ABM vs MARL
ABMs:
- Many agents
- Simple behaviour
MARL:
- Few agents
- Complicated behaviour ( lots of learning )
ABM vs MAS
ABMs:
- Goal is to study emergence
MAS:
- Engineering goal (coordination, cooperation, etc.)
Examples of ABMs
SIR on a graph
Parameters
- Infection probability
- Recovery probability
Examples of ABMs
Flocking model
Parameters
- Speed
- Cohere factor
- Separation
- Separate factor
- Match factor
- Visual distance
Calibration of ABMs
Typically hard because
- No access to the likelihood.
- Simulator is slow to run.
- Large parameter space.
Simulated minimum distance (SMD)
\hat\theta = \argmin_{\theta \in \Theta} f(\mathbb y, \theta)
observed data
ABM parameters
Calibration of ABMs,
the standard way
Limitations: Not a Bayesian approach, so no proper uncertainty quantification
Bayesian methods for ABM calibration
1. Approximate Bayesian Computation (ABC)
Typically x and y are summary statistics
Drawbacks:
- Choice of summary statistics
- Lots of simulations
Bayesian methods for ABM calibration
Advantages: black-box, simulation efficient, amortization
2. Neural methods
Idea: employ NN to estimate the posterior density
p(\theta | y)
Bayesian methods for ABM calibration
3. Gradient-assisted methods
(Generalized) Variational Inference
\nabla_\phi \;\mathbb E_{p(\theta | \phi)} \;[\, f(\theta)\,]
Need the gradient:
Score function estimator
Pathwise estimator
Requires differentiable simulator
Advantages: Efficiency, scaling
Differentiable agent-based models
(current line of work)
Possible to differentiate through discrete randomness and control flow
Compartmental vs Agent SIR equivalence
\frac{\mathrm d S}{\mathrm d t} = - \beta I S
\frac{\mathrm d I}{\mathrm d t} = \beta I S - \gamma I
\frac{\mathrm d R}{\mathrm d t} = \gamma I
No clear equivalence between
\beta
More infected -> More infections
Prob (infection) =
independent of number of infected neighbours
\beta
warwick-slides
By arnauqb
