Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This is done through either differentially private stochastic gradient descent, or with a differentially private metric for training models or generators. In this paper, we introduce a novel differentially private generative modeling approach based on parameter-free gradient flows in the space of probability measures. The proposed algorithm is a new discretized flow which operates through a particle scheme, utilizing drift derived from the sliced Wasserstein distance and computed in a private manner. Our experiments show that compared to a generator-based model, our proposed model can generate higher-fidelity data at a low privacy budget, offering a viable alternative to generator-based approaches.

We characterize the equilibrium properties of a model of $y$ coupled binary perceptrons in the teacher-student scenario, subject to a learning rule, with an explicit ferromagnetic coupling proportional to the Hamming distance between the students' weights. In contrast to recent works, we analyze a more general setting in which thermal noise is present that affects each student's generalization performance. In the nonzero temperature regime, we find that the coupling of replicas produces a bend of the phase diagram towards smaller values of $\alpha$: This suggests that the free energy landscape gets smoother around the solution with perfect generalization (i.e., the teacher's) at a fixed fraction of examples, allowing standard thermal updates such as Simulated Annealing to easily reach the teacher solution and avoid entrapment in metastable states as it happens in the unreplicated case, even in the so-called computationally easy regime. These results provide additional analytic and numerical evidence for the recently conjectured Bayes-optimal property of Replicated Simulated Annealing (RSA) for a sufficient number of replicas. From a learning perspective, these results also suggest that multiple students working together (in this case reviewing the same data) are able to learn the same rule both significantly faster and with fewer examples, a property that could be exploited in the context of cooperative and federated learning.

Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms, result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.

Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of acceleration in the literature. In this work, we aim to close the gap between theory and practice by showing that stochastic heavy ball momentum retains the fast linear rate of (deterministic) heavy ball momentum on quadratic optimization problems, at least when minibatching with a sufficiently large batch size. The algorithm we study can be interpreted as an accelerated randomized Kaczmarz algorithm with minibatching and heavy ball momentum. The analysis relies on carefully decomposing the momentum transition matrix, and using new spectral norm concentration bounds for products of independent random matrices. We provide numerical illustrations demonstrating that our bounds are reasonably sharp.

We present Integrated Multimodal Perception (IMP), a simple and scalable multimodal multi-task training and modeling approach. IMP integrates multimodal inputs including image, video, text, and audio into a single Transformer encoder with minimal modality-specific components. IMP makes use of a novel design that combines Alternating Gradient Descent (AGD) and Mixture-of-Experts (MoE) for efficient model and task scaling. We conduct extensive empirical studies and reveal the following key insights: 1) Performing gradient descent updates by alternating on diverse modalities, loss functions, and tasks, with varying input resolutions, efficiently improves the model. 2) Sparsification with MoE on a single modality-agnostic encoder substantially improves the performance, outperforming dense models that use modality-specific encoders or additional fusion layers and greatly mitigates the conflicts between modalities. IMP achieves competitive performance on a wide range of downstream tasks including video classification, image classification, image-text, and video-text retrieval. Most notably, we train a sparse IMP-MoE-L variant focusing on video tasks that achieves new state-of-the-art in zero-shot video classification: 77.0% on Kinetics-400, 76.8% on Kinetics-600, and 68.3% on Kinetics-700, improving the previous state-of-the-art by +5%, +6.7%, and +5.8%, respectively, while using only 15% of their total training computational cost.

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022a), and catapult (Lewkowycz et al., 2020). These phenomena cannot be well explained by classical optimization theory. Though significant theoretical progress has been made in understanding these implicit biases, it remains unclear for which objective functions would they be more likely. This paper provides an initial step in answering this question and also shows that these implicit biases are in fact various tips of the same iceberg. To establish these results, we develop a global convergence theory under large learning rates, for a family of nonconvex functions without globally Lipschitz continuous gradient, which was typically assumed in existing convergence analysis. Specifically, these phenomena are more likely to occur when the optimization objective function has good regularity. This regularity, together with gradient descent using a large learning rate that favors flatter regions, results in these nontrivial dynamical behaviors. Another corollary is the first non-asymptotic convergence rate bound for large-learning-rate gradient descent optimization of nonconvex functions. Although our theory only applies to specific functions so far, the possibility of extrapolating it to neural networks is also experimentally validated, for which different choices of loss, activation functions, and other techniques such as batch normalization can all affect regularity significantly and lead to very different training dynamics.

A fundamental trait of intelligence involves finding novel and creative solutions to address a given challenge or to adapt to unforeseen situations. Reflecting this, Quality-Diversity optimization is a family of Evolutionary Algorithms, that generates collections of both diverse and high-performing solutions. Among these, MAP-Elites is a prominent example, that has been successfully applied to a variety of domains, including evolutionary robotics. However, MAP-Elites performs a divergent search with random mutations originating from Genetic Algorithms, and thus, is limited to evolving populations of low-dimensional solutions. PGA-MAP-Elites overcomes this limitation using a gradient-based variation operator inspired by deep reinforcement learning which enables the evolution of large neural networks. Although high-performing in many environments, PGA-MAP-Elites fails on several tasks where the convergent search of the gradient-based variation operator hinders diversity. In this work, we present three contributions: (1) we enhance the Policy Gradient variation operator with a descriptor-conditioned critic that reconciles diversity search with gradient-based methods, (2) we leverage the actor-critic training to learn a descriptor-conditioned policy at no additional cost, distilling the knowledge of the population into one single versatile policy that can execute a diversity of behaviors, (3) we exploit the descriptor-conditioned actor by injecting it in the population, despite network architecture differences. Our method, DCG-MAP-Elites, achieves equal or higher QD score and coverage compared to all baselines on seven challenging continuous control locomotion tasks.

This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse optimisation problems on measures. By formulating the CPGD steps within a variational framework, we provide rigorous mathematical proofs demonstrating the following key findings: (i) The total variation norms of the solution measures along the descent trajectory remain bounded, ensuring stability and preventing undesirable divergence; (ii) We establish a global convergence guarantee with a convergence rate of $\mathcal{O}(\log(K)/\sqrt{K})$ over $K$ iterations, showcasing the efficiency and effectiveness of our algorithm; (iii) Additionally, we analyze and establish local control over the first-order condition discrepancy, contributing to a deeper understanding of the algorithm's behavior and reliability in practical applications.

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.

This study addresses the challenge of online learning in contexts where agents accumulate disparate data, face resource constraints, and use different local algorithms. This paper introduces the Switched Online Learning Algorithm (SOLA), designed to solve the heterogeneous online learning problem by amalgamating updates from diverse agents through a dynamic switching mechanism contingent upon their respective performance and available resources. We theoretically analyze the design of the selecting mechanism to ensure that the regret of SOLA is bounded. Our findings show that the number of changes in selection needs to be bounded by a parameter dependent on the performance of the different local algorithms. Additionally, two test cases are presented to emphasize the effectiveness of SOLA, first on an online linear regression problem and then on an online classification problem with the MNIST dataset.