CHAPTER 7. SUMMARY, CONCLUSIONS AND FUTURE WORK
7.3 Future Research Directions
Beyond the existing research work we have presented in this dissertation, this section presents the broad research areas that can emerge as extension of the work presented here.
1. Time-varying networks: In this dissertation, a generic assumption for the whole research is that the agent communication graph is static, i.e., time-invariant networks. While time- invariant networks simplifies the analysis in this context, the time-varying networks are more
general for most real-world problems. Therefore, one of future research directions should be focused on the time-varying networks in which the interaction among different agents is changing with time. In this case, the algorithmic frameworks and analysis need to be extended.
2. Nonsmooth objective functions in distributed nonconvex optimization: Convex op- timization has been studied well in literature and more attention should be paid to nonconvex optimization. By far most of existing algorithms can only be used to solve problems with smooth objective functions which is a quite strong assumption in complex problems. Relax- ing such an assumption should be the next research step. In deep learning, the relaxation is quite critical as some models involves nonsmooth function which may lead to the nonsmooth objective functions. More generalized algorithms should be proposed and developed.
3. Large-scale real-world problems: This research and many other existing works present some empirical results to validate the proposed algorithms. However, the benchmark datasets are always used and the scale is not large enough. The performance by using benchmark datasets can be high quality and simple, such as, MNIST, using which typically can produce good quality results. However, in a real-world problem, the quality of dataset may not be as good as expected such that the proposed algorithm can fail. Also, how to scale up the algorithms to more agents is another problem since we mostly use several agents and show the performance for validation. Although we claim that the proposed algorithms can be used for a large number of agents, the implementation may be quite difficult in the realistic situation. Therefore, how to apply the proposed algorithms to large-scale real-world problems should be one of the next research steps.
BIBLIOGRAPHY
(2008). Report on environment, final report epa/600/r-07/045f. Environmental Protection Agency. (2010). Energy resource station (ers) technical description. Iowa Energy Center Technical Report. Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., Devin, M., et al. (2016). Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467.
Agarwal, Y., Balaji, B., Gupta, R., Lyles, J., Wei, M., and Weng, T. (2010). Occupancy-driven energy management for smart building automation. In Proceedings of the 2nd ACM workshop
on embedded sensing systems for energy-efficiency in building, pages 1–6. ACM.
Akintayo, A., Lore, K. G., Sarkar, S., and Sarkar, S. (2016). Prognostics of combustion instabilities from hi-speed flame video using a deep convolutional selective autoencoder. International Journal
of Prognostics and Health Management, 7(023):1–14.
Altman, E., Avrachenkov, K., Miller, G., and Prabhu, B. (2007). Discrete power control: Coopera- tive and non-cooperative optimization. InINFOCOM 2007. 26th IEEE International Conference
on Computer Communications. IEEE, pages 37–45.
Arora, S. and Nabieva, E. (2002). Markov chains and random walks.
Atzeni, I., Ordonez, L., Scutari, G., Palomar, D., and Fonollosa, J. (2013). Noncooperative and cooperative optimization of distributed energy generation and storage in the demand-side of the smart grid. Signal Processing, IEEE Transactions on, 61(10):2454–2472.
Azar, E. and Menassa, C. C. (January, 2014). Framework to evaluate energy-saving potential from occupancy interventions in typical commercial buildins in the united states. Journal of
Computing in Civil Engineering, 28(1):63–78.
Baldi, P., Sadowski, P., and Whiteson, D. (2014). Searching for exotic particles in high-energy physics with deep learning. arXiv preprint arXiv:1402.4735.
Bengea, S. C., Li, P., Sarkar, S., Vichik, S., Adetola, V., Kang, K., Lovett, T., Leonardi, F., and Kelman, A. D. (2015). Fault-tolerant optimal control of a building hvac system. Science and
Technology for the Built Environment, 21(6):734–751.
Berahas, A. S., Bollapragada, R., Keskar, N. S., and Wei, E. (2017). Balancing communication and computation in distributed optimization. arXiv preprint arXiv:1709.02999.
Bian, Y., Mirzasoleiman, B., Buhmann, J. M., and Krause, A. (2016). Guaranteed non-convex opti- mization: Submodular maximization over continuous domains. arXiv preprint arXiv:1606.05615. Blot, M., Picard, D., Cord, M., and Thome, N. (2016). Gossip training for deep learning. arXiv
Borkar, V. and Varaiya, P. (1982). Asymptotic agreement in distributed estimation. Automatic
Control, IEEE Transactions on, 27:650–655.
Borodin, A., Filmus, Y., and Oren, J. (2010). Threshold models for competitive influence in social networks. In WINE, volume 6484, pages 539–550. Springer.
