In this paper,the authors propose a distributed gradient tracking algorithm with compressed communication to address an aggregative optimization problem under communication constraints.The problem involves minimizing ...In this paper,the authors propose a distributed gradient tracking algorithm with compressed communication to address an aggregative optimization problem under communication constraints.The problem involves minimizing the sum of local cost functions,where each cost function depends on both local and global state variables.The authors aim to solve this optimization problem through local computation and efficient communication among agents in a network,without the need for a central coordinator.The proposed algorithm combines the variable tracking method to estimate global state variables and a compressed communication scheme to reduce communication costs during the optimization process.Among which,the compressed scheme can encompass both biased and unbiased compressors.Despite the loss of some transmitting information due to quantization,the proposed algorithm can still achieve the exact optimal solution with a linear convergence rate.The authors validate the theoretical results through simulation experiments on an optimal placement problem.展开更多
This paper studies the distributed optimization problem over an undirected connected graph subject to digital communications with a finite data rate,where each agent holds a strongly convex and smooth cost function.Th...This paper studies the distributed optimization problem over an undirected connected graph subject to digital communications with a finite data rate,where each agent holds a strongly convex and smooth cost function.The agents need to cooperatively minimize the average of all agents’cost functions.Each agent builds an encoder/decoder pair that produces transmitted messages to its neighbors with a finite-level uniform quantizer,and recovers its neighbors’states by a recursive decoder with received quantized signals.Combining the adaptive encoder/decoder scheme with the gradient tracking method,the authors propose a distributed quantized algorithm.The authors prove that the optimization can be achieved at a linear rate,even when agents communicate at 1-bit data rate.Numerical examples are also conducted to illustrate theoretical results.展开更多
Temperature is one of the important loads for designing slab track. The characteristic of slab track tem- perature varies greatly with different regional climates. In this work, a bi-block slab track model was built u...Temperature is one of the important loads for designing slab track. The characteristic of slab track tem- perature varies greatly with different regional climates. In this work, a bi-block slab track model was built under outdoor conditions in Chengdu area; the statistical characteristic of temperature gradient in track slab and the relationship between temperature gradient and surface air temperature were tested and analyzed. The results show that the track slab temperature gradient will vary periodically according to the surface air temperature, and show a clear nonlinearity along the height direction. The temperature gradient distribution is extremely uneven： the temperature gradient in the top part of the track slab is larger than that in the bottom part; the most frequently occurring temperature gradient of the track slab is around -3.5 ℃/m and more than 75 % locates in the level -10 to 10 ℃/m; concrete with a relatively good heat exchange condition with the surrounding air has a narrower band distribution. In addition, the frequency distribution histogram should exclude the time zone from 00：00 to 06：00 because there is almost no traffic in this period. The amplitude of track slab temperature variation is obviously lower than that of the air temperature variation, and the former is approximately linear with the latter.展开更多
This paper studies distributed convex optimization over a multi-agent system,where each agent owns only a local cost function with convexity and Lipschitz continuous gradients.The goal of the agents is to cooperativel...This paper studies distributed convex optimization over a multi-agent system,where each agent owns only a local cost function with convexity and Lipschitz continuous gradients.The goal of the agents is to cooperatively minimize a sum of the local cost functions.The underlying communication networks are modelled by a sequence of random and balanced digraphs,which are not required to be spatially or temporally independent and have any special distributions.The authors use a distributed gradient-tracking-based optimization algorithm to solve the optimization problem.In the algorithm,each agent makes an estimate of the optimal solution and an estimate of the average of all the local gradients.The values of the estimates are updated based on a combination of a consensus method and a gradient tracking method.The authors prove that the algorithm can achieve convergence to the optimal solution at a geometric rate if the conditional graphs are uniformly strongly connected,the global cost function is strongly convex and the step-sizes don’t exceed some upper bounds.展开更多
