Prof. dr. ir. Jan H. Kwakkel

Multi-Actor Systems department

Faculty of Technology, Policy and Management

Model-based support for Decision Making under Deep Uncertainty

Problem 1

• Imagine you are a flood risk manager. You need to decide on an investment in dikes for the coming ten years. You have been given the following information

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• Chance of a severe flood is 1 in 6
• Damage in case of a flood is 1 million
• Costs of investment in dikes is 1.3 million
• If dikes are built, chance of flood falls below 1 in 50
• Assume a 10-year planning horizon

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• Will you invest in the dikes?

Problem 2

• Imagine you are a flood risk manager. You need to decide on an investment in dikes for the coming ten years. You have been given the following information

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• According to a first group of experts, the chance of a severe flood is 1 in 6
• According to a second group of experts, the chance of a severe flood is 1 in 10
• Damage in case of a flood is 1 million
• Costs of investment in dikes is 1.3 million
• If dikes are built, chance of flood falls below 1 in 50
• Will you invest in the dikes?

So what is deep uncertainty?

• Deep uncertainty refers to the situation where the various parties to a decision do not know or cannot agree on
• The system model that relates actions to consequences
• The prior probability distributions to put on the inputs to the system model(s)
• Which consequences to consider and their relative importance
• Deep uncertainty often involves decisions made over time in dynamic interaction with the system.

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• Kenneth Arrow first used the term in the late 1990s to characterize the climate change debate
• Formal work on dealing with deep uncertainty started in the early 2000s at the RAND Corporation and TU Delft.

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• Deep uncertainty is also known as radical uncertainty, Knightian uncertainty, or uncertainty proper

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Why use models?

Argument from complexity

• supplement human reasoning
• sensitivity to initial conditions

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Argument from uncertainty

• When confronted with uncertainty, instead of making an assumption, explore the consequences of alternative assumptions systematically to identify differences that make a difference

Decision-making under deep uncertainty

• Decision aiding – the aim of decision advise is to facilitate learning about a problem and potential courses of action, not to dictate the right solution. This entails a shift from a priori to a posteriori decision analysis.

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• Adaptive planning – plans should be designed from the outset to be adapted over time in response to how the future is unfolding

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• Exploratory scenario thinking– the future is uncertain and cannot be probabilistically constrained, we need systematic what-if analysis of the future which serves as a test bed for candidate strategies

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Aiding decision making

What is the role of models in decision making?�

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Computer assisted reasoning

• Arguments from ensembles
• Hypothesis generation
• Existence proofs
• Non-existence proofs
• Reasoning from special cases
• Assessing properties of the entire ensemble

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• Identifying differences that make a difference
• Ranking uncertainties
• Partitioning uncertainty space

Adaptive planning

Adaptation pathways

�Exploratory scenario thinking

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Often, more information can be captured in an ensemble of alternative plausible models than can be captured by any individual model.

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Bankes (2002) 10.1073􏰅pnas.092081399

XLRM framework

Running a model as a function

• X : uncertainties
• Model structure uncertainties as well as exogenous forces
• A point in uncertainty space is called a scenario
• L : levers
• A point in lever space is called a policy
• Policies to be tested over the uncertainties
• M : outcomes
• Outcomes of interest

Exploratory modelling in a nutshell

Exploratory modelling in a nutshell

Exploratory modelling in a nutshell

Exploratory modelling in a nutshell: scenario discovery

Exploratory modelling in a nutshell: scenario discovery

Exploratory modelling in a nutshell: scenario discovery

Exploratory modelling in a nutshell: scenario discovery

Manual scenario discovery exercise

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Click and download as zip file

• Unzip the downloaded file
• Open manual_scenario_discovery.html

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Scenario Discovery

Subspace partitioning

• Problem: find an (orthogonal) subspace in the model input space, which has a high concentration of cases of interest

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• Rule induction problem
• Regression vs. (binary) classification

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• Rule induction algorithms
• Classification and Regression Trees (CART)
• Patient Rule Induction Algorithm (PRIM
• Various other more specialized possibilities

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PRIM

PRIM

• Lenient hill-climbing optimization algorithm

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• Each step in the optimization is stored 🡪 peeling trajectory

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• Coverage: fraction of cases of interest within the box
• Density: fraction of cases in the box which is of interest
• Interpretability: number of restricted uncertainties
• Quasi p-values: one sided binomial test, proxy for statistical significance of each restricted uncertainty in isolation
• Resampling statistic: do random subsets of the same dataset produce essentially the same box?

Scenario Discovery

Scenario discovery for designing adaptation pathways

• Scenario discovery results can be understood as an n-dimensional generalization of adaptation tipping points

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• An adaptation tipping point is the level of an exogenous driver at which adaptation is required. These can be mapped to time for different scenarios

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• Scenario discovery finds n-dimensional boxes in the uncertainty space where a given policy fails

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• Some caveats
• Not all exogenous drivers change over time
• Mapping scenario discovery results onto the time axis is an open research question

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Scenario Discovery excercise

Working with Google Colab

• Go to Google Colab
• upload scenario discovery.ipynb
• Upload
• 100 experiments.tar.gz
• 10000 experiments.tar.gz
• Go through the notebook (shift + enter)

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EMA workbench: a python library for RDM

• Code: https://github.com/quaquel/EMAworkbench
• Documentation: https://emaworkbench.readthedocs.io/en/latest/

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• pip installable
• pip install ema_workbench[recommended]

