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The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth graph signals, few research has been devoted to non-smooth graph signals, especially to sparse graph signals, which are also of importance in many practical applications. This paper addresses the random sampling of non-smooth graph signals generated by diffusion of sparse inputs. We aim to present a solid theoretical analysis on the random sampling of diffused sparse graph signals, which can be parallel to that of band-limited graph signals, and thus present a sufficient condition to the number of samples ensuring the unique recovery for uniform random sampling. Then, we focus on two classes of widely used binary graph models, and give explicit and tighter estimations on the sampling numbers ensuring unique recovery. We also propose an adaptive variable-density sampling strategy to provide a better performance than uniform random sampling. Finally, simulation experiments are presented to validate the effectiveness of the theoretical results., Comment: 14 pages, 6 figures. arXiv admin note: text overlap with arXiv:1612.09565 by other authors

This paper studies a class of distributed bilevel optimization (DBO) problems with a coupled inner-level subproblem. Existing approaches typically rely on hypergradient estimations involving computationally expensive Hessian information. To address this, we propose an equivalent constrained reformulation by treating the inner-level subproblem as an inequality constraint, and introduce an adaptive penalty function to properly penalize both inequality and consensus constraints based on subproblem properties. Moreover, we propose a loopless distributed algorithm, \ALGNAME, that employs multiple-timescale updates to solve each subproblem asymptotically without requiring Hessian information. Theoretically, we establish convergence rates of $\mathcal{O}(\frac{\kappa^4}{(1-\rho)^2 K^{1/3}})$ for nonconvex-strongly-convex cases and $\mathcal{O}(\frac{\kappa^2}{(1-\rho)^2 K^{2/3}})$ for distributed min-max problems. Our analysis shows the clear dependence of convergence performance on bilevel heterogeneity, the adaptive penalty parameter, and network connectivity, with a weaker assumption on heterogeneity requiring only bounded first-order heterogeneity at the optimum. Numerical experiments validate our theoretical findings., Comment: 10 pages, 2 figures

Implicit neural representations and 3D Gaussian splatting (3DGS) have shown great potential for scene reconstruction. Recent studies have expanded their applications in autonomous reconstruction through task assignment methods. However, these methods are mainly limited to single robot, and rapid reconstruction of large-scale scenes remains challenging. Additionally, task-driven planning based on surface uncertainty is prone to being trapped in local optima. To this end, we propose the first 3DGS-based centralized multi-robot autonomous 3D reconstruction framework. To further reduce time cost of task generation and improve reconstruction quality, we integrate online open-vocabulary semantic segmentation with surface uncertainty of 3DGS, focusing view sampling on regions with high instance uncertainty. Finally, we develop a multi-robot collaboration strategy with mode and task assignments improving reconstruction quality while ensuring planning efficiency. Our method demonstrates the highest reconstruction quality among all planning methods and superior planning efficiency compared to existing multi-robot methods. We deploy our method on multiple robots, and results show that it can effectively plan view paths and reconstruct scenes with high quality.

In this paper, we show that applying adaptive methods directly to distributed minimax problems can result in non-convergence due to inconsistency in locally computed adaptive stepsizes. To address this challenge, we propose D-AdaST, a Distributed Adaptive minimax method with Stepsize Tracking. The key strategy is to employ an adaptive stepsize tracking protocol involving the transmission of two extra (scalar) variables. This protocol ensures the consistency among stepsizes of nodes, eliminating the steady-state error due to the lack of coordination of stepsizes among nodes that commonly exists in vanilla distributed adaptive methods, and thus guarantees exact convergence. For nonconvex-strongly-concave distributed minimax problems, we characterize the specific transient times that ensure time-scale separation of stepsizes and quasi-independence of networks, leading to a near-optimal convergence rate of $\tilde{\mathcal{O}} \left( \epsilon ^{-\left( 4+\delta \right)} \right)$ for any small $\delta > 0$, matching that of the centralized counterpart. To our best knowledge, D-AdaST is the first distributed adaptive method achieving near-optimal convergence without knowing any problem-dependent parameters for nonconvex minimax problems. Extensive experiments are conducted to validate our theoretical results.

