Lin Yang, A. Zeynali, M. Hajiesmaili, R. Sitaraman, D. Towsley
In this paper, we study the online multidimensional knapsack problem (called OMdKP) in which there is a knapsack whose capacity is represented in m dimensions, each dimension could have a different capacity. Then, n items with different scalar profit values and m-dimensional weights arrive in an online manner and the goal is to admit or decline items upon their arrival such that the total profit obtained by admitted items is maximized and the capacity of knapsack across all dimensions is respected. This is a natural generalization of the classic single-dimension knapsack problem and finds several relevant applications such as in virtual machine allocation, job scheduling, and all-or-nothing flow maximization over a graph. We develop two algorithms for OMdKP that use linear and exponential reservation functions to make online admission decisions. Our competitive analysis shows that the linear and exponential algorithms achieve the competitive ratios of O(θα ) and O(łogł(θα)), respectively, where α is the ratio between the aggregate knapsack capacity and the minimum capacity over a single dimension and θ is the ratio between the maximum and minimum item unit values. We also characterize a lower bound for the competitive ratio of any online algorithm solving OMdKP and show that the competitive ratio of our algorithm with exponential reservation function matches the lower bound up to a constant factor.
{"title":"Competitive Algorithms for Online Multidimensional Knapsack Problems","authors":"Lin Yang, A. Zeynali, M. Hajiesmaili, R. Sitaraman, D. Towsley","doi":"10.1145/3491042","DOIUrl":"https://doi.org/10.1145/3491042","url":null,"abstract":"In this paper, we study the online multidimensional knapsack problem (called OMdKP) in which there is a knapsack whose capacity is represented in m dimensions, each dimension could have a different capacity. Then, n items with different scalar profit values and m-dimensional weights arrive in an online manner and the goal is to admit or decline items upon their arrival such that the total profit obtained by admitted items is maximized and the capacity of knapsack across all dimensions is respected. This is a natural generalization of the classic single-dimension knapsack problem and finds several relevant applications such as in virtual machine allocation, job scheduling, and all-or-nothing flow maximization over a graph. We develop two algorithms for OMdKP that use linear and exponential reservation functions to make online admission decisions. Our competitive analysis shows that the linear and exponential algorithms achieve the competitive ratios of O(θα ) and O(łogł(θα)), respectively, where α is the ratio between the aggregate knapsack capacity and the minimum capacity over a single dimension and θ is the ratio between the maximum and minimum item unit values. We also characterize a lower bound for the competitive ratio of any online algorithm solving OMdKP and show that the competitive ratio of our algorithm with exponential reservation function matches the lower bound up to a constant factor.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"06 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130818672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cloud gaming platforms have witnessed tremendous growth over the past two years with a number of large Internet companies including Amazon, Facebook, Google, Microsoft, and Nvidia publicly launching their own platforms. While cloud gaming platforms continue to grow, the visibility in their performance and relative comparison is lacking. This is largely due to absence of systematic measurement methodologies which can generally be applied. As such, in this paper, we implement DECAF, a methodology to systematically analyze and dissect the performance of cloud gaming platforms across different game genres and game platforms. DECAF is highly automated and requires minimum manual intervention. By applying DECAF, we measure the performance of three commercial cloud gaming platforms including Google Stadia, Amazon Luna, and Nvidia GeForceNow, and uncover a number of important findings. First, we find that processing delays in the cloud comprise majority of the total round trip delay experienced by users, accounting for as much as 73.54% of total user-perceived delay. Second, we find that video streams delivered by cloud gaming platforms are characterized by high variability of bitrate, frame rate, and resolution. Platforms struggle to consistently serve 1080p/60 frames per second streams across different game genres even when the available bandwidth is 8-20× that of platform's recommended settings. Finally, we show that game platforms exhibit performance cliffs by reacting poorly to packet losses, in some cases dramatically reducing the delivered bitrate by up to 6.6× when loss rates increase from 0.1% to 1%. Our work has important implications for cloud gaming platforms and opens the door for further research on comprehensive measurement methodologies for cloud gaming.