Bottou, L. (2010). Large-scale machine learning with stochastic gradient descent. In Proceedings
of COMPSTAT’2010, pages 177–186. Springer.
Bottou, L., Curtis, F. E., and Nocedal, J. (2016). Optimization methods for large-scale machine learning. arXiv preprint arXiv:1606.04838.
Boyd, S., Ghosh, A., Prabhakar, B., and Shah, D. (2006). Randomized gossip algorithms.
IEEE/ACM Trans. Netw., 14:2508–2530.
Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and TrendsR
in Machine Learning, 3(1):1–122.
Boyd, S. and Vandenberghe, L. (2004). Convex optimization. Cambridge university press. Boyd, S., Xiao, L., and Mutapcic, A. (2003). Subgradient methods.
Cai, J., Kim, D., Putta, V. K., Braun, J. E., and Hu, J. (2015). Multi-agent control for central- ized air conditioning systems serving multi-zone buildings. in Proceedings of American Control
Conference, Chicago, IL.
Camponogara, E., Jia, D., Krogh, B. H., and Talukdar, S. (2002). Distributed model predictive control. IEEE Control Systems, 22(1):44–52.
Cavalcante, R. L. G. and Stanczak, S. (2013). A distributed subgradient method for dynamic convex optimization problems under noisy information exchange. IEEE journal of selected topics
in signal processing, 7(2):243–256.
Chakraborty, P., Adu-Gyamfi, Y. O., Poddar, S., Ahsani, V., Sharma, A., and Sarkar, S. (2018). Traffic congestion detection from camera images using deep convolution neural networks. Tech- nical report.
Chattopadhyay, P., Jha, D. K., Sarkar, S., and Ray, A. (2015). Path planning in GPS-denied environments: A collective intelligence approach. InProceedings of American Control Conference,
Chicago, IL, USA.
Chen, J., Taylor, J. E., and Wei, H.-H. (2014). Modeling building occupant network energy con- sumption decision-making: The interplay between network structure and conservation. Energy
and Buildings, 47:515–524.
Chilimbi, T. M., Suzue, Y., Apacible, J., and Kalyanaraman, K. (2014). Project adam: Building an efficient and scalable deep learning training system. In OSDI, volume 14, pages 571–582. Chinde, V., Heylmun, J. C., Kohl, A., Jiang, Z., Sarkar, S., and Kelkar, A. Comparative evaluation
of control-oriented zone temperature prediction modeling strategies in buildings. in Proceedings
Chinde, V., Kohl, A., Jiang, Z., Kelkar, A., and Sarkar, S. (2016). A volttron based implementation of supervisory control using generalized gossip for building energy systems. Proceedings in the
4th International High Performance Buildings Conference, West Lafayette, IN.
Chinde, V., Kosaraju, K., Kelkar, A., Pasumarthy, R., Sarkar, S., and Singh, N. (2017). A passivity- based power-shaping control of building hvac systems. Journal of Dynamic Systems, Measure-
ment, and Control, 139(11):111007.
Choi, H.-L. and How, J. P. (2010). Continuous trajectory planning of mobile sensors for informative forecasting. Automatica, 46(8):1266–1275.
Chollet, F. (2015). Keras. https://github.com/fchollet/keras.
Cochocki, A. and Unbehauen, R. (1993). Neural networks for optimization and signal processing. John Wiley & Sons, Inc.
Collobert, R. and Weston, J. (2008). A unified architecture for natural language processing: Deep neural networks with multitask learning. In Proceedings of the 25th international conference on
Machine learning, pages 160–167. ACM.
De, S. and Goldstein, T. (2016). Efficient distributed sgd with variance reduction. InData Mining
(ICDM), 2016 IEEE 16th International Conference on, pages 111–120. IEEE.
Dean, J., Corrado, G., Monga, R., Chen, K., Devin, M., Mao, M., Senior, A., Tucker, P., Yang, K., Le, Q. V., et al. (2012). Large scale distributed deep networks. InAdvances in neural information
processing systems, pages 1223–1231.
Dimakis, A. G., Kar, S., Moura, J. M., Rabbat, M. G., and Scaglione, A. (2010). Gossip algorithms for distributed signal processing. Proceedings of the IEEE, 98(11):1847–1864.
Evins, R. (2015). Multi-level optimization of building desing, energy system sizing and operation.
Energy, pages 1–15.
Ferrara, M., Fabrizio, E., Virgone, J., and Filippi, M. (2014). A simulation-based optimization method for cost-optimal analysis of nearly zero energy buildings. Energy and Buildings, 84:442– 457.