In this paper, we propose a differentially private decentralized learning method (termed PrivSGP-VR) which employs stochastic gradient push with variance reduction and guarantees $(\epsilon, \delta)$-differential privacy (DP) for each node. Our theoretical analysis shows that, under DP Gaussian noise with constant variance, PrivSGP-VR achieves a sub-linear convergence rate of $\mathcal{O}(1/\sqrt{nK})$, where $n$ and $K$ are the number of nodes and iterations, respectively, which is independent of stochastic gradient variance, and achieves a linear speedup with respect to $n$. Leveraging the moments accountant method, we further derive an optimal $K$ to maximize the model utility under certain privacy budget in decentralized settings. With this optimized $K$, PrivSGP-VR achieves a tight utility bound of $\mathcal{O}\left( \sqrt{d\log \left( \frac{1}{\delta} \right)}/(\sqrt{n}J\epsilon) \right)$, where $J$ and $d$ are the number of local samples and the dimension of decision variable, respectively, which matches that of the server-client distributed counterparts, and exhibits an extra factor of $1/\sqrt{n}$ improvement compared to that of the existing decentralized counterparts, such as A(DP)$^2$SGD. Extensive experiments corroborate our theoretical findings, especially in terms of the maximized utility with optimized $K$, in fully decentralized settings., Comment: This paper has been accepted by the 33rd International Joint Conference on Artificial Intelligence(IJCAI 2024)

The sim-to-real gap poses a significant challenge in RL-based multi-agent exploration due to scene quantization and action discretization. Existing platforms suffer from the inefficiency in sampling and the lack of diversity in Multi-Agent Reinforcement Learning (MARL) algorithms across different scenarios, restraining their widespread applications. To fill these gaps, we propose MAexp, a generic platform for multi-agent exploration that integrates a broad range of state-of-the-art MARL algorithms and representative scenarios. Moreover, we employ point clouds to represent our exploration scenarios, leading to high-fidelity environment mapping and a sampling speed approximately 40 times faster than existing platforms. Furthermore, equipped with an attention-based Multi-Agent Target Generator and a Single-Agent Motion Planner, MAexp can work with arbitrary numbers of agents and accommodate various types of robots. Extensive experiments are conducted to establish the first benchmark featuring several high-performance MARL algorithms across typical scenarios for robots with continuous actions, which highlights the distinct strengths of each algorithm in different scenarios.

Autonomous lane-change, a key feature of advanced driver-assistance systems, can enhance traffic efficiency and reduce the incidence of accidents. However, safe driving of autonomous vehicles remains challenging in complex environments. How to perform safe and appropriate lane change is a popular topic of research in the field of autonomous driving. Currently, few papers consider the safety of reinforcement learning in autonomous lane-change scenarios. We introduce safe hybrid-action reinforcement learning into discretionary lane change for the first time and propose Parameterized Soft Actor-Critic with PID Lagrangian (PASAC-PIDLag) algorithm. Furthermore, we conduct a comparative analysis of the Parameterized Soft Actor-Critic (PASAC), which is an unsafe version of PASAC-PIDLag. Both algorithms are employed to train the lane-change strategy of autonomous vehicles to output discrete lane-change decision and longitudinal vehicle acceleration. Our simulation results indicate that at a traffic density of 15 vehicles per kilometer (15 veh/km), the PASAC-PIDLag algorithm exhibits superior safety with a collision rate of 0%, outperforming the PASAC algorithm, which has a collision rate of 1%. The outcomes of the generalization assessments reveal that at low traffic density levels, both the PASAC-PIDLag and PASAC algorithms are proficient in attaining a 0% collision rate. Under conditions of high traffic flow density, the PASAC-PIDLag algorithm surpasses PASAC in terms of both safety and optimality.