This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning(MARL),where agents communicating over a network aim to find an optimal policy that maximizes the average of all the ...This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning(MARL),where agents communicating over a network aim to find an optimal policy that maximizes the average of all the agents'local returns.To address the challenges of high variance and bias in stochastic policy gradients for MARL,this paper proposes a distributed policy gradient method with variance reduction,combined with gradient tracking to correct the bias resulting from the difference between local and global gradients.The authors also utilize importance sampling to solve the distribution shift problem in the sampling process.The authors then show that the proposed algorithm finds anε-approximate stationary point,where the convergence depends on the number of iterations,the mini-batch size,the epoch size,the problem parameters,and the network topology.The authors further establish the sample and communication complexity to obtain anε-approximate stationary point.Finally,numerical experiments are performed to validate the effectiveness of the proposed algorithm.展开更多
We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOC...We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.展开更多
This study focuses on the distributed convex optimization problem with local boundary constraints and multiple in-equality constraints,specifically considering scenarios involving communication delays and inconsistent...This study focuses on the distributed convex optimization problem with local boundary constraints and multiple in-equality constraints,specifically considering scenarios involving communication delays and inconsistent updates between nodes.To tackle the problem with guaranteed constraint satisfaction,a distributed asynchronous optimization algorithm is proposed based on the parameter projection method.Moreover,an asynchronous gradient tracking mechanism is employed to accelerate convergence.In the convergence analysis,an augmented synchronous system with virtual nodes is adopted to transform the de-layed optimization problem into a problem without delays.Based on the generalized small gain theory,the proposed algorithm is proved to achieve a geometric convergence rate.Finally,numerical simulations and industrial experiments verify the effectiveness of the proposed algorithm.展开更多
This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Bot...This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.展开更多
基金supported by the National Key Research and Development Program of China under Grant No.2022YFA1004701the National Natural Science Foundation of China under Grant No.72271187+1 种基金the Fundamental Research Funds for the Central Universitiespartially by Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100。
文摘In this paper,the authors propose a distributed gradient tracking algorithm with compressed communication to address an aggregative optimization problem under communication constraints.The problem involves minimizing the sum of local cost functions,where each cost function depends on both local and global state variables.The authors aim to solve this optimization problem through local computation and efficient communication among agents in a network,without the need for a central coordinator.The proposed algorithm combines the variable tracking method to estimate global state variables and a compressed communication scheme to reduce communication costs during the optimization process.Among which,the compressed scheme can encompass both biased and unbiased compressors.Despite the loss of some transmitting information due to quantization,the proposed algorithm can still achieve the exact optimal solution with a linear convergence rate.The authors validate the theoretical results through simulation experiments on an optimal placement problem.
文摘This paper studies the distributed optimization problem over an undirected connected graph subject to digital communications with a finite data rate,where each agent holds a strongly convex and smooth cost function.The agents need to cooperatively minimize the average of all agents’cost functions.Each agent builds an encoder/decoder pair that produces transmitted messages to its neighbors with a finite-level uniform quantizer,and recovers its neighbors’states by a recursive decoder with received quantized signals.Combining the adaptive encoder/decoder scheme with the gradient tracking method,the authors propose a distributed quantized algorithm.The authors prove that the optimization can be achieved at a linear rate,even when agents communicate at 1-bit data rate.Numerical examples are also conducted to illustrate theoretical results.
