Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g., continuous relaxation and Gower distance based GP) or by using a direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous exponential kernels to handle mixed-categorical variables. The proposed kernel leads to a new GP surrogate that generalizes both the continuous relaxation and the Gower distance based GP models. We demonstrate, on both analytical and engineering problems, that our proposed GP model gives a higher likelihood and a smaller residual error than the other kernel-based state-of-the-art models. Our method is available in the open-source software SMT.

Adaptive Loop Closure Detection: Spurious loop closures are frequent in environments with repetitive appearances, such as long streets. On the one hand, false positive place I. SYSTEM OVERVIEW retrievals may easily break the global optimization system, As shown in Figure 1, AutoMerge provides an automatic and ideally 100% accuracy can avoid these optimization map merging system for the large-scale single-/multi-agent failures for large-scale mapping. On the other hand, low recalls mapping tasks. Each agent is equipped with a LiDAR mapping can provide partial data association, which will affect global module to enable the self-maintained sub-map generation and optimization performance. Hybrid loop closure detection takes odometry estimation. The AutoMerge system consists of three advantage of sequence matching to provide continuous true modules: 1) fusion-enhanced place descriptor extraction, 2) an positive retrievals over long overlaps, and RANSAC-based adaptive data-association mechanism to provide high accuracy single frame detection for local overlaps. By analyzing the and recall for segment-wise place retrievals, and 3) a partially feature correlation between segments, we can balance the place decentralized system to provide centralized map merging and retrievals from sequence-/single-frame matching to provide single agent self-localization in the world frame.

This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings for this learning problem depending on (i) what additional information we have about $f$ (known as a model class assumption), (ii) how we measure the accuracy of how well $\hat f$ predicts $f$, (iii) what is known about the data and data sites, (iv) whether the data observations are polluted by noise. A mathematical description of the optimal performance possible (the smallest possible error of recovery) is known in the presence of a model class assumption. Under standard model class assumptions, it is shown in this paper that a near optimal $\hat f$ can be found by solving a certain discrete over-parameterized optimization problem with a penalty term. Here, near optimal means that the error is bounded by a fixed constant times the optimal error. This explains the advantage of over-parameterization which is commonly used in modern machine learning. The main results of this paper prove that over-parameterized learning with an appropriate loss function gives a near optimal approximation $\hat f$ of the function $f$ from which the data is collected. Quantitative bounds are given for how much over-parameterization needs to be employed and how the penalization needs to be scaled in order to guarantee a near optimal recovery of $f$. An extension of these results to the case where the data is polluted by additive deterministic noise is also given.

Personalized treatment decisions have become an integral part of modern medicine. Thereby, the aim is to make treatment decisions based on individual patient characteristics. Numerous methods have been developed for learning such policies from observational data that achieve the best outcome across a certain policy class. Yet these methods are rarely interpretable. However, interpretability is often a prerequisite for policy learning in clinical practice. In this paper, we propose an algorithm for interpretable off-policy learning via hyperbox search. In particular, our policies can be represented in disjunctive normal form (i.e., OR-of-ANDs) and are thus intelligible. We prove a universal approximation theorem that shows that our policy class is flexible enough to approximate any measurable function arbitrarily well. For optimization, we develop a tailored column generation procedure within a branch-and-bound framework. Using a simulation study, we demonstrate that our algorithm outperforms state-of-the-art methods from interpretable off-policy learning in terms of regret. Using real-word clinical data, we perform a user study with actual clinical experts, who rate our policies as highly interpretable.

Advanced programmatic hyperparameter optimization (HPO) methods, such as Bayesian optimization, have high sample efficiency in reproducibly finding optimal hyperparameter values of machine learning (ML) models. Yet, ML practitioners often apply less sample-efficient HPO methods, such as grid search, which often results in under-optimized ML models. As a reason for this behavior, we suspect practitioners choose HPO methods based on individual motives, consisting of contextual factors and individual goals. However, practitioners' motives still need to be clarified, hindering the evaluation of HPO methods for achieving specific goals and the user-centered development of HPO tools. To understand practitioners' motives for using specific HPO methods, we used a mixed-methods approach involving 20 semi-structured interviews and a survey study with 71 ML experts to gather evidence of the external validity of the interview results. By presenting six main goals (e.g., improving model understanding) and 14 contextual factors affecting practitioners' selection of HPO methods (e.g., available computer resources), our study explains why practitioners use HPO methods that seem inappropriate at first glance. This study lays a foundation for designing user-centered and context-adaptive HPO tools and, thus, linking social and technical research on HPO.