This paper consider solving a class of nonconvex-strongly-convex distributed stochastic bilevel optimization (DSBO) problems with personalized inner-level objectives. Most existing algorithms require computational loops for hypergradient estimation, leading to computational inefficiency. Moreover, the impact of data heterogeneity on convergence in bilevel problems is not explicitly characterized yet. To address these issues, we propose LoPA, a loopless personalized distributed algorithm that leverages a tracking mechanism for iterative approximation of inner-level solutions and Hessian-inverse matrices without relying on extra computation loops. Our theoretical analysis explicitly characterizes the heterogeneity across nodes denoted by $b$, and establishes a sublinear rate of ${{\mathcal{O}}}( {\frac{{1}}{{(1-\rho)^2K}} + \frac{{b^{\frac{2}{3}} }}{{\left( {1 - \rho } \right)^{\frac{2}{3}}K^{\frac{2}{3}} }} + \frac{{1}}{\sqrt{ K }} ( \sigma_{\rm{p}} + \frac{1}{\sqrt{m}}\sigma_{\rm{c}}) } )$ without the boundedness of local hypergradients, where $\sigma_{\rm p}$ and $\sigma_{\rm c}$ represent the gradient sampling variances associated with the inner- and outer-level variables, respectively. We also develop a variant of LoPA based on gradient tracking to eliminate the impact of data heterogeneity, yielding an improved rate of ${{\mathcal{O}}}(\frac{{{1}}}{{ (1-\rho)^4K }} + \frac{1}{{\sqrt{K}}}( \sigma_{\rm{p}} + \frac{1}{\sqrt{m}}\sigma_{\rm{c}} ) )$. The computational complexity of LoPA is of ${{\mathcal{O}}}({\epsilon^{-2}})$ to an $\epsilon$-stationary point, matching the communication complexity due to the loopless structure, which outperforms existing counterparts for DSBO. Numerical experiments validate the effectiveness of the proposed algorithm., Comment: 50 pages, 22 figures

Perfect synchronization in distributed machine learning problems is inefficient and even impossible due to the existence of latency, package losses and stragglers. We propose a Robust Fully-Asynchronous Stochastic Gradient Tracking method (R-FAST), where each device performs local computation and communication at its own pace without any form of synchronization. Different from existing asynchronous distributed algorithms, R-FAST can eliminate the impact of data heterogeneity across devices and allow for packet losses by employing a robust gradient tracking strategy that relies on properly designed auxiliary variables for tracking and buffering the overall gradient vector. More importantly, the proposed method utilizes two spanning-tree graphs for communication so long as both share at least one common root, enabling flexible designs in communication architectures. We show that R-FAST converges in expectation to a neighborhood of the optimum with a geometric rate for smooth and strongly convex objectives; and to a stationary point with a sublinear rate for general non-convex settings. Extensive experiments demonstrate that R-FAST runs 1.5-2 times faster than synchronous benchmark algorithms, such as Ring-AllReduce and D-PSGD, while still achieving comparable accuracy, and outperforms existing asynchronous SOTA algorithms, such as AD-PSGD and OSGP, especially in the presence of stragglers., Comment: This paper has been accepted for publication as a regular paper in the IEEE Transactions on Signal and Information Processing over Networks

Energy management strategy (EMS) is a key technology for plug-in hybrid electric vehicles (PHEVs). The energy management of certain series-parallel PHEVs involves the control of continuous variables, such as engine torque, and discrete variables, such as clutch engagement/disengagement. We establish a control-oriented model for a series-parallel plug-in hybrid system with clutch engagement control from the perspective of mixed-integer programming. Subsequently, we design an EMS based on continuous-discrete reinforcement learning (CDRL), which enables simultaneous output of continuous and discrete variables. During training, we introduce state-of-charge (SOC) randomization to ensure that the hybrid system exhibits optimal energy-saving performance in both high and low SOC. Finally, the effectiveness of the proposed CDRL strategy is verified by comparing EMS based on charge-depleting charge-sustaining (CD-CS) with rule-based clutch engagement control, and Dynamic Programming (DP). The simulation results show that, under a high SOC, the CDRL strategy proposed in this paper can improve energy efficiency by 8.3% compared to CD-CS, and the energy consumption is just 6.6% higher than the global optimum based on DP, while under a low SOC, the numbers are 4.1% and 3.9%, respectively.

