. Furthermore, it allows for a massively parallel implementation, which is amenable to GPU acceleration via modern deep learning frameworks. Second, we present a novel activation-based branching strategy. By coupling an inexpensive heuristic with fast dual bounding, our branching scheme greatly reduces the size of the BaB tree compared to previous heuristic methods. Moreover, it performs competitively with a recent strategy based on learning algorithms, without its large offline training cost. Finally, we design a BaB framework, named Branch and Dual Network Bound (BaDNB), based on our novel bounding and branching algorithms. We show that BaDNB outperforms previous complete verification systems by a large margin, cutting average verification times by factors up to 50 on adversarial robustness properties.

Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms for any-angle path finding in static environments exist. However, when dynamic obstacles are present and time is the objective to be minimized, these algorithms can no longer guarantee optimality. In this work, we elaborate on why this is the case and what techniques can be used to solve the problem optimally. We present two algorithms, grounded in the same idea, that can obtain provably optimal solutions to the considered problem. One of them is a naive algorithm and the other one is much more involved. We conduct a thorough empirical evaluation showing that, in certain setups, the latter algorithm might be as fast as the previously-known greedy non-optimal solver while providing solutions of better quality. In some (rare) cases, the difference in cost is up to 76%, while on average it is lower than one percent (the same cost difference is typically observed between optimal and greedy any-angle solvers in static environments).

Many decisions involve choosing an uncertain course of actions in deep and wide decision trees, as when we plan to visit an exotic country for vacation. In these cases, exhaustive search for the best sequence of actions is not tractable due to the large number of possibilities and limited time or computational resources available to make the decision. Therefore, planning agents need to balance breadth (exploring many actions at each level of the tree) and depth (exploring many levels in the tree) to allocate optimally their finite search capacity. We provide efficient analytical solutions and numerical analysis to the problem of allocating finite sampling capacity in one shot to large decision trees. We find that in general the optimal policy is to allocate few samples per level so that deep levels can be reached, thus favoring depth over breadth search. In contrast, in poor environments and at low capacity, it is best to broadly sample branches at the cost of not sampling deeply, although this policy is marginally better than deep allocations. Our results provide a theoretical foundation for the optimality of deep imagination for planning and show that it is a generally valid heuristic that could have evolved from the finite constraints of cognitive systems.

We propose a novel policy update that combines regularized policy optimization with model learning as an auxiliary loss. The update (henceforth Muesli) matches MuZero's state-of-the-art performance on Atari. Notably, Muesli does so without using deep search: it acts directly with a policy network and has computation speed comparable to model-free baselines. The Atari results are complemented by extensive ablations, and by additional results on continuous control and 9x9 Go.

Machine Learning (ML) techniques are becoming an invaluable support for network intrusion detection, especially in revealing anomalous flows, which often hide cyber-threats. Typically, ML algorithms are exploited to classify/recognize data traffic on the basis of statistical features such as inter-arrival times, packets length distribution, mean number of flows, etc. Dealing with the vast diversity and number of features that typically characterize data traffic is a hard problem. This results in the following issues: i) the presence of so many features leads to lengthy training processes (particularly when features are highly correlated), while prediction accuracy does not proportionally improve; ii) some of the features may introduce bias during the classification process, particularly those that have scarce relation with the data traffic to be classified. To this end, by reducing the feature space and retaining only the most significant features, Feature Selection (FS) becomes a crucial pre-processing step in network management and, specifically, for the purposes of network intrusion detection. In this review paper, we complement other surveys in multiple ways: i) evaluating more recent datasets (updated w.r.t. obsolete KDD 99) by means of a designed-from-scratch Python-based procedure; ii) providing a synopsis of most credited FS approaches in the field of intrusion detection, including Multi-Objective Evolutionary techniques; iii) assessing various experimental analyses such as feature correlation, time complexity, and performance. Our comparisons offer useful guidelines to network/security managers who are considering the incorporation of ML concepts into network intrusion detection, where trade-offs between performance and resource consumption are crucial.