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Shuffling gradient methods are widely implemented in practice, particularly including three popular algorithms: Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG). Compared to the empirical success, the theoretical guarantee of shuffling gradient methods was not well-understood for a long time. Until recently, the convergence rates had just been established for the average iterate for convex functions and the last iterate for strongly convex problems (using squared distance as the metric). However, when using the function value gap as the convergence criterion, existing theories cannot interpret the good performance of the last iterate in different settings (e.g., constrained optimization). To bridge this gap between practice and theory, we prove the first last-iterate convergence rates for shuffling gradient methods with respect to the objective value even without strong convexity. Our new results either (nearly) match the existing last-iterate lower bounds or are as fast as the previous best upper bounds for the average iterate.

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The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a state of the art evolutionary algorithm that leverages linkage learning to efficiently exploit problem structure. By identifying and preserving important building blocks during variation, GOMEA has shown promising performance on various optimization problems. In this paper, we provide the first runtime analysis of GOMEA on the concatenated trap function, a challenging benchmark problem that consists of multiple deceptive subfunctions. We derived an upper bound on the expected runtime of GOMEA with a truthful linkage model, showing that it can solve the problem in $O(m^{3}2^k)$ with high probability, where $m$ is the number of subfunctions and $k$ is the subfunction length. This is a significant speedup compared to the (1+1) EA, which requires $O(ln{(m)}(mk)^{k})$ expected evaluations.

We provide an algorithm for the simultaneous system identification and model predictive control of nonlinear systems. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal (non-causal) controller. Particularly, the algorithm enjoys sublinear dynamic regret, defined herein as the suboptimality against an optimal clairvoyant controller that knows how the unknown disturbances and system dynamics will adapt to its actions. The algorithm is self-supervised and applies to control-affine systems with unknown dynamics and disturbances that can be expressed in reproducing kernel Hilbert spaces. Such spaces can model external disturbances and modeling errors that can even be adaptive to the system's state and control input. For example, they can model wind and wave disturbances to aerial and marine vehicles, or inaccurate model parameters such as inertia of mechanical systems. The algorithm first generates random Fourier features that are used to approximate the unknown dynamics or disturbances. Then, it employs model predictive control based on the current learned model of the unknown dynamics (or disturbances). The model of the unknown dynamics is updated online using least squares based on the data collected while controlling the system. We validate our algorithm in both hardware experiments and physics-based simulations. The simulations include (i) a cart-pole aiming to maintain the pole upright despite inaccurate model parameters, and (ii) a quadrotor aiming to track reference trajectories despite unmodeled aerodynamic drag effects. The hardware experiments include a quadrotor aiming to track a circular trajectory despite unmodeled aerodynamic drag effects, ground effects, and wind disturbances.

The zero-shot effectiveness of neural retrieval models is often evaluated on the BEIR benchmark -- a combination of different IR evaluation datasets. Interestingly, previous studies found that particularly on the BEIR subset Touch\'e 2020, an argument retrieval task, neural retrieval models are considerably less effective than BM25. Still, so far, no further investigation has been conducted on what makes argument retrieval so "special". To more deeply analyze the respective potential limits of neural retrieval models, we run a reproducibility study on the Touch\'e 2020 data. In our study, we focus on two experiments: (i) a black-box evaluation (i.e., no model retraining), incorporating a theoretical exploration using retrieval axioms, and (ii) a data denoising evaluation involving post-hoc relevance judgments. Our black-box evaluation reveals an inherent bias of neural models towards retrieving short passages from the Touch\'e 2020 data, and we also find that quite a few of the neural models' results are unjudged in the Touch\'e 2020 data. As many of the short Touch\'e passages are not argumentative and thus non-relevant per se, and as the missing judgments complicate fair comparison, we denoise the Touch\'e 2020 data by excluding very short passages (less than 20 words) and by augmenting the unjudged data with post-hoc judgments following the Touch\'e guidelines. On the denoised data, the effectiveness of the neural models improves by up to 0.52 in nDCG@10, but BM25 is still more effective. Our code and the augmented Touch\'e 2020 dataset are available at \url{//github.com/castorini/touche-error-analysis}.

Shared dynamics models are important for capturing the complexity and variability inherent in Human-Robot Interaction (HRI). Therefore, learning such shared dynamics models can enhance coordination and adaptability to enable successful reactive interactions with a human partner. In this work, we propose a novel approach for learning a shared latent space representation for HRIs from demonstrations in a Mixture of Experts fashion for reactively generating robot actions from human observations. We train a Variational Autoencoder (VAE) to learn robot motions regularized using an informative latent space prior that captures the multimodality of the human observations via a Mixture Density Network (MDN). We show how our formulation derives from a Gaussian Mixture Regression formulation that is typically used approaches for learning HRI from demonstrations such as using an HMM/GMM for learning a joint distribution over the actions of the human and the robot. We further incorporate an additional regularization to prevent "mode collapse", a common phenomenon when using latent space mixture models with VAEs. We find that our approach of using an informative MDN prior from human observations for a VAE generates more accurate robot motions compared to previous HMM-based or recurrent approaches of learning shared latent representations, which we validate on various HRI datasets involving interactions such as handshakes, fistbumps, waving, and handovers. Further experiments in a real-world human-to-robot handover scenario show the efficacy of our approach for generating successful interactions with four different human interaction partners.