{"title":"Dissecting Cloud Gaming Performance with DECAF","authors":"Hassan Iqbal, A. Khalid, Muhammad Shahzad","doi":"10.1145/3491043","DOIUrl":"https://doi.org/10.1145/3491043","url":null,"abstract":"Cloud gaming platforms have witnessed tremendous growth over the past two years with a number of large Internet companies including Amazon, Facebook, Google, Microsoft, and Nvidia publicly launching their own platforms. While cloud gaming platforms continue to grow, the visibility in their performance and relative comparison is lacking. This is largely due to absence of systematic measurement methodologies which can generally be applied. As such, in this paper, we implement DECAF, a methodology to systematically analyze and dissect the performance of cloud gaming platforms across different game genres and game platforms. DECAF is highly automated and requires minimum manual intervention. By applying DECAF, we measure the performance of three commercial cloud gaming platforms including Google Stadia, Amazon Luna, and Nvidia GeForceNow, and uncover a number of important findings. First, we find that processing delays in the cloud comprise majority of the total round trip delay experienced by users, accounting for as much as 73.54% of total user-perceived delay. Second, we find that video streams delivered by cloud gaming platforms are characterized by high variability of bitrate, frame rate, and resolution. Platforms struggle to consistently serve 1080p/60 frames per second streams across different game genres even when the available bandwidth is 8-20× that of platform's recommended settings. Finally, we show that game platforms exhibit performance cliffs by reacting poorly to packet losses, in some cases dramatically reducing the delivered bitrate by up to 6.6× when loss rates increase from 0.1% to 1%. Our work has important implications for cloud gaming platforms and opens the door for further research on comprehensive measurement methodologies for cloud gaming.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132688561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yun Seong Nam, Jianfei Gao, Chandan Bothra, Ehab Ghabashneh, Sanjay G. Rao, Bruno Ribeiro, Jibin Zhan, Hui Zhang
The performance of Adaptive Bitrate (ABR) algorithms for video streaming depends on accurately predicting the download time of video chunks. Existing prediction approaches (i) assume chunk download times are dominated by network throughput; and (ii) apriori cluster sessions (e.g., based on ISP and CDN) and only learn from sessions in the same cluster. We make three contributions. First, through analysis of data from real-world video streaming sessions, we show (i) apriori clustering prevents learning from related clusters; and (ii) factors such as the Time to First Byte (TTFB) are key components of chunk download times but not easily incorporated into existing prediction approaches. Second, we propose Xatu, a new prediction approach that jointly learns a neural network sequence model with an interpretable automatic session clustering method. Xatu learns clustering rules across all sessions it deems relevant, and models sequences with multiple chunk-dependent features (e.g., TTFB) rather than just throughput. Third, evaluations using the above datasets and emulation experiments show that Xatu significantly improves prediction accuracies by 23.8% relative to CS2P (a state-of-the-art predictor). We show Xatu provides substantial performance benefits when integrated with multiple ABR algorithms including MPC (a well studied ABR algorithm), and FuguABR (a recent algorithm using stochastic control) relative to their default predictors (CS2P and a fully connected neural network respectively). Further, Xatu combined with MPC outperforms Pensieve, an ABR based on deep reinforcement learning.
