Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447018
J. Wildman, Yusuf Osmanlioglu, S. Weber, A. Shokoufandeh
We study network utility maximization (NUM) within the context of cellular single user association (SUA) policies that map each mobile user (MU) to a single base station (BS) and make use of the generalized α-proportional fairness utility measure across downlink rates. Finding an exact solution to many such centralized user association problem is known to be NP-hard, so we are motivated to consider the integer relaxation of the SUA NUM problem. On this front, we provide separate characterizations of i) the fairness measures under which the SUA NUM problem integrality gap is exactly 1, and ii) the fairness measures yielding non-convex SUA NUM problem formulations. Next, we analyze the fairness measure corresponding to delay minimization and find a more natural linearization of the non-convex minimum delay SUA problem compared to our related previous work. We propose and construct a primal-dual algorithm to approximate the linearized minimum delay SUA problem. Our primal-dual algorithm is shown to achieve smaller performance gaps and runtimes over i) an intuitive baseline rounding algorithm applied to the linearized min delay SUA problem, as well as ii) two greedy heuristics that emphasize associations with minimal MU-BS distances and maximal downlink SINR ratios, respectively.
{"title":"A primal-dual approach to delay minimizing user association in cellular networks","authors":"J. Wildman, Yusuf Osmanlioglu, S. Weber, A. Shokoufandeh","doi":"10.1109/ALLERTON.2015.7447018","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447018","url":null,"abstract":"We study network utility maximization (NUM) within the context of cellular single user association (SUA) policies that map each mobile user (MU) to a single base station (BS) and make use of the generalized α-proportional fairness utility measure across downlink rates. Finding an exact solution to many such centralized user association problem is known to be NP-hard, so we are motivated to consider the integer relaxation of the SUA NUM problem. On this front, we provide separate characterizations of i) the fairness measures under which the SUA NUM problem integrality gap is exactly 1, and ii) the fairness measures yielding non-convex SUA NUM problem formulations. Next, we analyze the fairness measure corresponding to delay minimization and find a more natural linearization of the non-convex minimum delay SUA problem compared to our related previous work. We propose and construct a primal-dual algorithm to approximate the linearized minimum delay SUA problem. Our primal-dual algorithm is shown to achieve smaller performance gaps and runtimes over i) an intuitive baseline rounding algorithm applied to the linearized min delay SUA problem, as well as ii) two greedy heuristics that emphasize associations with minimal MU-BS distances and maximal downlink SINR ratios, respectively.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134458544","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7446988
Abhishek Sinha, Pradeepkumar Mani, Jie Liu, A. Flavel, D. Maltz
Anycast is an internet addressing protocol where multiple hosts share the same IP-address. A popular architecture for modern Content Distribution Networks (CDNs) for geo-replicated HTTP-services consists of multiple layers of proxy nodes for service and co-located DNS-servers for load-balancing on different proxies. Both the proxies and the DNS-servers use anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control. Due to the very nature of anycast, load-management actions by a co-located DNS-server also affects loads at nearby proxies in the network. This makes the problem of distributed load management highly challenging. In this paper, we propose an analytical framework to formulate and solve the load-management problem in this context. We consider two distinct algorithms. In the first half of the paper, we pose the load-management problem as a convex optimization problem. Following a dual decomposition technique, we propose a fully-distributed load-management algorithm by introducing FastControl packets. This algorithm utilizes the underlying anycast mechanism itself to enable effective coordination among the nodes, thus obviating the need for any external control channel. In the second half of the paper, we consider an alternative greedy load-management heuristic, currently in production in a major commercial CDN. We study its dynamical characteristics and analytically identify its operational and stability properties. Finally, we critically evaluate both the algorithms and explore their optimality-vs-complexity trade-off using trace-driven simulations.