Franceschelli, M., Giua, A., and Seatzu, C. (2010). A gossip-based algorithm for discrete consensus over heterogeneous networks. Automatic Control, IEEE Transactions on, 55(5):1244–1249. Gruber, J. K. and Prodancovic, M. (2014). Two-stage optimization for building energy manage-
ment. Energy Procedia, 62:346–354.
Guo, J., Hug, G., and Tonguz, O. K. (2016). A case for non-convex distributed optimization in large-scale power systems. IEEE Transactions on Power Systems.
Gupta, S., Zhang, W., and Milthorpe, J. (2015a). Model accuracy and runtime tradeoff in dis- tributed deep learning. arXiv preprint arXiv:1509.04210.
Gupta, S. K., Kar, K., Mishra, S., and Wen, J. T. (2015b). Collaborative energy and thermal com- fort management through distributed consensus algorithms. IEEE Transactions on Automation
Haack, J., Akyol, B., Carpenter, B., Tews, C., and Foglesong, L. (2013a). Volttron: an agent platform for the smart grid. InProceedings of the 2013 international conference on Autonomous
agents and multi-agent systems, pages 1367–1368. International Foundation for Autonomous
Agents and Multiagent Systems.
Haack, J., Akyol, B., Tenney, N., Carpenter, B., Pratt, R., and Carroll, T. (2013b). Volttron: An agent platform for integrating electric vehicles and smart grid. In Proceedings of 2013 Interna-
tional Conference on Automonous Agents and Multi-agent System, pages 1367 – 1368.
Hajinezhad, D., Hong, M., and Garcia, A. Zenith: A zeroth-order distributed algorithm for multi- agent nonconvex optimization.
Hasan, O. A., Defer, D., and Shahrour, I. (2014). A simplified building thermal model for the optimization of energy cosnumption: Use of a random number generator. Energy and Buildings, 82:322–329.
Heaton, J., Polson, N., and Witte, J. H. (2017). Deep learning for finance: deep portfolios. Applied
Stochastic Models in Business and Industry, 33(1):3–12.
Hestenes, M. R. (1975). Optimization theory: the finite dimensional case. New York.
Heyman, D. P. and Sobel, M. J. (1982). Stochastic models in operations research: stochastic
optimization, volume 2. Courier Corporation.
Jadbabaie, A., Lin, J., and Morse, A. S. (2006). Coordination of groups of mobile autonomous agents using nearest neighbor. Automatic Control, IEEE Transactions on, 48.
Jha, D. K., Chattopadhyay, P., Sarkar, S., and Ray, A. (2016). Path planning in gps-denied environments with collective intelligence of distributed sensor networks. International Journal
of Control, 89.
Jiang, Z., Balu, A., Hegde, C., and Sarkar, S. (2017a). Collaborative deep learning in fixed topology networks. Neural Information Processing Systems (NIPS).
Jiang, Z., Chinde, V., Kohl, A., Sarkar, S., and Kelkar, A. (2016). Scalable supervisory control of building energy systems using generalized gossip. InAmerican Control Conference (ACC), 2016, pages 581–586. IEEE.
Jiang, Z., Mukherjee, K., and Sarkar, S. (2017b). Generalised gossip-based subgradient method for distributed optimisation. International Journal of Control, pages 1–17.
Jiang, Z., Sarkar, S., and Mukherjee, K. (2015a). On distributed optimization using generalized gossip. InDecision and Control (CDC), 2015 IEEE 54th Annual Conference on, pages 2667–2672. IEEE.
Jiang, Z., Sarkar, S., and Mukherjee, K. (2015b). On distributed optimization using generalized gossip. in Proceedings of 54the IEEE Conference on Decision and Control, Osaka, Japan. Jin, P. H., Yuan, Q., Iandola, F., and Keutzer, K. (2016). How to scale distributed deep learning?
Johansson, B., Keviczky, T., Johansson, M., and Johansson, K. H. (2008). Subgradient methods and consensus algorithms for solving convex optimization problems. in Proceedings of the 47th
IEEE Conference on Decision and Control, Caucun, Mexico, pages 4185–4190.
Kar, S. and Moura, J. M. F. (2009). Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. Signal Processing, IEEE Transactions on, 57(1):355–369.
Khuller, S., Kim, Y.-A., and Wan, Y.-C. (2003). On generalized gossiping and broadcasting. In Di Battista, G. and Zwick, U., editors, Algorithms - ESA 2003, volume 2832 ofLecture Notes in
Computer Science, pages 373–384. Springer Berlin Heidelberg.
Kiwiel, K. C. (2004). Convergence of approximate and incremental subgradient methods for convex optimization. SIAM Journal on Optimization, 14:807–840.