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Upload scenario discovery.ipynb

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Open file viewer

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Click upload files

Working with Google Colab

• Go to Google Colab
• upload scenario discovery.ipynb
• Upload
• 100 experiments.tar.gz
• 10000 experiments.tar.gz
• Go through the notebook (shift + enter)

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Introduction to RDM

Robust Decision Making

• Robust decision making is the process of using computer simulations to iteratively stress test candidate strategies
• Decision Framing: structure the decision problem using the XLRM framework
• Evaluate strategy across futures: explore behavior of modeled system across the uncertainties for all outcomes of interest, for one or more candidate strategies
• Vulnerability analysis: scenario discovery
• Tradeoff analysis: if vulnerabilities are limited analyse robustness tradeoffs amongst objectives
• New futures and strategies: based on interpretation of 3 and 4, refine XLRM setup

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Experimental designs

How does a Latin Hypercube work?

How does a Latin Hypercube work?

How does a Latin Hypercube work?

How does a Latin Hypercube work?

Choosing a distribution

RDM exercise

Shallow lake problem

• How much anthropogenic pollution to release into the lake, while avoiding that the lake tips into an irreversible eutrophic state?

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• Adaptive version: what is a state based control rule that tells how much can be released?

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Hadka et al (2015). 10.1016/j.envsoft.2015.07.014.

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XLRM structuring of shallow lake problem

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Levers�parameters characterizing the control rule

Uncertainties

b: decay rate

q: recycling exponent

mean: mean of natural

inflows

stdev: stdev of natural

inflows

delta: discount rate

Outcomes

Maximum pollution level

Utility

Inertia

reliability

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Relations

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Working with Google Colab

• Go to Google Colab
• upload RDM.ipynb
• Upload
• lake_model_dps.py
• 4policies.tar.gz
• (optional) lake_1000.tar.gz
• Go through the notebook (shift + enter)

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Workflow

• Connect model to the workbench
• X: uncertainties
• L: levers which parameterize the control rule
• R: model of the shallow lake
• M: outcomes of interest

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• Develop basic system understanding by exploring the behavior of the system for one or more basic policies (i.e. control rules)
• Optimize policies for a reference scenario
• Re-evaluate (selected) policies over a much larger ensemble of scenarios
• Analyze robustness and vulnerabilities (i.e., scenario discovery)
• Iterate if necessary

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Robustness metrics

McPhail, C., et al (2018). "Robustness metrics: How are they calculated, when should they be used and why

do they give different results?" Earth's Future. 10.1002/2017EF000649 

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Robustness metrics

Figure adapted from Trindade et al. (2019) https://doi.org/10.1016/j.advwatres.2019.103442

How to summarize the distribution over scenarios in (preferably) one number?

Robustness per kpi, or one robustness number per policy?

3 families of robustness metrics

Satisficing robustness

• Absolute: the observed performance of a policy in each scenario compared to an absolute performance threshold

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Regret

• Relative: the difference between the observed performance of a policy in each scenario and the performance of some reference policy for each scenario

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Descriptive statistics

• Characterizing the distribution of performance of a policy over the set of scenarios using one or more moments of the distribution

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Robustness calculation

McPhail, C., et al (2018). "Robustness metrics: How are they calculated, when should they be used and why

do they give different results?" Earth's Future. 10.1002/2017EF000649 

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MORDM exercise continued

Example: Competitive position of the Port of Rotterdam

The world container model

Tavasszy, L. A., Minderhoud, M., Perrin, J.-F., & Notteboom, T. (2011). A strategic network choice model for global container flows: specification, estimation

and application. Journal of Transport Geography, 19, 1163–1172

Major uncertainties that might impact the port of Rotterdam

Identification of vulnerabilities�under what conditions does Rotterdam lose throughput?

Identification of vulnerabilities�under what conditions does Rotterdam lose throughput?

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• Increase of costs on all hinterland connections for ports in the Hamburg – le Havre range
• More than 1 additional day required for shipping from Rotterdam
• No substantial decrease in hinterland transport costs for Rotterdam

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• Together, these 3 factors explain 75% of the cases where Rotterdam loses throughput, with 71% accuracy

Worst case discovery

• Is there a perfect storm scenario?
• No, small changes in the uncertain factors do not lead to large change in throughput or transshipment

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Worst case discovery

• Is there a perfect storm scenario?
• No, small changes in the uncertain factors do not lead to large change in throughput or transshipment

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• Under what conditions do the Mediterranean ports become competitive?

Substantial increase in EU hinterland costs, substantial reduction in port handling costs and hinterland transport costs and time for Mediterranean ports, and the opening of the Northern passage

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• Limitation: shipping line network structure is kept static

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Income inequality in the Vietnam Mekong Delta

Bramka Arga Jafino

Maaike van Aalst

Integrated assessment model

Uncertainties

river discharge

upstream dam�development

farming preferences

drought impacts

Adaptation policies

more high dikes

less high dikes

fertilizer subsidies

seed upgrade

How can income patterns change?

43K scenarios

7 archetypical

income patterns

Classification tree mapping uncertainties and policies�to types of income patterns

How can income patterns change?

43K scenarios

7 archetypical

income patterns

Classification tree mapping uncertainties and policies�to types of income patterns

How sensitive are rankings to normative assumptions?

Closing remarks

Kwakkel & Haasnoot (2018) Supporting decision making under deep uncertainty: a synthesis of approaches and techniques