{"title":"Xatu: Richer Neural Network Based Prediction for Video Streaming","authors":"Yun Seong Nam, Jianfei Gao, Chandan Bothra, Ehab Ghabashneh, Sanjay G. Rao, Bruno Ribeiro, Jibin Zhan, Hui Zhang","doi":"10.1145/3491056","DOIUrl":"https://doi.org/10.1145/3491056","url":null,"abstract":"The performance of Adaptive Bitrate (ABR) algorithms for video streaming depends on accurately predicting the download time of video chunks. Existing prediction approaches (i) assume chunk download times are dominated by network throughput; and (ii) apriori cluster sessions (e.g., based on ISP and CDN) and only learn from sessions in the same cluster. We make three contributions. First, through analysis of data from real-world video streaming sessions, we show (i) apriori clustering prevents learning from related clusters; and (ii) factors such as the Time to First Byte (TTFB) are key components of chunk download times but not easily incorporated into existing prediction approaches. Second, we propose Xatu, a new prediction approach that jointly learns a neural network sequence model with an interpretable automatic session clustering method. Xatu learns clustering rules across all sessions it deems relevant, and models sequences with multiple chunk-dependent features (e.g., TTFB) rather than just throughput. Third, evaluations using the above datasets and emulation experiments show that Xatu significantly improves prediction accuracies by 23.8% relative to CS2P (a state-of-the-art predictor). We show Xatu provides substantial performance benefits when integrated with multiple ABR algorithms including MPC (a well studied ABR algorithm), and FuguABR (a recent algorithm using stochastic control) relative to their default predictors (CS2P and a fully connected neural network respectively). Further, Xatu combined with MPC outperforms Pensieve, an ABR based on deep reinforcement learning.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134480252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuanyuan Li, T. Si Salem, G. Neglia, Stratis Ioannidis
We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm. Our distributed policy achieves sublinear (1-1/e)-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.
{"title":"Online Caching Networks with Adversarial Guarantees","authors":"Yuanyuan Li, T. Si Salem, G. Neglia, Stratis Ioannidis","doi":"10.1145/3491047","DOIUrl":"https://doi.org/10.1145/3491047","url":null,"abstract":"We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm. Our distributed policy achieves sublinear (1-1/e)-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121589606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flash-based solid state drives (SSDs) have gained a central role in the infrastructure of large-scale datacenters, as well as in commodity servers and personal devices. The main limitation of flash media is its inability to support update-in-place: after data has been written to a physical location, it has to be erased before new data can be written to it. Moreover, SSDs support read and write operations in granularity of pages, while erasures are performed on entire blocks, which often contain hundreds of pages. When erasing a block, any valid data it stores must be rewritten to a clean location. As an SSD eventually wears out with progressing number of erasures, the efficiency of the management algorithm has a significant impact on its endurance. In this paper we first formally define the SSD management problem. We then explore this problem from an algorithmic perspective, considering it in both offline and online settings. In the offline setting, we present a near-optimal algorithm that, given any input, performs a negligible number of rewrites (relative to the input length). We also discuss the hardness of the offline problem. In the online setting, we first consider algorithms that have no prior knowledge about the input. We prove that no deterministic algorithm outperforms the greedy algorithm in this setting, and discuss the possible benefit of randomization. We then augment our model, assuming that each request for a page arrives with a prediction of the next time the page is updated. We design an online algorithm that uses such predictions, and show that its performance improves as the prediction error decreases. We also show that the performance of our algorithm is never worse than that guaranteed by the greedy algorithm, even when the prediction error is large. We complement our theoretical findings with an empirical evaluation of our algorithms, comparing them with the state-of-the-art scheme. The results confirm that our algorithms exhibit an improved performance for a wide range of input traces.
{"title":"Offline and Online Algorithms for SSD Management","authors":"Tomer Lange, J. Naor, G. Yadgar","doi":"10.1145/3491045","DOIUrl":"https://doi.org/10.1145/3491045","url":null,"abstract":"Flash-based solid state drives (SSDs) have gained a central role in the infrastructure of large-scale datacenters, as well as in commodity servers and personal devices. The main limitation of flash media is its inability to support update-in-place: after data has been written to a physical location, it has to be erased before new data can be written to it. Moreover, SSDs support read and write operations in granularity of pages, while erasures are performed on entire blocks, which often contain hundreds of pages. When erasing a block, any valid data it stores must be rewritten to a clean location. As an SSD eventually wears out with progressing number of erasures, the efficiency of the management algorithm has a significant impact on its endurance. In this paper we first formally define the SSD management problem. We then explore this problem from an algorithmic perspective, considering it in both offline and online settings. In the offline setting, we present a near-optimal algorithm that, given any input, performs a negligible number of rewrites (relative to the input length). We also discuss the hardness of the offline problem. In the online setting, we first consider algorithms that have no prior knowledge about the input. We prove that no deterministic algorithm outperforms the greedy algorithm in this setting, and discuss the possible benefit of randomization. We then augment our model, assuming that each request for a page arrives with a prediction of the next time the page is updated. We design an online algorithm that uses such predictions, and show that its performance improves as the prediction error decreases. We also show that the performance of our algorithm is never worse than that guaranteed by the greedy algorithm, even when the prediction error is large. We complement our theoretical findings with an empirical evaluation of our algorithms, comparing them with the state-of-the-art scheme. The results confirm that our algorithms exhibit an improved performance for a wide range of input traces.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125197181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.