Kuhn, M. and Johnson, K. (2013). Applied predictive modeling, volume 810. Springer.
Lan, G., Lee, S., and Zhou, Y. (2017). Communication-efficient algorithms for decentralized and stochastic optimization. arXiv preprint arXiv:1701.03961.
LeCun, Y., Bengio, Y., and Hinton, G. (2015). Deep learning. Nature, 521(7553):436–444.
Lian, X., Zhang, C., Zhang, H., Hsieh, C.-J., Zhang, W., and Liu, J. (2017). Can decentralized algorithms outperform centralized algorithms? a case study for decentralized parallel stochastic gradient descent. In Advances in Neural Information Processing Systems, pages 5336–5346. Liang, W., Quinte, R., Jia, X., and Sun, J.-Q. (2015). Mpc control for improving energy efficiency
of a building air handler for multi-zone vavs. Building and Environment, 92:256–268.
Liu, C., Gong, Y., Laflamme, S., Phares, B., and Sarkar, S. (2017). Bridge damage detection using spatiotemporal patterns extracted from dense sensor network. Measurement Science and
Technology, 28(1):014011.
Liu, P. and Fu, Y. (2013). Optimal operation of energy-efficiency building: A robust optimization approach. in Proceedings of Power and Energy Society General Meeting, 2013 IEEE, Vancouver, BC, pages 1–5.
Long, Q., Wu, C., and Wang, X. (2015). A system of nonsmooth equations solver based upon subgradient method. Applied Mathematics and Computation, pages 284–299.
Lore, K. G., Stoecklein, D., Davies, M., Ganapathysubramanian, B., and Sarkar, S. (2018). A deep learning framework for causal shape transformation. Neural Networks, 98:305–317.
Lu, J., Tang, C. Y., Regier, P. R., and Bow, T. D. (2010). A gossip algorithm for convex con- sensus optimization over networks. in Proceedings of American Control Conference, Marriott
Waterfront, Baltimore, MD, pages 301–308.
Lutes, R. G., Haack, J., Katipamula, S., Monson, K., Akyol, B., Carpenter, B., and Tenney, N. (2014). Volttron: User guide.
Ma, X., Yu, H., Wang, Y., and Wang, Y. (2015). Large-scale transportation network congestion evolution prediction using deep learning theory. PloS one, 10(3):e0119044.
Ma, Y., Anderson, G., and Borrelli, F. (2011). A distributed predictive control approach to building temperature regulation. in Proceedings of 2011 American Control Conference, San Francisco,
California.
Magnier, L. and Haghighat, F. (2010). Multiobjective optimization of building design using trnsys simulations, genetic algorithm, and artificial neural network. Building and Environment, 45:739– 746.
Matei, I., Somarakis, C., and Baras, J. S. (2014). A generalized gossip algorithm on convex metric spaces. Automatic Control, IEEE Transactions on, PP.
McMahan, H. B., Moore, E., Ramage, D., Hampson, S., et al. (2016). Communication-efficient learning of deep networks from decentralized data. arXiv preprint arXiv:1602.05629.
Menassa, C. C., Kamat, V. R., Lee, SangHyun, A. E., Feng, C., and Anderson, K. (January, 2014). Conceptual framework to optimize building energy consumption by coupling distributed energy simulation and occupancy models. Journal of Computing in Civil Engineering, 28:50–62. Mukherjee, K., Ray, A., Wettergren, T., Gupta, S., and Phoha, S. (2011). Real-time adaptation of
decision thresholds in sensor networks for detection of moving targets. Automatica, 47(1):185 – 191.
Nedi, A. and Olshevsky, A. (2016). Stochastic gradient-push for strongly convex functions on time-varying directed graphs. IEEE Transactions on Automatic Control 61.12, pages 3936–3947. Nedic, A. and Bertsekas, D. (2001a). Convergence rate of incremental subgradient algorithms.
Stochastic Optimization: Algorithms and Applications, pages 263–304.
Nedic, A. and Bertsekas, D. (2008). The effect of deterministic noise in subgradient methods.Math.
Program. Ser. A.
Nedic, A. and Bertsekas, D. P. (2001b). Incremental subgradient methods for nondifferentiable optimization. SIAM Journal on Optimization, 12(1):109–138.
Nedic, A. and Lee, S. (2014). On stochastic subgradient mirror-descent algorithm with weighted averaging. SIAM Journal on Optimization, 24(1):84–107.
Nedic, A. and Olshevsky, A. (2015). Distributed optimization over time-varying directed graphs.
IEEE Transactions on Automatic Control, 60:601–615.