{"title":"Distributed load management in anycast-based CDNs","authors":"Abhishek Sinha, Pradeepkumar Mani, Jie Liu, A. Flavel, D. Maltz","doi":"10.1109/ALLERTON.2015.7446988","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7446988","url":null,"abstract":"Anycast is an internet addressing protocol where multiple hosts share the same IP-address. A popular architecture for modern Content Distribution Networks (CDNs) for geo-replicated HTTP-services consists of multiple layers of proxy nodes for service and co-located DNS-servers for load-balancing on different proxies. Both the proxies and the DNS-servers use anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control. Due to the very nature of anycast, load-management actions by a co-located DNS-server also affects loads at nearby proxies in the network. This makes the problem of distributed load management highly challenging. In this paper, we propose an analytical framework to formulate and solve the load-management problem in this context. We consider two distinct algorithms. In the first half of the paper, we pose the load-management problem as a convex optimization problem. Following a dual decomposition technique, we propose a fully-distributed load-management algorithm by introducing FastControl packets. This algorithm utilizes the underlying anycast mechanism itself to enable effective coordination among the nodes, thus obviating the need for any external control channel. In the second half of the paper, we consider an alternative greedy load-management heuristic, currently in production in a major commercial CDN. We study its dynamical characteristics and analytically identify its operational and stability properties. Finally, we critically evaluate both the algorithms and explore their optimality-vs-complexity trade-off using trace-driven simulations.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133158464","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447185
A. Haghi, Neda Mohammadizadeh, A. Khandani
Delay, guaranteeing causality, is inevitable in cooperative communication systems. Traditionally, delay granularity has been limited to one symbol; however, channel delay is in fact governed by channel memory and can be shorter. For example, the delay requirement in orthogonal frequency-division multiplexing (OFDM), captured in the cyclic prefix, is typically much shorter than the OFDM symbol itself. This perspective is used to study the two-user Gaussian interference channel with full-duplex transmitters. By superimposing the signal from the other node on its own signal, each transmitter cancels the interference at its receiver. Among other results, it is shown that under a mild condition, the maximum multiplexing gain of this channel is in fact two, rather than the limit of one, previously proved under the traditional constraint of causal delay [1]. Further, the optimal power allocation among orthogonal sub-carriers, which maximizes the achievable sum-rate, is shown to be a generalization of the well-known water filling.
{"title":"Delay in cooperative communications: Higher multiplexing gain in Gaussian interference channels with full-duplex transmitters","authors":"A. Haghi, Neda Mohammadizadeh, A. Khandani","doi":"10.1109/ALLERTON.2015.7447185","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447185","url":null,"abstract":"Delay, guaranteeing causality, is inevitable in cooperative communication systems. Traditionally, delay granularity has been limited to one symbol; however, channel delay is in fact governed by channel memory and can be shorter. For example, the delay requirement in orthogonal frequency-division multiplexing (OFDM), captured in the cyclic prefix, is typically much shorter than the OFDM symbol itself. This perspective is used to study the two-user Gaussian interference channel with full-duplex transmitters. By superimposing the signal from the other node on its own signal, each transmitter cancels the interference at its receiver. Among other results, it is shown that under a mild condition, the maximum multiplexing gain of this channel is in fact two, rather than the limit of one, previously proved under the traditional constraint of causal delay [1]. Further, the optimal power allocation among orthogonal sub-carriers, which maximizes the achievable sum-rate, is shown to be a generalization of the well-known water filling.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124757097","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447095
Vitaly Abdrashitov, M. Médard
In distributed cloud storages fault tolerance is maintained by regenerating the lost coded data from the surviving clouds. Recent studies suggest using maximum distance separable (MDS) network codes in cloud storage systems to allow efficient and reliable recovery after node faults. MDS codes are designed to use a substantial number of repair nodes and rely on centralized management and a static fully connected network between the nodes. However, in highly dynamic environments, like edge caching in communication networks or peer-to-peer networks, availability of the nodes and the communication links is very volatile. In these scenarios MDS codes functionality is limited. In this paper we study a non-MDS network coded approach, which operates in a decentralized manner and requires a small number of repair nodes for node recovery. We investigate long-term behavior and durability of the modeled system in terms of the storage life time, i.e. the number of the cycles of nodes failure and recovery after which the storage no longer have enough data to decode the original source packets. We demonstrate, analytically and numerically, the life time gains over uncoded storage.