基金supported by the National Key Basic Research Program of China (973 Program) (2013CB036202)the National Natural Science Foundation of China (51008258)Fundamental Research Funds for the Central Universities (SWJTU12CX065)
文摘Temperature is one of the important loads for designing slab track. The characteristic of slab track tem- perature varies greatly with different regional climates. In this work, a bi-block slab track model was built under outdoor conditions in Chengdu area; the statistical characteristic of temperature gradient in track slab and the relationship between temperature gradient and surface air temperature were tested and analyzed. The results show that the track slab temperature gradient will vary periodically according to the surface air temperature, and show a clear nonlinearity along the height direction. The temperature gradient distribution is extremely uneven： the temperature gradient in the top part of the track slab is larger than that in the bottom part; the most frequently occurring temperature gradient of the track slab is around -3.5 ℃/m and more than 75 % locates in the level -10 to 10 ℃/m; concrete with a relatively good heat exchange condition with the surrounding air has a narrower band distribution. In addition, the frequency distribution histogram should exclude the time zone from 00：00 to 06：00 because there is almost no traffic in this period. The amplitude of track slab temperature variation is obviously lower than that of the air temperature variation, and the former is approximately linear with the latter.
基金supported by the Basic Research Project of Shanghai Science and Technology Commission under Grant No.20JC1414000。
文摘This paper studies distributed convex optimization over a multi-agent system,where each agent owns only a local cost function with convexity and Lipschitz continuous gradients.The goal of the agents is to cooperatively minimize a sum of the local cost functions.The underlying communication networks are modelled by a sequence of random and balanced digraphs,which are not required to be spatially or temporally independent and have any special distributions.The authors use a distributed gradient-tracking-based optimization algorithm to solve the optimization problem.In the algorithm,each agent makes an estimate of the optimal solution and an estimate of the average of all the local gradients.The values of the estimates are updated based on a combination of a consensus method and a gradient tracking method.The authors prove that the algorithm can achieve convergence to the optimal solution at a geometric rate if the conditional graphs are uniformly strongly connected,the global cost function is strongly convex and the step-sizes don’t exceed some upper bounds.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62003245,72171172,and 92367101the National Natural Science Foundation of China Basic Science Research Center Program under Grant No.62088101+1 种基金the Aeronautical Science Foundation of China under Grant No.2023Z066038001Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100。
文摘This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning(MARL),where agents communicating over a network aim to find an optimal policy that maximizes the average of all the agents'local returns.To address the challenges of high variance and bias in stochastic policy gradients for MARL,this paper proposes a distributed policy gradient method with variance reduction,combined with gradient tracking to correct the bias resulting from the difference between local and global gradients.The authors also utilize importance sampling to solve the distribution shift problem in the sampling process.The authors then show that the proposed algorithm finds anε-approximate stationary point,where the convergence depends on the number of iterations,the mini-batch size,the epoch size,the problem parameters,and the network topology.The authors further establish the sample and communication complexity to obtain anε-approximate stationary point.Finally,numerical experiments are performed to validate the effectiveness of the proposed algorithm.
基金financially supported by the National Key Basic Research Program of China(973 program,grant no.:2013CB733302,2013CB733301)the Major International(Regional) Joint Research Project(grant no.:41210006)+1 种基金DAAD Thematic Network Project(grant no.:57173947)the National Natural Science Foundation of China(grant No.41374022)
文摘We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB3305900)the National Natural Science Foundation of China(Grant No.61988101)+1 种基金Shanghai Committee of Science and Technology,China(Grant No.22DZ1101500)the Fundamental Research Funds for the Central Universities.
文摘This study focuses on the distributed convex optimization problem with local boundary constraints and multiple in-equality constraints,specifically considering scenarios involving communication delays and inconsistent updates between nodes.To tackle the problem with guaranteed constraint satisfaction,a distributed asynchronous optimization algorithm is proposed based on the parameter projection method.Moreover,an asynchronous gradient tracking mechanism is employed to accelerate convergence.In the convergence analysis,an augmented synchronous system with virtual nodes is adopted to transform the de-layed optimization problem into a problem without delays.Based on the generalized small gain theory,the proposed algorithm is proved to achieve a geometric convergence rate.Finally,numerical simulations and industrial experiments verify the effectiveness of the proposed algorithm.
基金supported by National Nature Science Foundation of China (Nos. 61663026, 62066026, 61963028 and 61866023)Jiangxi NSF (No. 20192BAB 207025)。
文摘This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.