We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the customer has patience to view can be stochastic and dependent on the products seen. We develop a framework that views the interaction with each customer as an abstract resource consumption process, and derive new results for these online matching problems under the adversarial, non-stationary, and IID arrival models, assuming we can (approximately) solve the product ranking problem for each single customer. To that end, we show new results for product ranking under two cascade-click models: an optimal algorithm when each item has its own hazard rate for making the customer depart, and a 1/2-approximate algorithm when the customer has a general item-independent patience distribution. We also present a constant-factor 0.027-approximate algorithm in a new model where items are not initially available and arrive over time. We complement these positive results by presenting three additional negative results relating to these problems.

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative material discovery experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.

In the context of adversarial robustness, we make three strongly related contributions. First, we prove that while attacking ReLU classifiers is $\mathit{NP}$-hard, ensuring their robustness at training time is $\Sigma^2_P$-hard (even on a single example). This asymmetry provides a rationale for the fact that robust classifications approaches are frequently fooled in the literature. Second, we show that inference-time robustness certificates are not affected by this asymmetry, by introducing a proof-of-concept approach named Counter-Attack (CA). Indeed, CA displays a reversed asymmetry: running the defense is $\mathit{NP}$-hard, while attacking it is $\Sigma_2^P$-hard. Finally, motivated by our previous result, we argue that adversarial attacks can be used in the context of robustness certification, and provide an empirical evaluation of their effectiveness. As a byproduct of this process, we also release UG100, a benchmark dataset for adversarial attacks.

Trust-region methods based on Kullback-Leibler divergence are pervasively used to stabilize policy optimization in reinforcement learning. In this paper, we exploit more flexible metrics and examine two natural extensions of policy optimization with Wasserstein and Sinkhorn trust regions, namely Wasserstein policy optimization (WPO) and Sinkhorn policy optimization (SPO). Instead of restricting the policy to a parametric distribution class, we directly optimize the policy distribution and derive their closed-form policy updates based on the Lagrangian duality. Theoretically, we show that WPO guarantees a monotonic performance improvement, and SPO provably converges to WPO as the entropic regularizer diminishes. Moreover, we prove that with a decaying Lagrangian multiplier to the trust region constraint, both methods converge to global optimality. Experiments across tabular domains, robotic locomotion, and continuous control tasks further demonstrate the performance improvement of both approaches, more robustness of WPO to sample insufficiency, and faster convergence of SPO, over state-of-art policy gradient methods.

Community detection is a fundamental problem in computational sciences with extensive applications in various fields. The most commonly used methods are the algorithms designed to maximize modularity over different partitions of the network nodes. Using 80 real and random networks from a wide range of contexts, we investigate the extent to which current heuristic modularity maximization algorithms succeed in returning maximum-modularity (optimal) partitions. We evaluate (1) the ratio of the algorithms' output modularity to the maximum modularity for each input graph, and (2) the maximum similarity between their output partition and any optimal partition of that graph. We compare eight existing heuristic algorithms against an exact integer programming method that globally maximizes modularity. The average modularity-based heuristic algorithm returns optimal partitions for only 19.4% of the 80 graphs considered. Additionally, results on adjusted mutual information reveal substantial dissimilarity between the sub-optimal partitions and any optimal partition of the networks in our experiments. More importantly, our results show that near-optimal partitions are often disproportionately dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of commonly used modularity-based heuristics for discovering communities: they rarely produce an optimal partition or a partition resembling an optimal partition. If modularity is to be used for detecting communities, exact or approximate optimization algorithms are recommendable for a more methodologically sound usage of modularity within its applicability limits.