Machine learning pipelines that include a combinatorial optimization layer can give surprisingly efficient heuristics for difficult combinatorial optimization problems. Three questions remain open: which architecture should be used, how should the parameters of the machine learning model be learned, and what performance guarantees can we expect from the resulting algorithms? Following the intuitions of geometric deep learning, we explain why equivariant layers should be used when designing such pipelines, and illustrate how to build such layers on routing, scheduling, and network design applications. We introduce a learning approach that enables to learn such pipelines when the training set contains only instances of the difficult optimization problem and not their optimal solutions, and show its numerical performance on our three applications. Finally, using tools from statistical learning theory, we prove a theorem showing the convergence speed of the estimator. As a corollary, we obtain that, if an approximation algorithm can be encoded by the pipeline for some parametrization, then the learned pipeline will retain the approximation ratio guarantee. On our network design problem, our machine learning pipeline has the approximation ratio guarantee of the best approximation algorithm known and the numerical efficiency of the best heuristic.

This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions. We first establish algorithm-agnostic generalization bounds via uniform convergence between the empirical minimax problem and the population minimax problem. The sample complexities for achieving $\epsilon$-generalization are $\tilde{\mathcal{O}}(d\kappa^2\epsilon^{-2})$ and $\tilde{\mathcal{O}}(d\epsilon^{-4})$ for NC-SC and NC-C settings, respectively, where $d$ is the dimension and $\kappa$ is the condition number. We further study the algorithm-dependent generalization bounds via stability arguments of algorithms. In particular, we introduce a novel stability notion for minimax problems and build a connection between generalization bounds and the stability notion. As a result, we establish algorithm-dependent generalization bounds for stochastic gradient descent ascent (SGDA) algorithm and the more general sampling-determined algorithms.

It is well-known that for sparse linear bandits, when ignori ng the dependency on sparsity which is much smaller than the ambient dimension, t he worst-case mini-max regret is null Θ null dT null where d is the ambient dimension and T is the number of rounds. On the other hand, in the benign setting where ther e is no noise and the action set is the unit sphere, one can use divide-and-con quer to achieve null O (1) regret, which is (nearly) independent of d and T . This bound naturally interpolates the regret bounds for the worst-case constant -variance regime (i.e., σ To achieve this variance-aware regret guarantee, we develop a general framework that converts any variance-aware linear bandit algorithm to a varia nce-aware algorithm for sparse linear bandits in a "black-box" manner. Specifica lly, we take two recent algorithms as black boxes to illustrate that the claimed bou nds indeed hold, where the first algorithm can handle unknown-variance cases and th e second one is more efficient. This paper studies the sparse linear stochastic bandit prob lem, which is a special case of linear stochastic bandits. In linear bandits ( Dani et al., 2008), the agent is facing a sequential decision-making problem lasting for T rounds. Dani et al. ( 2008) proved that the minimax optimal regret for linear bandits is null Θ(d T) when the noises are independent Gaussian random variables with means 0 and variances 1 and both θ In real-world applications such as recommendation systems, only a few features may be relevant despite a large candidate feature space. In other words, the high-dimensional linear regime may actually allow a low-dimensional structure.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

Large-scale AI systems that combine search and learning have reached super-human levels of performance in game-playing, but have also been shown to fail in surprising ways. The brittleness of such models limits their efficacy and trustworthiness in real-world deployments. In this work, we systematically study one such algorithm, AlphaZero, and identify two phenomena related to the nature of exploration. First, we find evidence of policy-value misalignment -- for many states, AlphaZero's policy and value predictions contradict each other, revealing a tension between accurate move-selection and value estimation in AlphaZero's objective. Further, we find inconsistency within AlphaZero's value function, which causes it to generalize poorly, despite its policy playing an optimal strategy. From these insights we derive VISA-VIS: a novel method that improves policy-value alignment and value robustness in AlphaZero. Experimentally, we show that our method reduces policy-value misalignment by up to 76%, reduces value generalization error by up to 50%, and reduces average value error by up to 55%.