We propose a flexible gradient tracking approach with adjustable computation and communication steps for solving distributed stochastic optimization problem over networks. The proposed method allows each node to perform multiple local gradient updates and multiple inter-node communications in each round, aiming to strike a balance between computation and communication costs according to the properties of objective functions and network topology in non-i.i.d. settings. Leveraging a properly designed Lyapunov function, we derive both the computation and communication complexities for achieving arbitrary accuracy on smooth and strongly convex objective functions. Our analysis demonstrates sharp dependence of the convergence performance on graph topology and properties of objective functions, highlighting the trade-off between computation and communication. Numerical experiments are conducted to validate our theoretical findings., Comment: This manuscript was submitted to the 62nd IEEE Conference on Decision and Control in March 2023

Many optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are usually formulated as mixed-integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch-and-bound are computationally expensive and undesirable for real-time control. This paper proposes a novel hybrid-action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor-Q (TD3AQ), for MIOC problems. TD3AQ combines the advantages of both actor-critic and Q-learning methods, and can handle the discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug-in hybrid electric vehicle (PHEV) energy management problem, where real-time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation outcomes demonstrate that TD3AQ achieves control results close to optimality when compared with dynamic programming (DP), with just 4.69% difference. Furthermore, it surpasses the performance of baseline reinforcement learning algorithms.

Autonomous drone racing is becoming an excellent platform to challenge quadrotors' autonomy techniques including planning, navigation and control technologies. However, most research on this topic mainly focuses on single drone scenarios. In this paper, we describe a novel time-optimal trajectory generation method for generating time-optimal trajectories for a swarm of quadrotors to fly through pre-defined waypoints with their maximum maneuverability without collision. We verify the method in the Gazebo simulations where a swarm of 5 quadrotors can fly through a complex 6-waypoint racing track in a 35m * 35m space with a top speed of 14m/s. Flight tests are performed on two quadrotors passing through 3 waypoints in a 4m * 2m flight arena to demonstrate the feasibility of the proposed method in the real world. Both simulations and real-world flight tests show that the proposed method can generate the optimal aggressive trajectories for a swarm of autonomous racing drones. The method can also be easily transferred to other types of robot swarms.

We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented graph consisting of nodes modeling the samples and edges modeling both the inter-device communication and intra-device stochastic gradient computation. By designing properly the topology of the augmented graph, we are able to recover as special cases the renowned Local-SGD and DSGD algorithms, and provide a unified perspective for variance-reduction (VR) and gradient-tracking (GT) methods such as SAGA, Local-SVRG and GT-SAGA. We also provide a unified convergence analysis for smooth and (strongly) convex objectives relying on a proper structured Lyapunov function, and the obtained rate can recover the best known results for many existing algorithms. The rate results further reveal that VR and GT methods can effectively eliminate data heterogeneity within and across devices, respectively, enabling the exact convergence of the algorithm to the optimal solution. Numerical experiments confirm the findings in this paper., Comment: This work will appear in ICML 2022