We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to control the divergence of the field. The approximation space for the original variables is constructed by patch reconstruction with exactly one degree of freedom per element in each dimension and the auxiliary variable is approximated by the piecewise constant space. We prove the optimal convergence rate under the energy norm and also suboptimal $L^2$ convergence using a duality approach. Numerical results are provided to verify the theoretical analysis.

With the emergence of large language models, such as LLaMA and OpenAI GPT-3, In-Context Learning (ICL) gained significant attention due to its effectiveness and efficiency. However, ICL is very sensitive to the choice, order, and verbaliser used to encode the demonstrations in the prompt. Retrieval-Augmented ICL methods try to address this problem by leveraging retrievers to extract semantically related examples as demonstrations. While this approach yields more accurate results, its robustness against various types of adversarial attacks, including perturbations on test samples, demonstrations, and retrieved data, remains under-explored. Our study reveals that retrieval-augmented models can enhance robustness against test sample attacks, outperforming vanilla ICL with a 4.87% reduction in Attack Success Rate (ASR); however, they exhibit overconfidence in the demonstrations, leading to a 2% increase in ASR for demonstration attacks. Adversarial training can help improve the robustness of ICL methods to adversarial attacks; however, such a training scheme can be too costly in the context of LLMs. As an alternative, we introduce an effective training-free adversarial defence method, DARD, which enriches the example pool with those attacked samples. We show that DARD yields improvements in performance and robustness, achieving a 15% reduction in ASR over the baselines. Code and data are released to encourage further research: //github.com/simonucl/adv-retreival-icl

In differentially private (DP) machine learning, the privacy guarantees of DP mechanisms are often reported and compared on the basis of a single $(\varepsilon, \delta)$-pair. This practice overlooks that DP guarantees can vary substantially even between mechanisms sharing a given $(\varepsilon, \delta)$, and potentially introduces privacy vulnerabilities which can remain undetected. This motivates the need for robust, rigorous methods for comparing DP guarantees in such cases. Here, we introduce the $\Delta$-divergence between mechanisms which quantifies the worst-case excess privacy vulnerability of choosing one mechanism over another in terms of $(\varepsilon, \delta)$, $f$-DP and in terms of a newly presented Bayesian interpretation. Moreover, as a generalisation of the Blackwell theorem, it is endowed with strong decision-theoretic foundations. Through application examples, we show that our techniques can facilitate informed decision-making and reveal gaps in the current understanding of privacy risks, as current practices in DP-SGD often result in choosing mechanisms with high excess privacy vulnerabilities.

The Chambolle-Pock algorithm (CPA), also known as the primal-dual hybrid gradient method, has gained popularity over the last decade due to its success in solving large-scale convex structured problems. This work extends its convergence analysis for problems with varying degrees of (non)monotonicity, quantified through a so-called oblique weak Minty condition on the associated primal-dual operator. Our results reveal novel stepsize and relaxation parameter ranges which do not only depend on the norm of the linear mapping, but also on its other singular values. In particular, in nonmonotone settings, in addition to the classical stepsize conditions, extra bounds on the stepsizes and relaxation parameters are required. On the other hand, in the strongly monotone setting, the relaxation parameter is allowed to exceed the classical upper bound of two. Moreover, we build upon the recently introduced class of semimonotone operators, providing sufficient convergence conditions for CPA when the individual operators are semimonotone. Since this class of operators encompasses traditional operator classes including (hypo)- and co(hypo)-monotone operators, this analysis recovers and extends existing results for CPA. Tightness of the proposed stepsize ranges is demonstrated through several examples.

Graph Neural Networks (GNNs) are gaining popularity across various domains due to their effectiveness in learning graph-structured data. Nevertheless, they have been shown to be susceptible to backdoor poisoning attacks, which pose serious threats to real-world applications. Meanwhile, graph reduction techniques, including coarsening and sparsification, which have long been employed to improve the scalability of large graph computational tasks, have recently emerged as effective methods for accelerating GNN training on large-scale graphs. However, the current development and deployment of graph reduction techniques for large graphs overlook the potential risks of data poisoning attacks against GNNs. It is not yet clear how graph reduction interacts with existing backdoor attacks. This paper conducts a thorough examination of the robustness of graph reduction methods in scalable GNN training in the presence of state-of-the-art backdoor attacks. We performed a comprehensive robustness analysis across six coarsening methods and six sparsification methods for graph reduction, under three GNN backdoor attacks against three GNN architectures. Our findings indicate that the effectiveness of graph reduction methods in mitigating attack success rates varies significantly, with some methods even exacerbating the attacks. Through detailed analyses of triggers and poisoned nodes, we interpret our findings and enhance our understanding of how graph reduction influences robustness against backdoor attacks. These results highlight the critical need for incorporating robustness considerations in graph reduction for GNN training, ensuring that enhancements in computational efficiency do not compromise the security of GNN systems.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

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