Learning in Complex Networks

1
Learning in Complex Networks

• Christina Fang
• New York University
• Jeho Lee
• Korea Advanced Institute of Science and
  Technology
• Melissa A. Schilling
• New York University

2
Exploration versus Exploitation in Learning

• One key way that individuals learn is through
  sharing ideas with each other
• Individuals that rapidly identify and adopt
  higher performing ideas from others learn
  efficiently
• However, too rapid diffusion of higher performing
  beliefs through a population eliminates variety ?
  lower organizational performance in long run
  (March, 1991).

3
Learning Rates and Interpersonal Structure

• Learning Rates (March, 1991)
• Fast learning results in convergence on common
  set of ideas
• Slow learning permits more exploration and
  higher long-term performance
• Interpersonal Structure
• Interpersonal structure also influences speed of
  idea diffusion ? speed of convergence
• Some amount of isolation may be beneficial

4
Assumptions and Research Questions

• Key Assumption of Our Work
• We extend Marchs model by assuming that
  individuals learn from other individuals.
• Questions
• How does organizational structure influence
  organizational learning?
• Is there any way to improve the balance between
  learning speed and performance?

5
Interpersonal Network Structure

• Begin with a sparse clustered network, and
  systematically vary rewiring rate ?

6
Simulation Model

• Individuals initially join organization with
  randomly generated m-dimensional belief sets
• Individuals learn probabilistically from others
  to which they are directly linked
• Payoff function with tunable parameter s (an
  increase in s makes the search problem more
  interdependent and difficult)

?(x)
where dj 1 if jth belief for an individual
corresponds with reality on that dimension, dj
0 otherwise.
7
Simulation Parameters

• Basic Model
• Individuals (n) 280
• Initial number of nearest neighbors (k) 10
• Dimensions (m) 100
• Learning rate (p) 0.3
• Sensitivity analyses run with varying levels of
  s, n, k and p.

8
Learning Performance Equilibrium Outcomes

• Organizational performance highest when subgroups
  are semi-isolated with a modest fraction of
  cross-group links.
• Is lower when subgroups are completely or
  nearly isolated.
• Is lower when subgroups do not exist.
• Fully connected
• Too many cross-group links

9
Graph of Results
Semi-isolated
No Sub-group Identity
Nearly-isolated
10
Diversity of Belief Sets

• Diversity is lost very quickly in fully connected
  networks or networks with many cross-group links.
• Diversity is lost very slowly in nearly isolated
  networks.
• Diversity is lost at a moderate pace in the
  semi-isolated subgroup structure.

11
Dissimilarity of Belief Sets over Time
Nearly-isolated
No Sub-group Identity
Semi-isolated
12
Dissimilarity of Belief Sets over Time (without
Beta 0)
Semi-isolated
No Sub-group Identity
13
Key Findings

• Localized subpopulations (subgroup structure)
  preserve heterogeneous knowledge, and foster
  requisite variety for exploration (akin to
  genetic drift Wright, 1932)
• However, need a modest amount of cross-group
  links to reap the value of this heterogeneity
• Sensitivity analyses suggest a tradeoff
  (compensating effect) between learning rates and
  cross-group links at low levels of either
  parameter.

14
Implications, Limitations, and Future Directions

• Provides support for arguments that RD groups
  should be moderately isolated from others,
  particularly for breakthrough innovations (Bower
  Christensen, 1995)
• Simulations are highly stylized models of reality
  will attempt to replicate findings in
  experimental setting, then field setting.
• Majority rule of simulation is crucial to
  outcomes future research should explore effect
  of other types of decision rules.