We study decentralized multiagent optimization over networks, modeled as undirected graphs. The optimization problem consists of minimizing a nonconvex smooth function plus a convex extended-value function, which enforces constraints or extra structure on the solution (e.g., sparsity, low-rank). We further assume that the objective function satisfies the Kurdyka-{\L}ojasiewicz (KL) property, with given exponent $\theta\in [0,1)$. The KL property is satisfied by several (nonconvex) functions of practical interest, e.g., arising from machine learning applications; in the centralized setting, it permits to achieve strong convergence guarantees. Here we establish convergence of the same type for the notorious decentralized gradient-tracking-based algorithm SONATA. Specifically, $\textbf{(i)}$ when $\theta\in (0,1/2]$, the sequence generated by SONATA converges to a stationary solution of the problem at R-linear rate;$ \textbf{(ii)} $when $\theta\in (1/2,1)$, sublinear rate is certified; and finally $\textbf{(iii)}$ when $\theta=0$, the iterates will either converge in a finite number of steps or converges at R-linear rate. This matches the convergence behavior of centralized proximal-gradient algorithms except when $\theta=0$. Numerical results validate our theoretical findings.

Aligning AI systems with human preferences typically suffers from the infamous reward hacking problem, where optimization of an imperfect reward model leads to undesired behaviors. In this paper, we investigate reward hacking in offline preference optimization, which aims to improve an initial model using a preference dataset. We identify two types of reward hacking stemming from statistical fluctuations in the dataset: Type I Reward Hacking due to subpar choices appearing more favorable, and Type II Reward Hacking due to decent choices appearing less favorable. We prove that many (mainstream or theoretical) preference optimization methods suffer from both types of reward hacking. To mitigate Type I Reward Hacking, we propose POWER, a new preference optimization method that combines Guiasu's weighted entropy with a robust reward maximization objective. POWER enjoys finite-sample guarantees under general function approximation, competing with the best covered policy in the data. To mitigate Type II Reward Hacking, we analyze the learning dynamics of preference optimization and develop a novel technique that dynamically updates preference labels toward certain "stationary labels", resulting in diminishing gradients for untrustworthy samples. Empirically, POWER with dynamic labels (POWER-DL) consistently outperforms state-of-the-art methods on alignment benchmarks, achieving improvements of up to 13.0 points on AlpacaEval 2.0 and 11.5 points on Arena-Hard over DPO, while also improving or maintaining performance on downstream tasks such as mathematical reasoning. Strong theoretical guarantees and empirical results demonstrate the promise of POWER-DL in mitigating reward hacking.

Traditional data influence estimation methods, like influence function, assume that learning algorithms are permutation-invariant with respect to training data. However, modern training paradigms, especially for foundation models using stochastic algorithms and multi-stage curricula, are sensitive to data ordering, thus violating this assumption. This mismatch renders influence functions inadequate for answering a critical question in machine learning: How can we capture the dependence of data influence on the optimization trajectory during training? To address this gap, we formalize the concept of trajectory-specific leave-one-out (LOO) influence, which quantifies the impact of removing a data point from a specific iteration during training, accounting for the exact sequence of data encountered and the model's optimization trajectory. However, exactly evaluating the trajectory-specific LOO presents a significant computational challenge. To address this, we propose data value embedding, a novel technique enabling efficient approximation of trajectory-specific LOO. Specifically, we compute a training data embedding that encapsulates the cumulative interactions between data and the evolving model parameters. The LOO can then be efficiently approximated through a simple dot-product between the data value embedding and the gradient of the given test data. As data value embedding captures training data ordering, it offers valuable insights into model training dynamics. In particular, we uncover distinct phases of data influence, revealing that data points in the early and late stages of training exert a greater impact on the final model. These insights translate into actionable strategies for managing the computational overhead of data selection by strategically timing the selection process, potentially opening new avenues in data curation research.

Gaussian Processes (GPs) are widely seen as the state-of-the-art surrogate models for Bayesian optimization (BO) due to their ability to model uncertainty and their performance on tasks where correlations are easily captured (such as those defined by Euclidean metrics) and their ability to be efficiently updated online. However, the performance of GPs depends on the choice of kernel, and kernel selection for complex correlation structures is often difficult or must be made bespoke. While Bayesian neural networks (BNNs) are a promising direction for higher capacity surrogate models, they have so far seen limited use due to poor performance on some problem types. In this paper, we propose an approach which shows competitive performance on many problem types, including some that BNNs typically struggle with. We build on variational Bayesian last layers (VBLLs), and connect training of these models to exact conditioning in GPs. We exploit this connection to develop an efficient online training algorithm that interleaves conditioning and optimization. Our findings suggest that VBLL networks significantly outperform GPs and other BNN architectures on tasks with complex input correlations, and match the performance of well-tuned GPs on established benchmark tasks.