{"title":"Real-time Bidding for Time Constrained Impression Contracts in First and Second Price Auctions - Theory and Algorithms","authors":"R. Kinnear, R. Mazumdar, P. Marbach","doi":"10.1145/3491049","DOIUrl":"https://doi.org/10.1145/3491049","url":null,"abstract":"We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124863247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However, constant stepsize SA algorithms do not converge to the optimal solution, but instead have a stationary distribution, which in general cannot be analytically characterized. In this work, we study the asymptotic behavior of the appropriately scaled stationary distribution, in the limit when the constant stepsize goes to zero. Specifically, we consider the following three settings: (1) SGD algorithm with a smooth and strongly convex objective, (2) linear SA algorithm involving a Hurwitz matrix, and (3) nonlinear SA algorithm involving a contractive operator. When the iterate is scaled by 1/α, where α is the constant stepsize, we show that the limiting scaled stationary distribution is a solution of an implicit equation. Under a uniqueness assumption (which can be removed in certain settings) on this equation, we further characterize the limiting distribution as a Gaussian distribution whose covariance matrix is the unique solution of a suitable Lyapunov equation. For SA algorithms beyond these cases, our numerical experiments suggest that unlike central limit theorem type results: (1) the scaling factor need not be 1/α, and (2) the limiting distribution need not be Gaussian. Based on the numerical study, we come up with a heuristic formula to determine the right scaling factor, and make insightful connection to the Euler-Maruyama discretization scheme for approximating stochastic differential equations.
{"title":"Stationary Behavior of Constant Stepsize SGD Type Algorithms","authors":"Zaiwei Chen, Shancong Mou, S. T. Maguluri","doi":"10.1145/3508039","DOIUrl":"https://doi.org/10.1145/3508039","url":null,"abstract":"Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However, constant stepsize SA algorithms do not converge to the optimal solution, but instead have a stationary distribution, which in general cannot be analytically characterized. In this work, we study the asymptotic behavior of the appropriately scaled stationary distribution, in the limit when the constant stepsize goes to zero. Specifically, we consider the following three settings: (1) SGD algorithm with a smooth and strongly convex objective, (2) linear SA algorithm involving a Hurwitz matrix, and (3) nonlinear SA algorithm involving a contractive operator. When the iterate is scaled by 1/α, where α is the constant stepsize, we show that the limiting scaled stationary distribution is a solution of an implicit equation. Under a uniqueness assumption (which can be removed in certain settings) on this equation, we further characterize the limiting distribution as a Gaussian distribution whose covariance matrix is the unique solution of a suitable Lyapunov equation. For SA algorithms beyond these cases, our numerical experiments suggest that unlike central limit theorem type results: (1) the scaling factor need not be 1/α, and (2) the limiting distribution need not be Gaussian. Based on the numerical study, we come up with a heuristic formula to determine the right scaling factor, and make insightful connection to the Euler-Maruyama discretization scheme for approximating stochastic differential equations.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129837837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics A_t, B_t. The sequence of dynamics matrices can be arbitrary, but with a total variation, V_T, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of O(V_T^2/5 T^3/5 ). With piecewise constant dynamics, our algorithm achieves the optimal regret of O(sqrtST ) where S is the number of switches. The crux of our algorithm is an adaptive non-stationarity detection strategy, which builds on an approach recently developed for contextual Multi-armed Bandit problems. We also argue that non-adaptive forgetting (e.g., restarting or using sliding window learning with a static window size) may not be regret optimal for the LQR problem, even when the window size is optimally tuned with the knowledge of $V_T$. The main technical challenge in the analysis of our algorithm is to prove that the ordinary least squares (OLS) estimator has a small bias when the parameter to be estimated is non-stationary. Our analysis also highlights that the key motif driving the regret is that the LQR problem is in spirit a bandit problem with linear feedback and locally quadratic cost. This motif is more universal than the LQR problem itself, and therefore we believe our results should find wider application.