{"title":"Durable network coded distributed storage","authors":"Vitaly Abdrashitov, M. Médard","doi":"10.1109/ALLERTON.2015.7447095","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447095","url":null,"abstract":"In distributed cloud storages fault tolerance is maintained by regenerating the lost coded data from the surviving clouds. Recent studies suggest using maximum distance separable (MDS) network codes in cloud storage systems to allow efficient and reliable recovery after node faults. MDS codes are designed to use a substantial number of repair nodes and rely on centralized management and a static fully connected network between the nodes. However, in highly dynamic environments, like edge caching in communication networks or peer-to-peer networks, availability of the nodes and the communication links is very volatile. In these scenarios MDS codes functionality is limited. In this paper we study a non-MDS network coded approach, which operates in a decentralized manner and requires a small number of repair nodes for node recovery. We investigate long-term behavior and durability of the modeled system in terms of the storage life time, i.e. the number of the cycles of nodes failure and recovery after which the storage no longer have enough data to decode the original source packets. We demonstrate, analytically and numerically, the life time gains over uncoded storage.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124840725","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447110
Son Hoang Dau, Wentu Song, A. Sprintson, C. Yuen
Vandermonde and Cauchy matrices are commonly used in the constructions of maximum distance separable (MDS) codes. However, when additional design constraints are imposed on the code construction in addition to the MDS requirement, a Vandermonde or Cauchy matrix may not always suffice. We discuss some related coding problems of that nature that arise in different practical settings. We present a useful technique to tackle the constrained coding problems that includes random selection of the evaluation points of a Vandermonde or a Cauchy matrix. Our solutions require small finite fields whose sizes are polynomial in the dimensions of the generator matrices. We believe that this technique will be useful for solving a broad range of coding problems.
{"title":"Constructions of MDS codes via random Vandermonde and Cauchy matrices over small fields","authors":"Son Hoang Dau, Wentu Song, A. Sprintson, C. Yuen","doi":"10.1109/ALLERTON.2015.7447110","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447110","url":null,"abstract":"Vandermonde and Cauchy matrices are commonly used in the constructions of maximum distance separable (MDS) codes. However, when additional design constraints are imposed on the code construction in addition to the MDS requirement, a Vandermonde or Cauchy matrix may not always suffice. We discuss some related coding problems of that nature that arise in different practical settings. We present a useful technique to tackle the constrained coding problems that includes random selection of the evaluation points of a Vandermonde or a Cauchy matrix. Our solutions require small finite fields whose sizes are polynomial in the dimensions of the generator matrices. We believe that this technique will be useful for solving a broad range of coding problems.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127665624","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447121
Krishnamurthy Dvijotham
We study multivariate systems of quadratic equations of the form F (x) = s where F : ℝn → ℝn and Fi a quadratic function of x for i = 1, ..., n. These types of equations arise across a variety of applications including sensor network localization, power systems and matrix factorization. In general, solving systems of quadratic equations is a challenging task, and in its most general form is NP-hard. In this paper, we approach this problem from a different perspective: We characterize domains over which the problem can be solved efficiently. For any such domain, we develop an efficient algorithm that terminates with: a) a solution in the domain, or b) a certificate of non-existence of the solution in the domain. Further, we derive conditions on s that guarantee the existence of a solution in the domain. We show how this result can be used to construct convex inner approximations to the feasible set of a Quadratically Constrained Quadratic Program (QCQP). Finally, we illustrate the results on simple examples from these application domains.
{"title":"Systems of quadratic equations: Efficient solution algorithms and conditions for solvability","authors":"Krishnamurthy Dvijotham","doi":"10.1109/ALLERTON.2015.7447121","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447121","url":null,"abstract":"We study multivariate systems of quadratic equations of the form F (x) = s where F : ℝn → ℝn and Fi a quadratic function of x for i = 1, ..., n. These types of equations arise across a variety of applications including sensor network localization, power systems and matrix factorization. In general, solving systems of quadratic equations is a challenging task, and in its most general form is NP-hard. In this paper, we approach this problem from a different perspective: We characterize domains over which the problem can be solved efficiently. For any such domain, we develop an efficient algorithm that terminates with: a) a solution in the domain, or b) a certificate of non-existence of the solution in the domain. Further, we derive conditions on s that guarantee the existence of a solution in the domain. We show how this result can be used to construct convex inner approximations to the feasible set of a Quadratically Constrained Quadratic Program (QCQP). Finally, we illustrate the results on simple examples from these application domains.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129928505","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447000
Chung-Han Hsieh, B. Barmish
The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the logarithmic growth of wealth. While significant literature exists providing the rationale for such an optimization, this paper concentrates on the limitations of the Kelly-based theory. To this end, we fill a void in published results by providing specific examples quantifying what difficulties are encountered when Taylor-style approximations are used and when wealth drawdowns are considered. For the case of drawdown, we describe some research directions which we feel are promising for improvement of the theory.