As data-privacy requirements are becoming increasingly stringent and statistical models based on sensitive data are being deployed and used more routinely, protecting data-privacy becomes pivotal. Partial Least Squares (PLS) regression is the premier tool for building such models in analytical chemistry, yet it does not inherently provide privacy guarantees, leaving sensitive (training) data vulnerable to privacy attacks. To address this gap, we propose an $(\epsilon, \delta)$-differentially private PLS (edPLS) algorithm, which integrates well-studied and theoretically motivated Gaussian noise-adding mechanisms into the PLS algorithm to ensure the privacy of the data underlying the model. Our approach involves adding carefully calibrated Gaussian noise to the outputs of four key functions in the PLS algorithm: the weights, scores, $X$-loadings, and $Y$-loadings. The noise variance is determined based on the global sensitivity of each function, ensuring that the privacy loss is controlled according to the $(\epsilon, \delta)$-differential privacy framework. Specifically, we derive the sensitivity bounds for each function and use these bounds to calibrate the noise added to the model components. Experimental results demonstrate that edPLS effectively renders privacy attacks, aimed at recovering unique sources of variability in the training data, ineffective. Application of edPLS to the NIR corn benchmark dataset shows that the root mean squared error of prediction (RMSEP) remains competitive even at strong privacy levels (i.e., $\epsilon=1$), given proper pre-processing of the corresponding spectra. These findings highlight the practical utility of edPLS in creating privacy-preserving multivariate calibrations and for the analysis of their privacy-utility trade-offs.

We consider the Gaussian kernel density estimator with bandwidth $\beta^{-\frac12}$ of $n$ iid Gaussian samples. Using the Kac-Rice formula and an Edgeworth expansion, we prove that the expected number of modes on the real line scales as $\Theta(\sqrt{\beta\log\beta})$ as $\beta,n\to\infty$ provided $n^c\lesssim \beta\lesssim n^{2-c}$ for some constant $c>0$. An impetus behind this investigation is to determine the number of clusters to which Transformers are drawn in a metastable state.

Large scale Bayesian nonparametrics (BNP) learner such as stochastic variational inference (SVI) can handle datasets with large class number and large training size at fractional cost. Like its predecessor, SVI rely on the assumption of conjugate variational posterior to approximate the true posterior. A more challenging problem is to consider large scale learning on non-conjugate posterior. Recent works in this direction are mostly associated with using Monte Carlo methods for approximating the learner. However, these works are usually demonstrated on non-BNP related task and less complex models such as logistic regression, due to higher computational complexity. In order to overcome the issue faced by SVI, we develop a novel approach based on the recently proposed variational maximization-maximization (VMM) learner to allow large scale learning on non-conjugate posterior. Unlike SVI, our VMM learner does not require closed-form expression for the variational posterior expectatations. Our only requirement is that the variational posterior is differentiable. In order to ensure convergence in stochastic settings, SVI rely on decaying step-sizes to slow its learning. Inspired by SVI and Adam, we propose the novel use of decaying step-sizes on both gradient and ascent direction in our VMM to significantly improve its learning. We show that our proposed methods is compatible with ResNet features when applied to large class number datasets such as MIT67 and SUN397. Finally, we compare our proposed learner with several recent works such as deep clustering algorithms and showed we were able to produce on par or outperform the state-of-the-art methods in terms of clustering measures.

Studies of the functional role of the primate ventral visual stream have traditionally focused on object categorization, often ignoring -- despite much prior evidence -- its role in estimating "spatial" latents such as object position and pose. Most leading ventral stream models are derived by optimizing networks for object categorization, which seems to imply that the ventral stream is also derived under such an objective. Here, we explore an alternative hypothesis: Might the ventral stream be optimized for estimating spatial latents? And a closely related question: How different -- if at all -- are representations learned from spatial latent estimation compared to categorization? To ask these questions, we leveraged synthetic image datasets generated by a 3D graphic engine and trained convolutional neural networks (CNNs) to estimate different combinations of spatial and category latents. We found that models trained to estimate just a few spatial latents achieve neural alignment scores comparable to those trained on hundreds of categories, and the spatial latent performance of models strongly correlates with their neural alignment. Spatial latent and category-trained models have very similar -- but not identical -- internal representations, especially in their early and middle layers. We provide evidence that this convergence is partly driven by non-target latent variability in the training data, which facilitates the implicit learning of representations of those non-target latents. Taken together, these results suggest that many training objectives, such as spatial latents, can lead to similar models aligned neurally with the ventral stream. Thus, one should not assume that the ventral stream is optimized for object categorization only. As a field, we need to continue to sharpen our measures of comparing models to brains to better understand the functional roles of the ventral stream.

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers.

Intersectional fairness is a critical requirement for Machine Learning (ML) software, demanding fairness across subgroups defined by multiple protected attributes. This paper introduces FairHOME, a novel ensemble approach using higher order mutation of inputs to enhance intersectional fairness of ML software during the inference phase. Inspired by social science theories highlighting the benefits of diversity, FairHOME generates mutants representing diverse subgroups for each input instance, thus broadening the array of perspectives to foster a fairer decision-making process. Unlike conventional ensemble methods that combine predictions made by different models, FairHOME combines predictions for the original input and its mutants, all generated by the same ML model, to reach a final decision. Notably, FairHOME is even applicable to deployed ML software as it bypasses the need for training new models. We extensively evaluate FairHOME against seven state-of-the-art fairness improvement methods across 24 decision-making tasks using widely adopted metrics. FairHOME consistently outperforms existing methods across all metrics considered. On average, it enhances intersectional fairness by 47.5%, surpassing the currently best-performing method by 9.6 percentage points.