研究一类线性二次型调节器(LQR)系统在有限视界T上的控制问题，该系统具有固定且已知的代价矩阵Q,R，但未知且非平稳的动态矩阵A_t, B_t。动力学矩阵的序列可以是任意的，但是总变化量V_T假设为0 (T)，并且控制器未知。假设对所有t都有一个稳定但可能次优的控制器序列，我们提出了一个实现最优动态后悔0 (V_T^2/5 t ^3/5)的算法。通过分段恒动态，我们的算法实现了0 (sqrtST)的最优遗憾，其中S为开关数。该算法的关键是自适应非平稳检测策略，该策略基于最近开发的上下文多臂强盗问题的方法。我们还认为，非自适应遗忘(例如，重新启动或使用静态窗口大小的滑动窗口学习)对于LQR问题可能不是遗憾的最佳选择，即使窗口大小是根据V_T的知识进行最佳调整。在分析我们的算法时，主要的技术挑战是证明当待估计的参数是非平稳时，普通最小二乘(OLS)估计量具有较小的偏差。我们的分析还强调了驱动后悔的关键主题是LQR问题在精神上是一个具有线性反馈和局部二次代价的强盗问题。这个基序比LQR问题本身更普遍，因此我们相信我们的结果应该有更广泛的应用。
{"title":"Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems","authors":"Yuwei Luo, Varun Gupta, M. Kolar","doi":"10.1145/3508029","DOIUrl":"https://doi.org/10.1145/3508029","url":null,"abstract":"We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics A_t, B_t. The sequence of dynamics matrices can be arbitrary, but with a total variation, V_T, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of O(V_T^2/5 T^3/5 ). With piecewise constant dynamics, our algorithm achieves the optimal regret of O(sqrtST ) where S is the number of switches. The crux of our algorithm is an adaptive non-stationarity detection strategy, which builds on an approach recently developed for contextual Multi-armed Bandit problems. We also argue that non-adaptive forgetting (e.g., restarting or using sliding window learning with a static window size) may not be regret optimal for the LQR problem, even when the window size is optimally tuned with the knowledge of $V_T$. The main technical challenge in the analysis of our algorithm is to prove that the ordinary least squares (OLS) estimator has a small bias when the parameter to be estimated is non-stationary. Our analysis also highlights that the key motif driving the regret is that the LQR problem is in spirit a bandit problem with linear feedback and locally quadratic cost. This motif is more universal than the LQR problem itself, and therefore we believe our results should find wider application.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128995970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as n interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers. Mean field approximation is asymptotically exact for systems composed of n homogeneous objects under mild conditions. In this paper, we study what happens when objects are heterogeneous. This can represent servers with different speeds or contents with different popularities. We define an interaction model that allows obtaining asymptotic convergence results for stochastic systems with heterogeneous object behavior, and show that the error of the mean field approximation is of order $O(1/n)$. More importantly, we show how to adapt the refined mean field approximation, developed by Gast et al., and show that the error of this approximation is reduced to O(1/n^2). To illustrate the applicability of our result, we present two examples. The first addresses a list-based cache replacement model, RANDOM(m), which is an extension of the RANDOM policy. The second is a heterogeneous supermarket model. These examples show that the proposed approximations are computationally tractable and very accurate. They also show that for moderate system sizes (30) the refined mean field approximation tends to be more accurate than simulations for any reasonable simulation time.
