Federated Learning (FL) provides a privacy-preserving framework for training machine learning models on mobile edge devices. Traditional FL algorithms, e.g., FedAvg, impose a heavy communication workload on these devices. To mitigate this issue, Hierarchical Federated Edge Learning (HFEL) has been proposed, leveraging edge servers as intermediaries for model aggregation. Despite its effectiveness, HFEL encounters challenges such as a slow convergence rate and high resource consumption, particularly in the presence of system and data heterogeneity. However, existing works are mainly focused on improving training efficiency for traditional FL, leaving the efficiency of HFEL largely unexplored. In this paper, we consider a two-tier HFEL system, where edge devices are connected to edge servers and edge servers are interconnected through peer-to-peer (P2P) edge backhauls. Our goal is to enhance the training efficiency of the HFEL system through strategic resource allocation and topology design. Specifically, we formulate an optimization problem to minimize the total training latency by allocating the computation and communication resources, as well as adjusting the P2P connections. To ensure convergence under dynamic topologies, we analyze the convergence error bound and introduce a model consensus constraint into the optimization problem. The proposed problem is then decomposed into several subproblems, enabling us to alternatively solve it online. Our method facilitates the efficient implementation of large-scale FL at edge networks under data and system heterogeneity. Comprehensive experiment evaluation on benchmark datasets validates the effectiveness of the proposed method, demonstrating significant reductions in training latency while maintaining the model accuracy compared to various baselines.

Federated learning (FL) enables edge devices to collaboratively train a machine learning model without sharing their raw data. Due to its privacy-protecting benefits, FL has been deployed in many real-world applications. However, deploying FL over mobile edge networks with constrained resources such as power, bandwidth, and computation suffers from high training latency and low model accuracy, particularly under data and system heterogeneity. In this paper, we investigate the optimal client scheduling and resource allocation for FL over mobile edge networks under resource constraints and uncertainty to minimize the training latency while maintaining the model accuracy. Specifically, we first analyze the impact of client sampling on model convergence in FL and formulate a stochastic optimization problem that captures the trade-off between the running time and model performance under heterogeneous and uncertain system resources. To solve the formulated problem, we further develop an online control scheme based on Lyapunov-based optimization for client sampling and resource allocation without requiring the knowledge of future dynamics in the FL system. Extensive experimental results demonstrate that the proposed scheme can improve both the training latency and resource efficiency compared with the existing schemes.

Machine Learning (ML) optimization frameworks have gained attention for their ability to accelerate the optimization of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning shared problem structures. However, existing ML frameworks often rely heavily on strong problem assumptions and large-scale solvers. This paper introduces NeuralQP, a general hypergraph-based framework for large-scale QCQPs. NeuralQP features two main components: Hypergraph-based Neural Prediction, which generates embeddings and predicted solutions for QCQPs without problem assumptions, and Parallel Neighborhood Optimization, which employs a McCormick relaxation-based repair strategy to identify and correct illegal variables, iteratively improving the solution with a small-scale solver. We further prove that our framework UniEGNN with our hypergraph representation is equivalent to the Interior-Point Method (IPM) for quadratic programming. Experiments on two benchmark problems and large-scale real-world instances from QPLIB demonstrate that NeuralQP outperforms state-of-the-art solvers (e.g., Gurobi and SCIP) in both solution quality and time efficiency, further validating the efficiency of ML optimization frameworks for QCQPs.

\emph{TxGraffiti} is a data-driven, heuristic-based computer program developed to automate the process of generating conjectures across various mathematical domains. Since its creation in 2017, \emph{TxGraffiti} has contributed to numerous mathematical publications, particularly in graph theory. In this paper, we present the design and core principles of \emph{TxGraffiti}, including its roots in the original \emph{Graffiti} program, which pioneered the automation of mathematical conjecturing. We describe the data collection process, the generation of plausible conjectures, and methods such as the \emph{Dalmatian} heuristic for filtering out redundant or transitive conjectures. Additionally, we highlight its contributions to the mathematical literature and introduce a new web-based interface that allows users to explore conjectures interactively. While we focus on graph theory, the techniques demonstrated extend to other areas of mathematics.

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is lacking. This paper introduces an energy conservation approach for analyzing continuous-time dynamical systems in dilated coordinates. Instead of directly analyzing dynamics in the original coordinate system, we establish a conserved quantity, akin to physical energy, in the dilated coordinate system. Consequently, convergence rates can be explicitly expressed in terms of the inverse time-dilation factor. Leveraging this generalized approach, we formulate a novel second-order distributed accelerated gradient flow with a convergence rate of $O\left(1/t^{2-\epsilon}\right)$ in time $t$ for $\epsilon>0$. We then employ a semi second-order symplectic Euler discretization to derive a rate-matching algorithm with a convergence rate of $O\left(1/k^{2-\epsilon}\right)$ in $k$ iterations. To the best of our knowledge, this represents the most favorable convergence rate for any distributed optimization algorithm designed for smooth convex optimization. Its accelerated convergence behavior is benchmarked against various state-of-the-art distributed optimization algorithms on practical, large-scale problems.

Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs) were proposed initially to model chaotic dynamic systems without external inputs. They require less data for training since Ordinary Differential Equations (ODEs) of the considered system help to regularize the ESN. In this work, the PI-ESN is extended with external inputs to model controllable nonlinear dynamic systems. Additionally, an existing self-adaptive balancing loss method is employed to balance the contributions of the residual regression term and the physics-informed loss term in the total loss function. The experiments with two nonlinear systems modeled by ODEs, the Van der Pol oscillator and the four-tank system, and with one differential-algebraic (DAE) system, an electric submersible pump, revealed that the proposed PI-ESN outperforms the conventional ESN, especially in scenarios with limited data availability, showing that PI-ESNs can regularize an ESN model with external inputs previously trained on just a few datapoints, reducing its overfitting and improving its generalization error (up to 92% relative reduction in the test error). Further experiments demonstrated that the proposed PI-ESN is robust to parametric uncertainties in the ODE equations and that model predictive control using PI-ESN outperforms the one using plain ESN, particularly when training data is scarce.

The demand for executing Deep Neural Networks (DNNs) with low latency and minimal power consumption at the edge has led to the development of advanced heterogeneous Systems-on-Chips (SoCs) that incorporate multiple specialized computing units (CUs), such as accelerators. Offloading DNN computations to a specific CU from the available set often exposes accuracy vs efficiency trade-offs, due to differences in their supported operations (e.g., standard vs. depthwise convolution) or data representations (e.g., more/less aggressively quantized). A challenging yet unresolved issue is how to map a DNN onto these multi-CU systems to maximally exploit the parallelization possibilities while taking accuracy into account. To address this problem, we present ODiMO, a hardware-aware tool that efficiently explores fine-grain mapping of DNNs among various on-chip CUs, during the training phase. ODiMO strategically splits individual layers of the neural network and executes them in parallel on the multiple available CUs, aiming to balance the total inference energy consumption or latency with the resulting accuracy, impacted by the unique features of the different hardware units. We test our approach on CIFAR-10, CIFAR-100, and ImageNet, targeting two open-source heterogeneous SoCs, i.e., DIANA and Darkside. We obtain a rich collection of Pareto-optimal networks in the accuracy vs. energy or latency space. We show that ODiMO reduces the latency of a DNN executed on the Darkside SoC by up to 8x at iso-accuracy, compared to manual heuristic mappings. When targeting energy, on the same SoC, ODiMO produced up to 50.8x more efficient mappings, with minimal accuracy drop (< 0.3%).

Developing sophisticated control architectures has endowed robots, particularly humanoid robots, with numerous capabilities. However, tuning these architectures remains a challenging and time-consuming task that requires expert intervention. In this work, we propose a methodology to automatically tune the gains of all layers of a hierarchical control architecture for walking humanoids. We tested our methodology by employing different gradient-free optimization methods: Genetic Algorithm (GA), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Evolution Strategy (ES), and Differential Evolution (DE). We validated the parameter found both in simulation and on the real ergoCub humanoid robot. Our results show that GA achieves the fastest convergence (10 x 10^3 function evaluations vs 25 x 10^3 needed by the other algorithms) and 100% success rate in completing the task both in simulation and when transferred on the real robotic platform. These findings highlight the potential of our proposed method to automate the tuning process, reducing the need for manual intervention.

Causal Graph Discovery (CGD) is the process of estimating the underlying probabilistic graphical model that represents joint distribution of features of a dataset. CGD-algorithms are broadly classified into two categories: (i) Constraint-based algorithms (outcome depends on conditional independence (CI) tests), (ii) Score-based algorithms (outcome depends on optimized score-function). Since, sensitive features of observational data is prone to privacy-leakage, Differential Privacy (DP) has been adopted to ensure user privacy in CGD. Adding same amount of noise in this sequential-natured estimation process affects the predictive performance of the algorithms. As initial CI tests in constraint-based algorithms and later iterations of the optimization process of score-based algorithms are crucial, they need to be more accurate, less noisy. Based on this key observation, we present CURATE (CaUsal gRaph AdapTivE privacy), a DP-CGD framework with adaptive privacy budgeting. In contrast to existing DP-CGD algorithms with uniform privacy budgeting across all iterations, CURATE allows adaptive privacy budgeting by minimizing error probability (for constraint-based), maximizing iterations of the optimization problem (for score-based) while keeping the cumulative leakage bounded. To validate our framework, we present a comprehensive set of experiments on several datasets and show that CURATE achieves higher utility compared to existing DP-CGD algorithms with less privacy-leakage.

Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.), though, such functions are defined over large $\textit{combinatorial and unstructured}$ spaces. This makes existing BO algorithms not feasible due to the intractable maximization of the acquisition function over these domains. To address this issue, we propose $\textbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO. $\textbf{GameOpt}$ establishes a cooperative game between the different optimization variables, and selects points that are game $\textit{equilibria}$ of an upper confidence bound acquisition function. These are stable configurations from which no variable has an incentive to deviate$-$ analog to local optima in continuous domains. Crucially, this allows us to efficiently break down the complexity of the combinatorial domain into individual decision sets, making $\textbf{GameOpt}$ scalable to large combinatorial spaces. We demonstrate the application of $\textbf{GameOpt}$ to the challenging $\textit{protein design}$ problem and validate its performance on four real-world protein datasets. Each protein can take up to $20^{X}$ possible configurations, where $X$ is the length of a protein, making standard BO methods infeasible. Instead, our approach iteratively selects informative protein configurations and very quickly discovers highly active protein variants compared to other baselines.