As technology scaling is approaching the physical limit, lithography hotspot detection has become an essential task in design for manufacturability. While the deployment of pattern matching or machine learning in hotspot detection can help save significant simulation time, such methods typically demand for non-trivial quality data to build the model, which most design houses are short of. Moreover, the design houses are also unwilling to directly share such data with the other houses to build a unified model, which can be ineffective for the design house with unique design patterns due to data insufficiency. On the other hand, with data homogeneity in each design house, the locally trained models can be easily over-fitted, losing generalization ability and robustness. In this paper, we propose a heterogeneous federated learning framework for lithography hotspot detection that can address the aforementioned issues. On one hand, the framework can build a more robust centralized global sub-model through heterogeneous knowledge sharing while keeping local data private. On the other hand, the global sub-model can be combined with a local sub-model to better adapt to local data heterogeneity. The experimental results show that the proposed framework can overcome the challenge of non-independent and identically distributed (non-IID) data and heterogeneous communication to achieve very high performance in comparison to other state-of-the-art methods while guaranteeing a good convergence rate in various scenarios., Comment: 8 pages, 9 figures

In this paper, we investigate the problem of coordination between economic dispatch (ED) and demand response (DR) in multi-energy systems (MESs), aiming to improve the economic utility and reduce the waste of energy in MESs. Since multiple energy sources are coupled through energy hubs (EHs), the supply-demand constraints are nonconvex. To deal with this issue, we propose a linearization method to transform the coordination problem to a convex social welfare optimization one. Then a decentralized algorithm based on parallel Alternating Direction Method of Multipliers (ADMM) and dynamic average tracking protocol is developed, where each agent could only make decisions based on information from their neighbors. Moreover, by using variational inequality and Lyapunov-based techniques, we show that our algorithm could always converge to the global optimal solution. Finally, a case study on the modified IEEE 14-bus network verifies the feasibility and effectiveness of our algorithm., Comment: The paper has been submitted to 2021 60th IEEE Conference on Decision and Control (CDC)

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic framework for such a class of problems and provide a unified convergence analysis leveraging the theory of operator splitting. Distinguishing features of our scheme are: (i) When the agents' functions are strongly convex, the algorithm converges at a linear rate, whose dependence on the agents' functions and network topology is decoupled, matching the typical rates of centralized optimization; the rate expression improves on existing results; (ii) When the objective function is convex (but not strongly convex), similar separation as in (i) is established for the coefficient of the proved sublinear rate; (iii) The algorithm can adjust the ratio between the number of communications and computations to achieve a rate (in terms of computations) independent on the network connectivity; and (iv) A by-product of our analysis is a tuning recommendation for several existing (non accelerated) distributed algorithms yielding the fastest provably (worst-case) convergence rate. This is the first time that a general distributed algorithmic framework applicable to composite optimization enjoys all such properties., Comment: arXiv admin note: text overlap with arXiv:1910.09817

This paper proposes a novel family of primal-dual-based distributed algorithms for smooth, convex, multi-agent optimization over networks that uses only gradient information and gossip communications. The algorithms can also employ acceleration on the computation and communications. We provide a unified analysis of their convergence rate, measured in terms of the Bregman distance associated to the saddle point reformation of the distributed optimization problem. When acceleration is employed, the rate is shown to be optimal, in the sense that it matches (under the proposed metric) existing complexity lower bounds of distributed algorithms applicable to such a class of problem and using only gradient information and gossip communications. Preliminary numerical results on distributed least-square regression problems show that the proposed algorithm compares favorably on existing distributed schemes., Comment: final version for AISTATS 2020

We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework for such a class of problems and provide a unified convergence analysis leveraging the theory of operator splitting. Our results unify several approaches proposed in the literature of distributed optimization for special instances of our formulation. Distinguishing features of our scheme are: (i) when the agents' functions are strongly convex, the algorithm converges at a linear rate, whose dependencies on the agents' functions and the network topology are decoupled, matching the typical rates of centralized optimization; (ii) the step-size does not depend on the network parameters but only on the optimization ones; and (iii) the algorithm can adjust the ratio between the number of communications and computations to achieve the same rate of the centralized proximal gradient scheme (in terms of computations). This is the first time that a distributed algorithm applicable to composite optimization enjoys such properties., Comment: To appear in the Proc. of the 2019 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 19)