1. Decentralized Network Optimization: Algorithms and Theories
Qing Ling
Department of Automation, University of Science and Technology of China (USTC)
Joint work with
Aryan Mokhtari (Penn), Alejandro Ribeiro (Penn), Wei Shi (USTC, now UIUC),
Gang Wu (USTC), Wotao Yin (UCLA), Kun Yuan (USTC, now UCLA)
Institute of System Science, Chinese Academy of Sciences (CAS)
2015/12/14 1

2. Motivation: network data processing
We are in a world of networks and in a sea of networked data
Autonomous agents
- Collect data
- Process data
- Communicate
RESERCH PROBLEM: how to efficiently accomplish in-network
information processing tasks through collaboration of agents?
OUR FOCUS: decentralized optimization, control, and decision-making

3. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future research directions 3 3

4. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future research directions 4 4

5. 100,000 users connected by FireChat, HongKong, September 2014
Decentralized network: our future?
100,000 users connected by FireChat, HongKong, September 2014
- No transmission to fusion center (bandwidth, latency, privacy, etc)
- Decentralized processing via collaboration of neighboring agents

6. Example: multi-sensor target localization6 6

7. Example: network flow optimization7 7

8. More examples Network Machine Learning Wireless sensing Temperature
Magnus Egerstedt (GaTech)
Wireless sensing
Temperature
Humidity
Other factors
Wireless actuating
Circulating fan
Wet curtain
Other actuators
Vijay Kumar (Penn)
Wireless Precise Agriculture
Robot & Drone Networks 8 8

9. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future research directions 9 9

10. Decentralized consensus optimization10 10

11. Example: multi-sensor target localization11 11

12. Example: network flow optimization12 12

13. Tradeoff in designing decentralized algorithms
How fast is the convergence?
Where do the iterates converge?
Convergence
Speed
Solution
Accuracy
Computation
Cost
Is the computation affordable? 13 13

14. Related works 14 14

15. Theories for algorithms & from theories to algorithms15 15

16. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future directions 16 16

17. References of DADMM and DGM17 17

18. Assumptions in designing and analyzing algorithms18 18

19. ADMM: alternating direction method of multipliers19 19

20. Reformulating to use ADMM20 20

21. Outline of DADMM 21 21

22. Linear convergence rate of DADMM22 22

23. Simulation settings of DADMM23 23

24. Simulation results of DADMM: linear convergence24 24

25. Simulation results of DADMM: topology versus speed25 25

26. Decentralized gradient method (DGM)26 26

27. Mixing matrix 27 27

28. Existing convergence analysis28 28

29. Reinterpreting DGM 29

30. Analyzing DGM through reinterpretation30 30

31. Linear convergence rate of DGM31 31

32. Simulation settings of DGM32 32

33. Simulation results of DGM33 33

34. Summarizing DADMM & DGM34 34

35. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future research directions 35 35

36. References of DLM, NN, and EXTRA36

37. Assumptions in designing and analyzing algorithms37 37

38. Decentralized linearized ADMM (DLM)38 38

39. From DADMM to DLM 39

40. Outline of DLM 40 40

41. Linear convergence rate of DLM41 41

42. Simulation settings of DLM42 42

43. Simulation results of DLM43 43

44. From DGM to network Newton (NN)44 44

45. Approximate Hessian inverse on decentralized network45 45

46. Outline of NN-T 46 46

47. Linear and quadratic convergence rates of NN47 47

48. Simulation settings of NN48 48

49. Simulation results of NN49 49

50. Revisiting DGM 50 50

51. EXact firsT-ordeR Algorithm (EXTRA)51 51

52. Mixing matrices 52 52

53. Explanations of EXTRA 53 53

54. Sublinear convergence of EXTRA54 54

55. Linear convergence of EXTRA55 55

56. Simulation settings of EXTRA56 56

57. Simulation of EXTRA

58. Summarizing DLM, NN & EXTRA
DADMM
Convergence
Speed
Solution
Accuracy
DLM NN
EXTRA
DGM
Computation
Cost 58 58

59. Outline Decentralized network optimization Background and applications
Problem statement and related works
With particular focus on decentralized consensus optimization
Analysis of existing algorithms
Dual domain: decentralized ADMM (DADMM)
Primal domain: decentralized gradient method (DGM)
Design and analysis of new algorithms
Dual domain: decentralized linearized ADMM (DLM)
Primal domain: network Newton (NN)
Cross primal and dual domains: exact first-order algorithm (EXTRA)
Concluding remarks and future research directions 59 59

60. Summarizing the whole work
Decentralized Optimization
Primal Domain Methods
Dual Domain Methods
Correction
Network Newton
Gradient Method
EXTRA
DADMM
Penalty
Methods
DLM
Dilemma
Decaying Stepsize
Slow Convergence
Accurate Solution
Fixed Stepsize
Fast Convergence
Inaccurate Solution
Fixed Stepsize
Fast Convergence
Accurate Solution
Linear
Convergence 60 60

61. Concluding remarks and future research directions
Thank you 61 61