In this paper, we propose SCANING, an unsupervised framework for paraphrasing via controlled noise injection. We focus on the novel task of paraphrasing algebraic word problems having practical applications in online pedagogy as a means to reduce plagiarism as well as ensure understanding on the part of the student instead of rote memorization. This task is more complex than paraphrasing general-domain corpora due to the difficulty in preserving critical information for solution consistency of the paraphrased word problem, managing the increased length of the text and ensuring diversity in the generated paraphrase. Existing approaches fail to demonstrate adequate performance on at least one, if not all, of these facets, necessitating the need for a more comprehensive solution. To this end, we model the noising search space as a composition of contextual and syntactic aspects and sample noising functions consisting of either one or both aspects. This allows for learning a denoising function that operates over both aspects and produces semantically equivalent and syntactically diverse outputs through grounded noise injection. The denoising function serves as a foundation for learning a paraphrasing function which operates solely in the input-paraphrase space without carrying any direct dependency on noise. We demonstrate SCANING considerably improves performance in terms of both semantic preservation and producing diverse paraphrases through extensive automated and manual evaluation across 4 datasets.

Jobs on high-performance computing (HPC) clusters can suffer significant performance degradation due to inter-job network interference. Topology-aware job allocation problem (TJAP) is such a problem that decides how to dedicate nodes to specific applications to mitigate inter-job network interference. In this paper, we study the window-based TJAP on a fat-tree network aiming at minimizing the cost of communication hop, a defined inter-job interference metric. The window-based approach for scheduling repeats periodically taking the jobs in the queue and solving an assignment problem that maps jobs to the available nodes. Two special allocation strategies are considered, i.e., static continuity assignment strategy (SCAS) and dynamic continuity assignment strategy (DCAS). For the SCAS, a 0-1 integer programming is developed. For the DCAS, an approach called neural simulated algorithm (NSA), which is an extension to simulated algorithm (SA) that learns a repair operator and employs them in a guided heuristic search, is proposed. The efficacy of NSA is demonstrated with a computational study against SA and SCIP. The results of numerical experiments indicate that both the model and algorithm proposed in this paper are effective.

How to interpret a data mining model has received much attention recently, because people may distrust a black-box predictive model if they do not understand how the model works. Hence, it will be trustworthy if a model can provide transparent illustrations on how to make the decision. Although many rule-based interpretable classification algorithms have been proposed, all these existing solutions cannot directly construct an interpretable model to provide personalized prediction for each individual test sample. In this paper, we make a first step towards formally introducing personalized interpretable classification as a new data mining problem to the literature. In addition to the problem formulation on this new issue, we present a greedy algorithm called PIC (Personalized Interpretable Classifier) to identify a personalized rule for each individual test sample. To demonstrate the necessity, feasibility and advantages of such a personalized interpretable classification method, we conduct a series of empirical studies on real data sets. The experimental results show that: (1) The new problem formulation enables us to find interesting rules for test samples that may be missed by existing non-personalized classifiers. (2) Our algorithm can achieve the same-level predictive accuracy as those state-of-the-art (SOTA) interpretable classifiers. (3) On a real data set for predicting breast cancer metastasis, such a personalized interpretable classifier can outperform SOTA methods in terms of both accuracy and interpretability.

The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP) can be solved by convex $\ell_1$-minimization. While these classes have been very successful, they leave out many practical applications. In this paper, we consider adaptable classes that are tractable after training on a curriculum of increasingly difficult samples. The setup is intended as a candidate model for a human mathematician, who may not be able to tackle an arbitrary proof right away, but may be successful in relatively flexible subclasses, or areas of expertise, after training on a suitable curriculum.

The construction of machine learning models involves many bi-level multi-objective optimization problems (BL-MOPs), where upper level (UL) candidate solutions must be evaluated via training weights of a model in the lower level (LL). Due to the Pareto optimality of sub-problems and the complex dependency across UL solutions and LL weights, an UL solution is feasible if and only if the LL weight is Pareto optimal. It is computationally expensive to determine which LL Pareto weight in the LL Pareto weight set is the most appropriate for each UL solution. This paper proposes a bi-level multi-objective learning framework (BLMOL), coupling the above decision-making process with the optimization process of the UL-MOP by introducing LL preference $r$. Specifically, the UL variable and $r$ are simultaneously searched to minimize multiple UL objectives by evolutionary multi-objective algorithms. The LL weight with respect to $r$ is trained to minimize multiple LL objectives via gradient-based preference multi-objective algorithms. In addition, the preference surrogate model is constructed to replace the expensive evaluation process of the UL-MOP. We consider a novel case study on multi-task graph neural topology search. It aims to find a set of Pareto topologies and their Pareto weights, representing different trade-offs across tasks at UL and LL, respectively. The found graph neural network is employed to solve multiple tasks simultaneously, including graph classification, node classification, and link prediction. Experimental results demonstrate that BLMOL can outperform some state-of-the-art algorithms and generate well-representative UL solutions and LL weights.