{"title":"On Kelly betting: Some limitations","authors":"Chung-Han Hsieh, B. Barmish","doi":"10.1109/ALLERTON.2015.7447000","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447000","url":null,"abstract":"The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the logarithmic growth of wealth. While significant literature exists providing the rationale for such an optimization, this paper concentrates on the limitations of the Kelly-based theory. To this end, we fill a void in published results by providing specific examples quantifying what difficulties are encountered when Taylor-style approximations are used and when wealth drawdowns are considered. For the case of drawdown, we describe some research directions which we feel are promising for improvement of the theory.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"462 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129464914","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447175
A. Makur, Lizhong Zheng
In this paper, we delineate how the contraction coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation that forces the input KL divergence to vanish, and achieves a contraction coefficient equivalent to the squared maximal correlation using a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.
{"title":"Bounds between contraction coefficients","authors":"A. Makur, Lizhong Zheng","doi":"10.1109/ALLERTON.2015.7447175","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447175","url":null,"abstract":"In this paper, we delineate how the contraction coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation that forces the input KL divergence to vanish, and achieves a contraction coefficient equivalent to the squared maximal correlation using a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"26 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120837862","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447140
Fengming Cao, A. Ganesh, S. Armour, M. Sooriyabandara
This paper exploits the distribution and mean of received power for cellular network with stochastic network modeling to study the difference between the two cell association criteria, i.e. the strongest received power based cell association and the closest distance based cell association. Consequently we derive the analytical expression of the distribution and the mean of the nth strongest received power and the received power from the nth nearest base station and the derivations have been confirmed by simulation results. From both the simulation results and analytical results, we can see that the distributions of received power with both association criteria vary with different path loss exponents a: there is a clear gap between the two when the exponent is small and the two are almost the same with larger exponent. Meanwhile, the analysis on the mean of the received power suggests that under a certain converged condition, i.e. n > α/2, the average of the received power from the nth closest BS is actually larger than the nth strongest one.
{"title":"On the distribution and mean of received power in stochastic cellular network","authors":"Fengming Cao, A. Ganesh, S. Armour, M. Sooriyabandara","doi":"10.1109/ALLERTON.2015.7447140","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447140","url":null,"abstract":"This paper exploits the distribution and mean of received power for cellular network with stochastic network modeling to study the difference between the two cell association criteria, i.e. the strongest received power based cell association and the closest distance based cell association. Consequently we derive the analytical expression of the distribution and the mean of the nth strongest received power and the received power from the nth nearest base station and the derivations have been confirmed by simulation results. From both the simulation results and analytical results, we can see that the distributions of received power with both association criteria vary with different path loss exponents a: there is a clear gap between the two when the exponent is small and the two are almost the same with larger exponent. Meanwhile, the analysis on the mean of the received power suggests that under a certain converged condition, i.e. n > α/2, the average of the received power from the nth closest BS is actually larger than the nth strongest one.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124563934","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}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447161
M. Hanawal, Venkatesh Saligrama
We consider stochastic sequential learning problems where the learner can observe the average reward of several actions. Such a setting is interesting in many applications involving monitoring and surveillance, where the set of the actions to observe represent some (geographical) area. The importance of this setting is that in these applications, it is actually cheaper to observe average reward of a group of actions rather than the reward of a single action. We show that when the reward is smooth over a given graph representing the neighboring actions, we can maximize the cumulative reward of learning while minimizing the sensing cost. In this paper we propose CheapSpectralEliminator, an algorithm that matches the regret guarantees of the known algorithms for this setting and at the same time guarantees a linear cost again over them. We show that the algorithm achieves the lower bound of Ω(√dT) on the cumulative regret, where d denotes the effective dimension.
{"title":"Cost effective algorithms for spectral bandits","authors":"M. Hanawal, Venkatesh Saligrama","doi":"10.1109/ALLERTON.2015.7447161","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447161","url":null,"abstract":"We consider stochastic sequential learning problems where the learner can observe the average reward of several actions. Such a setting is interesting in many applications involving monitoring and surveillance, where the set of the actions to observe represent some (geographical) area. The importance of this setting is that in these applications, it is actually cheaper to observe average reward of a group of actions rather than the reward of a single action. We show that when the reward is smooth over a given graph representing the neighboring actions, we can maximize the cumulative reward of learning while minimizing the sensing cost. In this paper we propose CheapSpectralEliminator, an algorithm that matches the regret guarantees of the known algorithms for this setting and at the same time guarantees a linear cost again over them. We show that the algorithm achieves the lower bound of Ω(√dT) on the cumulative regret, where d denotes the effective dimension.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114178680","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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