Nedi´c, A. and Olshevsky, A. (2015). Distributed optimization over time-varying directed graphs.
IEEE Transactions on Automatic Control, 60(3):601–615.
Nedic, A. and Ozdaglar, A. (2008). Subgradient methods in network resource allocation: rate anal- ysis. in Proceedins of 42nd Annual Conference on Information Sciences and Systems, Princeton,
NJ.
Nedic, A. and Ozdaglar, A. (2009). Distributed subgradient methods for multi-agent optimization.
Automatic Control, IEEE Transactions on, 54:48–61.
Nesterov, Y. (2013). Introductory lectures on convex optimization: A basic course, volume 87. Springer Science & Business Media.
Nitanda, A. (2014). Stochastic proximal gradient descent with acceleration techniques. InAdvances
in Neural Information Processing Systems, pages 1574–1582.
Patterson, S., Bamieh, B., and El Abbadi, A. (2010). Convergence rates of distributed average consensus with stochastic link failures. Automatic Control, IEEE Transactions on, 55(4):880– 892.
Polyak, B. T. (1964). Some methods of speeding up the convergence of iteration methods. USSR
Computational Mathematics and Mathematical Physics, 4(5):1–17.
Qu, G. and Li, N. (2017). Accelerated distributed nesterov gradient descent. arXiv preprint
arXiv:1705.07176.
Raffard, R. L., Tomlin, C. J., and Boyd, S. P. (2004). Distributed optimization for cooperative agents: Application to formation flight. In Decision and Control, 2004. CDC. 43rd IEEE Con-
ference on, volume 3, pages 2453–2459. IEEE.
Ram, S., Nedic, A., and Veeravalli, V. (2012). A new class of distributed optimization algorithms: application to regression of distributed data. Optimization Methods and Software, 27(1):71 88. Ram, S. S., Nedic, A., and Veeravalli, V. V. (2009). Asynchronous gossip algorithms for stochastic
optimization. in Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th
Chinese Control Conference, Shanghai, China.
Ram, S. S., Nedich, A., and Veeravalli, V. V. (2008). Distributed stochastic subgradient projection algorithms for convex optimization. arXiv:0811.2595v1[math.OC].
Ramallo-Conzalez, A. and Coley, D. A. (2014). Using self-adaptive optimization methods to perform sequential optimization for low-energy building design. Energy and Buildings, 81:18–29.
Rardin, R. L. and Rardin, R. L. (1998). Optimization in operations research, volume 166. Prentice Hall Upper Saddle River, NJ.
Razmara, M., Maasoumy, M., Shahbakhti, M., and Robinett III, R. (2015). Optimal exergy control of building hvac system. Applied Energy, 156:555–565.
Ronami, Z., Draoui, A., and Allard, F. (2015). Metamodeling the heating and cooling energy needs and simultabeous building envelope optimization for low energy building design in morocco.
Energy and Buildings.
Saber, R. O., Fax, J. A., and Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95:215–233.
Salehi Tahbaz, A. and Jadbabaie, A. (2010). Consensus over ergodic stationary graph processes.
Automatic Control, IEEE Transactions on, 55:225–230.
Sarkar, S. and Mukherjee, K. (2014). Event-triggered decision propagation in proximity networks.
Frontiers in Robotics and AI, 1:15.
Sarkar, S., Mukherjee, K., and Ray, A. (2013). Distributed decision propagation in mobile-agent proximity networks. International Journal of Control, 86(6):1118–1130.
Sarkar, S., Mukherjee, K., Srivastav, A., and Ray, A. (2010). Distributed decision propagation in mobile agent networks. In Proceedings of Conference on Decision and Control, Atlanta, GA. Scaman, K., Bach, F., Bubeck, S., Lee, Y. T., and Massouli´e, L. (2017). Optimal algo-
rithms for smooth and strongly convex distributed optimization in networks. arXiv preprint
arXiv:1702.08704.
Scherer, H., Pasamontes, M., Guzman, J., and Alvarez, J. (2014). Efficient building energy man- agement using distributed model predictive control. Journal of Process Control, 24:740–749. Shah, D. (2008). Gossip algorithms. Foundations and Trends in Networking, 3:1–125.
Song, S., Chaudhuri, K., and Sarwate, A. (2015). Learning from data with heterogeneous noise using sgd. pages 894–902.
Spielman, D. A. (2009). Spectral graph theory-the laplacian. Lecture 2.
Sra, S., Nowozin, S., and Wright, S. J. (2012). Optimization for machine learning. Mit Press. Srivastava, K. and Nedic, A. (2011). Distributed asynchronous constrained stochastic optimization.