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