This paper develops a general framework for multi-agent control synthesis, which applies to a wide range of problems with convergence guarantees, regardless of the complexity of the underlying graph topology and the explicit time dependence of the objective function. The proposed framework systematically addresses a particularly challenging problem in multi-agent systems, i.e., decentralization of entangled dynamics among different agents, and it naturally supports multi-objective robotics and real-time implementations. To demonstrate its generality and effectiveness, the framework is implemented across three experiments, namely time-varying leader-follower formation control, decentralized coverage control for time-varying density functions without any approximations, which is a long-standing open problem, and safe formation navigation in dense environments.

--We investigate privacy-preserving spectral clustering for community detection within stochastic block models (SBMs). Specifically, we focus on edge differential privacy (DP) and propose private algorithms for community recovery. Our work explores the fundamental trade-offs between the privacy budget and the accurate recovery of community labels. Furthermore, we establish information-theoretic conditions that guarantee the accuracy of our methods, providing theoretical assurances for successful community recovery under edge DP . Community detection within networks is a pivotal challenge in graph mining and unsupervised learning [1].

--Decentralized federated learning (DFL) is a promising machine learning paradigm for bringing artificial intelligence (AI) capabilities to the network edge. Running DFL on top of edge networks, however, faces severe performance challenges due to the extensive parameter exchanges between agents. Most existing solutions for these challenges were based on simplistic communication models, which cannot capture the case of learning over a multi-hop bandwidth-limited network. In this work, we address this problem by jointly designing the communication scheme for the overlay network formed by the agents and the mixing matrix that controls the communication demands between the agents. By carefully analyzing the properties of our problem, we cast each design problem into a tractable optimization and develop an efficient algorithm with guaranteed performance. Our evaluations based on real topology and data show that the proposed algorithm can reduce the total training time by over 80% compared to the baseline without sacrificing accuracy, while significantly improving the computational efficiency over the state of the art. I NTRODUCTION Decentralized federated learning (DFL) [1] is an emerging machine learning paradigm that allows multiple learning agents to collaboratively learn a shared model from their local data without directly sharing the data. In contrast to the centralized federated learning (FL) paradigm [2], DFL gets rid of parameter servers by letting the learning agents directly exchange model updates with their neighbors through peer-to-peer connections, which are then aggregated locally [3]. Since its introduction, DFL has attracted significant attention due to its robustness against a single point of failure and ability to balance the communication complexity across nodes without increasing the computational complexity [1]. Meanwhile, DFL still faces significant performance challenges due to the extensive data transfer between agents.

-- 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].

Learning from noisy labels is a critical challenge in machine learning, with vast implications for numerous real-world scenarios. While supervised contrastive learning has recently emerged as a powerful tool for navigating label noise, many existing solutions remain heuristic, often devoid of a systematic theoretical foundation for crafting robust supervised contrastive losses. To address the gap, in this paper, we propose a unified theoretical framework for robust losses under the pairwise contrastive paradigm. In particular, we for the first time derive a general robust condition for arbitrary contrastive losses, which serves as a criterion to verify the theoretical robustness of a supervised contrastive loss against label noise. The theory indicates that the popular InfoNCE loss is in fact non-robust, and accordingly inspires us to develop a robust version of InfoNCE, termed Symmetric InfoNCE (SymNCE). Moreover, we highlight that our theory is an inclusive framework that provides explanations to prior robust techniques such as nearest-neighbor (NN) sample selection and robust contrastive loss. Validation experiments on benchmark datasets demonstrate the superiority of SymNCE against label noise.

For many multiagent control problems, neural networks (NNs) have enabled promising new capabilities. However, many of these systems lack formal guarantees (e.g., collision avoidance, robustness), which prevents leveraging these advances in safety-critical settings. While there is recent work on formal verification of NN-controlled systems, most existing techniques cannot handle scenarios with more than one agent. To address this research gap, this paper presents a backward reachability-based approach for verifying the collision avoidance properties of Multi-Agent Neural Feedback Loops (MA-NFLs). Given the dynamics models and trained control policies of each agent, the proposed algorithm computes relative backprojection sets by (simultaneously) solving a series of Mixed Integer Linear Programs (MILPs) offline for each pair of agents. We account for state measurement uncertainties, making it well aligned with real-world scenarios. Using those results, the agents can quickly check for collision avoidance online by solving low-dimensional Linear Programs (LPs). We demonstrate the proposed algorithm can verify collision-free properties of a MA-NFL with agents trained to imitate a collision avoidance algorithm (Reciprocal Velocity Obstacles). We further demonstrate the computational scalability of the approach on systems with up to 10 agents.

The recovery of magnetic resonance (MR) images from undersampled measurements is a key problem that has seen extensive research in recent years. Unrolled approaches, which rely on end-to-end training of convolutional neural network (CNN) blocks within iterative reconstruction algorithms, offer state-of-the-art performance. These algorithms require a large amount of memory during training, making them difficult to employ in high-dimensional applications. Deep equilibrium (DEQ) models and the recent monotone operator learning (MOL) approach were introduced to eliminate the need for unrolling, thus reducing the memory demand during training. Both approaches require a Lipschitz constraint on the network to ensure that the forward and backpropagation iterations converge. Unfortunately, the constraint often results in reduced performance compared to unrolled methods. The main focus of this work is to relax the constraint on the CNN block in two different ways. Inspired by convex-non-convex regularization strategies, we now impose the monotone constraint on the sum of the gradient of the data term and the CNN block, rather than constrain the CNN itself to be a monotone operator. This approach enables the CNN to learn possibly non-monotone score functions, which can translate to improved performance. In addition, we only restrict the operator to be monotone in a local neighborhood around the image manifold. Our theoretical results show that the proposed algorithm is guaranteed to converge to the fixed point and that the solution is robust to input perturbations, provided that it is initialized close to the true solution. Our empirical results show that the relaxed constraints translate to improved performance and that the approach enjoys robustness to input perturbations similar to MOL.

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis functions DeePC behavioral predictor and we identify necessary and sufficient conditions for equivalence with a corresponding basis functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.

This paper considers an online control problem over a linear time-invariant system with unknown dynamics, bounded disturbance, and adversarial cost. We propose a data-driven strategy to reduce the regret of the controller. Unlike model-based methods, our algorithm does not identify the system model, instead, it leverages a single noise-free trajectory to calculate the accumulation of disturbance and makes decisions using the accumulated disturbance action controller we design, whose parameters are updated by online gradient descent. We prove that the regret of our algorithm is $\mathcal{O}(\sqrt{T})$ under mild assumptions, suggesting that its performance is on par with model-based methods.

Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected prediction error on future data. To the best of our knowledge, the rate of convergence of neural networks shown by existing works is bounded by at most the order of $n^{-1/4}$ for a sample size of $n$. In this paper, we show that a class of variation-constrained neural networks, with arbitrary width, can achieve near-parametric rate $n^{-1/2+\delta}$ for an arbitrarily small positive constant $\delta$. It is equivalent to $n^{-1 +2\delta}$ under the mean squared error. This rate is also observed by numerical experiments. The result indicates that the neural function space needed for approximating smooth functions may not be as large as what is often perceived. Our result also provides insight to the phenomena that deep neural networks do not easily suffer from overfitting when the number of neurons and learning parameters rapidly grow with $n$ or even surpass $n$. We also discuss the rate of convergence regarding other network parameters, including the input dimension, network layer, and coefficient norm.