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Dynamic Resource Allocation in Conservation Planning

1California Institute of Technology Center for the Mathematics of Information

Daniel Golovin Andreas Krause

Beth Gardner Sarah Converse Steve Morey

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Ecological Reserve Design

How should we select land for conservationto protect rare & endangered species?

Case Study: Planned Reserve in Washington State

Mazama pocket gopherstreaked horned lark Taylor’s checkerspot

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Land parcel details About 5,300 parcelssoil types, vegetation, slopeconservation cost

Problem Ingredients

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Land parcel details Geography: Roads, Rivers, etc

Problem Ingredients

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Land parcel details Geography: Roads, Rivers, etc Model of Species’ Population

DynamicsReproduction, Colonization, Predation,

Disease, Famine, Harsh Weather, …

Problem Ingredients

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Time t+1

Population Dynamics

EnvironmentalConditions (Markovian)

Our Choices

Protected Parcels

Time t

Modeled using a Dynamic Bayesian

Network

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Time t+1

Population Dynamics

EnvironmentalConditions (Markovian)

Our Choices

Protected Parcels

Time t

Modeled using a Dynamic Bayesian

Network

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Model Paramters From the ecology literature, or Elicited from panels of domain experts

An

nu

al

Patc

h S

urv

ival

Pro

bab

ilit

y

Patch Size (Acres)

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From Parcels to Patches

So we group parcels into larger patches.

Patch 1 Patch 2

Most parcels are too small to sustain a gopher family

We assume no colonization between patches,and model only colonization within patches.We optimize over (sets of) patches.

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The Objective Function

In practice, use sample average approximation

Selected patches R

Pr[alive after 50yrs]

0.8

0.7

0.5

f(R)= 2.0 (Expected # alive)

Choose R to maximize species persistence

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“Static” Conservation Planning

Select a reserve of maximum utility, subject to budget constraint

NP-hard

But f is submodular We can find a near-optimal solution

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Structure in Reserve Design

Diminishing returns: helps more in case A

than in case B

Utility function f is submodular:

A B

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Theorem [Sviridenko ‘04]: We can efficiently obtain reserve R such that

Solving the “Static” Conservation Planning Problem

More efficient algorithm with slightly weaker guarantees [Leskovec et al. ‘07]

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Selected patches are very diverse

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Results: “Static” Planning

• Can get large gain through optimization

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Time t+1

Build up reserve over time At each time step t, the budget Bt

and the set Vt of available parcels may change

Need to dynamically allocate budget tomaximize value of final reserve

Dynamic Conservation Planning

Time t

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Opportunistic Allocation forDynamic Conservation

In each time step: Available parcels and budget appear Opportunistically choose near-optimal allocation

Theorem: We get at least 38.7% of the value of the best clairvoyant algorithm*

* Even under adversarial selection of available parcels & budgets.

Time t=1Time t=2

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• Large gain from optimization & dynamic selection

Results: Dynamic Planning

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Dynamic Planning w/Failures Parcel selection may fail

Purchase recommendations unsuccessfulPatches may turn out to be uninhabitable

Can adaptively replan, based on observations

Opportunistic allocation still near-optimalProof uses adaptive submodularity

[Golovin & Krause ‘10]

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Dynamic Planning w/Failures

Failures increase the benefit of adaptivity

50% failure rate

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Related Work

Existing softwareMarxan [Ball, Possingham & Watts ‘09]Zonation [Moilanen and Kujala ‘08]General purpose softwareNo population dynamics modeling, no

guarantees

Sheldon et al. ‘10Models non-submodular population

dynamicsOnly considers static problemRelies on mixed integer programming

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Conclusions Reserve design: prototypical

optimization problem in CompSustAI

Large scale, partial observability, uncertainty,

long-term planning, …

Exploit structure near-optimal solutions

General competitiveness result about opportunistic allocation with submodularity