This paper investigates federated multimodal learning (FML) assisted by unmanned aerial vehicles (UAVs) with a focus on minimizing system latency and providing convergence analysis. In this framework, UAVs are distributed throughout the network to collect data, participate in model training, and collaborate with a base station (BS) to build a global model. By utilizing multimodal sensing, the UAVs overcome the limitations of unimodal systems, enhancing model accuracy, generalization, and offering a more comprehensive understanding of the environment. The primary objective is to optimize FML system latency in UAV networks by jointly addressing UAV sensing scheduling, power control, trajectory planning, resource allocation, and BS resource management. To address the computational complexity of our latency minimization problem, we propose an efficient iterative optimization algorithm combining block coordinate descent and successive convex approximation techniques, which provides high-quality approximate solutions. We also present a theoretical convergence analysis for the UAV-assisted FML framework under a non-convex loss function. Numerical experiments demonstrate that our FML framework outperforms existing approaches in terms of system latency and model training performance under different data settings.

We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus step that enables a linear convergence beyond Hadamard manifolds. Building on this step, we establish a $O(\sqrt{T})$ regret bound for the decentralized online Riemannian gradient descent algorithm. Then, we investigate the two-point bandit feedback setup, where we employ computationally efficient gradient estimators using smoothing techniques, and we demonstrate the same $O(\sqrt{T})$ regret bound through the subconvexity analysis of smoothed objectives.

We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for adaptively tuning the proximal term. It allows the penalty parameter to grow rapidly in the early stages to speed up progress, while ameliorating the issue of ill-conditioning in later iterations, a well-known drawback of the traditional approach of linearly increasing the penalty parameters. A key element in our analysis lies in the observation that the augmented Lagrangian can be controlled effectively along the iterates, provided an initial feasible point is available. Our analysis, while simple, provides a new theoretical perspective about P-ALM and, as a by-product, results in similar convergence properties for its non-proximal variant, the classical augmented Lagrangian method (ALM). Numerical experiments, including convex and nonconvex problem instances, demonstrate the effectiveness of our approach.

-- Domain randomization (DR) enables sim-to-real transfer by training controllers on a distribution of simulated environments, with the goal of achieving robust performance in the real world. Although DR is widely used in practice and is often solved using simple policy gradient (PG) methods, understanding of its theoretical guarantees remains limited. T oward addressing this gap, we provide the first convergence analysis of PG methods for domain-randomized linear quadratic regulation (LQR). We show that PG converges globally to the minimizer of a finite-sample approximation of the DR objective under suitable bounds on the heterogeneity of the sampled systems. We also quantify the sample-complexity associated with achieving a small performance gap between the sample-average and population-level objectives. Additionally, we propose and analyze a discount-factor annealing algorithm that obviates the need for an initial jointly stabilizing controller, which may be challenging to find. Empirical results support our theoretical findings and highlight promising directions for future work, including risk-sensitive DR formulations and stochastic PG algorithms. Domain randomization (DR) has emerged as a dominant paradigm to enable transfer of policies optimized in simulation to the real world by randomizing simulator parameters during training [1-3]. In doing so, just as with robust control, DR accounts for discrepancies between the model used in simulation to synthesize a policy and the system that it is deployed on. Since DR does not solely focus on optimizing the worst-case performance, it can result in less conservative controller performance while still ensuring robust stability with high probability. Furthermore, DR can be easily implemented via first order methods. This makes it straightforward to incorporate into a wide variety of reinforcement learning schemes and to benefit from the increasing availability of parallel computation. Despite the ease with which DR can be implemented using first order methods, ensuring convergence of these methods remains a critical challenge, with practitioners relying upon complex scheduling of various hyperparameters in the optimization procedure [3].

Both cri teria are related by the key component of information retention, which leaves feature engineers with the challenging task of balancing the discriminative power of the feature extracto r (i.e., the ability to disentangle the driving factors for va riance within the data) and the potential loss of information (as a result of transforming the input). In this contribution, we focus on the premise that deep feature extractors should contain m ost of the (relevant) information about their input signals, wh ich is expressed by the aggregate energy content of the features . A. Prior work Information retention is a key component of successful feature extraction. It has hence already been addressed by prior works--mainly in the context of scattering CNNs, both over Euclidean domains [5]-[10] and graphs [11], [12].

The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cram\'er-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise.

Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.

An inherent fragility of quadrotor systems stems from model inaccuracies and external disturbances. These factors hinder performance and compromise the stability of the system, making precise control challenging. Existing model-based approaches either make deterministic assumptions, utilize Gaussian-based representations of uncertainty, or rely on nominal models, all of which often fall short in capturing the complex, multimodal nature of real-world dynamics. This work introduces DroneDiffusion, a novel framework that leverages conditional diffusion models to learn quadrotor dynamics, formulated as a sequence generation task. DroneDiffusion achieves superior generalization to unseen, complex scenarios by capturing the temporal nature of uncertainties and mitigating error propagation. We integrate the learned dynamics with an adaptive controller for trajectory tracking with stability guarantees. Extensive experiments in both simulation and real-world flights demonstrate the robustness of the framework across a range of scenarios, including unfamiliar flight paths and varying payloads, velocities, and wind disturbances.

Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these methods generally lack generalization guarantees or depend on strong assumptions, leaving a gap in understanding the underlying mechanism of distribution matching. In this work, we formulate domain generalization from a novel probabilistic perspective, ensuring robustness while avoiding overly conservative solutions. Through comprehensive information-theoretic analysis, we provide key insights into the roles of gradient and representation matching in promoting generalization. Our results reveal the complementary relationship between these two components, indicating that existing works focusing solely on either gradient or representation alignment are insufficient to solve the domain generalization problem. In light of these theoretical findings, we introduce IDM to simultaneously align the inter-domain gradients and representations. Integrated with the proposed PDM method for complex distribution matching, IDM achieves superior performance over various baseline methods. ISTRIBUTION shifts are prevalent in various real-world learning contexts, often leading to machine learning systems overfitting environment-specific correlations that may negatively impact performance when facing out-of-distribution (OOD) data [1]-[4]. Domain generalization (DG) is then introduced to address this challenge: By assuming the training data constitutes multiple domains that share some invariant underlying correlations, DG algorithms then attempt to learn this invariance so that domain-specific variations do not affect the model's performance. To this end, various DG approaches have been proposed, including invariant representation learning [5], [6], adversarial learning [7], [8], causal inference [9], [10], gradient manipulation [11]-[13], and robust optimization [14]-[16]. DG is typically formulated as an average-case [17], [18] or worst-case [9], [14] optimization problem, which however either lacks robustness against OOD data [9], [19] or leads to overly conservative solutions [16]. In this paper, we introduce a novel probabilistic formulation that aims to minimize the gap between training and test-domain population risks with high probability.

The Chambolle-Pock algorithm (CPA), also known as the primal-dual hybrid gradient method (PDHG), has surged in popularity in the last decade due to its success in solving convex/monotone structured problems. This work provides convergence results 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 for CPA, 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, sufficient convergence conditions are obtained when the individual operators belong to the recently introduced class of semimonotone operators. Since this class of operators encompasses many traditional operator classes including (hypo)- and co(hypo)monotone operators, this analysis recovers and extends existing results for CPA. Several examples are provided for the aforementioned problem classes to demonstrate and establish tightness of the proposed stepsize ranges.