{"title":"Mean Field and Refined Mean Field Approximations for Heterogeneous Systems","authors":"Sebastian Allmeier, Nicolas Gast","doi":"10.1145/3508033","DOIUrl":"https://doi.org/10.1145/3508033","url":null,"abstract":"Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as n interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers. Mean field approximation is asymptotically exact for systems composed of n homogeneous objects under mild conditions. In this paper, we study what happens when objects are heterogeneous. This can represent servers with different speeds or contents with different popularities. We define an interaction model that allows obtaining asymptotic convergence results for stochastic systems with heterogeneous object behavior, and show that the error of the mean field approximation is of order $O(1/n)$. More importantly, we show how to adapt the refined mean field approximation, developed by Gast et al., and show that the error of this approximation is reduced to O(1/n^2). To illustrate the applicability of our result, we present two examples. The first addresses a list-based cache replacement model, RANDOM(m), which is an extension of the RANDOM policy. The second is a heterogeneous supermarket model. These examples show that the proposed approximations are computationally tractable and very accurate. They also show that for moderate system sizes (30) the refined mean field approximation tends to be more accurate than simulations for any reasonable simulation time.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124428943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Convolutional neural networks (CNNs) are used in numerous real-world applications such as vision-based autonomous driving and video content analysis. To run CNN inference on various target devices, hardware-aware neural architecture search (NAS) is crucial. A key requirement of efficient hardware-aware NAS is the fast evaluation of inference latencies in order to rank different architectures. While building a latency predictor for each target device has been commonly used in state of the art, this is a very time-consuming process, lacking scalability in the presence of extremely diverse devices. In this work, we address the scalability challenge by exploiting latency monotonicity --- the architecture latency rankings on different devices are often correlated. When strong latency monotonicity exists, we can re-use architectures searched for one proxy device on new target devices, without losing optimality. In the absence of strong latency monotonicity, we propose an efficient proxy adaptation technique to significantly boost the latency monotonicity. Finally, we validate our approach and conduct experiments with devices of different platforms on multiple mainstream search spaces, including MobileNet-V2, MobileNet-V3, NAS-Bench-201, ProxylessNAS and FBNet. Our results highlight that, by using just one proxy device, we can find almost the same Pareto-optimal architectures as the existing per-device NAS, while avoiding the prohibitive cost of building a latency predictor for each device.
{"title":"One Proxy Device Is Enough for Hardware-Aware Neural Architecture Search","authors":"Bingqian Lu, Jianyi Yang, Weiwen Jiang, Yiyu Shi, Shaolei Ren","doi":"10.1145/3491046","DOIUrl":"https://doi.org/10.1145/3491046","url":null,"abstract":"Convolutional neural networks (CNNs) are used in numerous real-world applications such as vision-based autonomous driving and video content analysis. To run CNN inference on various target devices, hardware-aware neural architecture search (NAS) is crucial. A key requirement of efficient hardware-aware NAS is the fast evaluation of inference latencies in order to rank different architectures. While building a latency predictor for each target device has been commonly used in state of the art, this is a very time-consuming process, lacking scalability in the presence of extremely diverse devices. In this work, we address the scalability challenge by exploiting latency monotonicity --- the architecture latency rankings on different devices are often correlated. When strong latency monotonicity exists, we can re-use architectures searched for one proxy device on new target devices, without losing optimality. In the absence of strong latency monotonicity, we propose an efficient proxy adaptation technique to significantly boost the latency monotonicity. Finally, we validate our approach and conduct experiments with devices of different platforms on multiple mainstream search spaces, including MobileNet-V2, MobileNet-V3, NAS-Bench-201, ProxylessNAS and FBNet. Our results highlight that, by using just one proxy device, we can find almost the same Pareto-optimal architectures as the existing per-device NAS, while avoiding the prohibitive cost of building a latency predictor for each device.","PeriodicalId":426760,"journal":{"name":"Proceedings of the ACM on Measurement and Analysis of Computing Systems","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124950623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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