dynamic resource allocation in conservation planning
DESCRIPTION
Dynamic Resource Allocation in Conservation Planning. Daniel Golovin. Andreas Krause. Beth Gardner Sarah Converse Steve Morey. California Institute of Technology Center for the Mathematics of Information. 1. Ecological Reserve Design. How should we select land for conservation - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/1.jpg)
1
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
![Page 2: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/2.jpg)
2
Ecological Reserve DesignHow should we select land for conservation
to protect rare & endangered species?
Case Study: Planned Reserve in Washington State
Mazama pocket gopherstreaked horned lark Taylor’s checkerspot
![Page 3: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/3.jpg)
3
Land parcel details About 5,300 parcelssoil types, vegetation, slopeconservation cost
Problem Ingredients
![Page 4: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/4.jpg)
4
Land parcel details Geography: Roads, Rivers, etc
Problem Ingredients
![Page 5: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/5.jpg)
5
Land parcel details Geography: Roads, Rivers, etc Model of Species’ Population
DynamicsReproduction, Colonization, Predation,
Disease, Famine, Harsh Weather, …
Problem Ingredients
![Page 6: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/6.jpg)
6
Time t+1
Population Dynamics
EnvironmentalConditions (Markovian)
Our Choices
Protected Parcels
Time t
Modeled using a Dynamic Bayesian
Network
![Page 7: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/7.jpg)
7
Time t+1
Population Dynamics
EnvironmentalConditions (Markovian)
Our Choices
Protected Parcels
Time t
Modeled using a Dynamic Bayesian
Network
![Page 8: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/8.jpg)
8
Model Paramters From the ecology literature, or Elicited from panels of domain experts
Annu
al P
atch
Sur
viva
l Pro
babi
lity
Patch Size (Acres)
![Page 9: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/9.jpg)
9
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.
![Page 10: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/10.jpg)
10
The Objective Function
In practice, use sample average approximation
Selected patches R
Pr[alive after 50yrs]
0.8
0.7
0.5f(R)= 2.0 (Expected # alive)
Choose R to maximize species persistence
![Page 11: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/11.jpg)
11
“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
![Page 12: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/12.jpg)
12
Structure in Reserve Design
Diminishing returns: helps more in case A
than in case B
Utility function f is submodular:
A B
![Page 13: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/13.jpg)
13
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]
![Page 14: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/14.jpg)
14
Selected patches are very diverse
![Page 15: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/15.jpg)
15
Results: “Static” Planning
• Can get large gain through optimization
![Page 16: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/16.jpg)
16
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
![Page 17: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/17.jpg)
17
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
![Page 18: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/18.jpg)
18
• Large gain from optimization & dynamic selection
Results: Dynamic Planning
![Page 19: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/19.jpg)
19
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]
![Page 20: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/20.jpg)
20
Dynamic Planning w/Failures
Failures increase the benefit of adaptivity
50% failure rate
![Page 21: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/21.jpg)
21
Related Work Existing software
Marxan [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
![Page 22: Dynamic Resource Allocation in Conservation Planning](https://reader036.vdocuments.site/reader036/viewer/2022062521/568168aa550346895ddf4e28/html5/thumbnails/22.jpg)
22
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