Rescuing an Endangered Species with Monte Carlo AI - PowerPoint Presentation

Slide1

Rescuing an Endangered Species with Monte Carlo AI

Tom Dietterichbased on work by Dan Sheldon et al.

1Slide2

Overview

Collaborative project to develop optimal conservation strategies for Red-Cockaded Woodpecker (RCW)

Institute for Computational Sustainability (Cornell and OSU)

:

Daniel Sheldon, Bistra Dilkina, Adam Elmachtoub, Ryan Finseth, Ashish Sabharwal, Jon Conrad, Carla P. Gomes, David ShmoysThe Conservation Fund: Will Allen, Ole Amundsen, Buck VaughanRecent paper: Maximizing the Spread of Cascades Using Network Design, UAI 2010

2Slide3

Red-Cockaded Woodpecker

Originally wide-spread species in S. US

Population now shrunken to 1% of original size

5000 breeding groups

~12,000 birdsFederally-listed endangered speciesLifestyle:nests in holes in 80yo+ Longleaf pine treessap from the trees defends the nesttakes several years to excavate the holeWill colonize man-made holes

Wikipedia

3Slide4

Spatial Conservation Planning

What is the best land acquisition and management strategy to support the recovery of the Red-Cockaded Woodpecker (RCW)?

4Slide5

Problem Setup

Given

limited budget, what parcels should

we

conserve to maximize the expected number of occupied patches in T years?

Conserved parcels

Available parcels

Current

patches

Potential

patches

5Slide6

Metapopulation Model

Population dynamics in fragmented landscape

Stochastic patch occupancy model (SPOM

)

Patches = occupied / unoccupiedColonizationLocal extinction6Slide7

SPOM: Stochastic Patch Occupancy Model

Patches are either occupied

or

unoccupied

Two types of stochastic events:Local extinction: occupied  unoccupiedColonization: unoccupied  occupied (from neighbor)Independence among all events

Time 1

Time 2

7Slide8

Network Cascades

Models for diffusion in (social) networksSpread of information, behavior, disease, etc.

E.g.: suppose each individual passes rumor to friends independently with probability ½

Note: “activated” nodes are those reachable by red edges

8Slide9

SPOM Probability Model

k

j

i

j

p

ij

1-

β

j

p

lj

l

i

k

l

9

To determine occupancy of patch

at time

For each

occupied

patch

from time

,

flip coin with probability

to see if

colonizes

If

is occupied at time

, flip a coin with probability

to determine survival (non-extinction)

If any of these events occurs,

is occupied

Parameters:

: colonization probability

: extinction probability

Simple parametric functions of patch-size, inter-patch distance, etc.

 Slide10

Monte Carlo Simulation of a SPOM

Key idea

: a

metapopulation

model is a cascade in the layered graph representing patches over timeab

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Colonization

Non-extinction

Patches

Time

10Slide11

Metapopulation = Cascade

Key idea

: a

metapopulation

model is a cascade in the layered graph representing patches over timeab

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Patches

Time

11Slide12

Metapopulation = Cascade

Key idea

: a

metapopulation

model is a cascade in the layered graph representing patches over timeab

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Patches

Time

12Slide13

Metapopulation = Cascade

Key idea

: a

metapopulation

model is a cascade in the layered graph representing patches over timeab

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Patches

Time

13Slide14

Metapopulation = Cascade

Key idea

: a

metapopulation

model is a cascade in the layered graph representing patches over timeab

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Patches

14Slide15

Monte Carlo Simulations

Each simulation can produce a different cascade

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

1

2

3

4

5

Patches

15Slide16

Insight #1: Objective as Network Connectivity

Conservation objective: maximize expected # occupied patches at time

T

Cascade objective: maximize expected # of target nodes reachable by live edges

ij

k

l

m

i

j

k

l

m

i

j

k

l

m

i

j

k

l

m

i

j

k

l

m

targets

Live edges

16Slide17

Insight #2: Management as Network Building

Conserving parcels adds nodes and (stochastic) edges to the network

Parcel 1

Parcel 2

Initial network

17Slide18

Insight #2: Management as Network Building

Conserving parcels adds nodes to the network

Parcel 1

Parcel 2

Initial network

18Slide19

Insight #2: Management as Network Building

Conserving parcels adds nodes to the network

Parcel 1

Parcel 2

Initial network

19Slide20

Monte Carlo Evaluation of a Proposed Purchase Plan

set of reachable

nodes at

time Goal is to maximize , where

is our purchasing plan

Run multiple simulations. Count the number of occupied parcels

at time

. Compute the average:

20Slide21

Research Question

How many samples

do we need to get a good estimate?

Answer: We can use basic statistical methods (confidence intervals and hypothesis tests) to measure the accuracy of our estimate.

95% confidence interval for the mean is our estimate; is the true value

We can increase

until the accuracy is high enough

21Slide22

Evaluating a Purchase Plan

Plan 1: Purchase nothing

Initial network

Parcel 1

Parcel 2

22Slide23

Plan 2: Purchase Parcel #1

Initial network

Parcel 1

Parcel 2

23Slide24

Plan 3: Purchase Parcels 1 and 2

Initial network

Parcel 1

Parcel 2

24Slide25

How many different purchasing plans are there for

parcels?

We can’t afford to evaluate them all

25Slide26

Solution

Strategy(aka Sample Average Approximation)

26

Assume we own

all parcels. Run multiple simulations of bird propagationJoin all of those simulations into a single giant graphGoal of maximizing expected # of occupied patches at time is approximated by # of reachable patches in the giant graphDefine a set of variables

, one for each parcel that we can buy

Solve a mixed integer program to decide which

variables are

and which are

 Slide27

Solving the Deterministic Problem

CPLEX commercial optimization package (sold by IBM; free to universities)Applies a method known as Branch and Bound

NP-Hard, so can take a long time but often finds a solution if the problem isn’t too big or too hard

27Slide28

Experiments

443 available parcels2500

territories

63 initially occupied

100 yearsPopulation model is parameterized based (loosely) on RCW ecology

Short-range

colonizations

(<3km)

within the foraging radius of the RCW are much more likely than long-range

colonizations

28Slide29

Greedy Baselines

Adapted from previous work on

influence maximization

Start with empty set, add actions until exhaust budget

Greedy-uc – choose action that results in biggest immediate increase in objective [Kempe et al. 2003]Greedy-cb – use ratio of benefit to cost [Leskovec et al. 2007]These heuristics lack performance guarantees!29Slide30

Results

M

= 50,

N

= 10,

N

test

= 500

Upper bound

!

30Slide31

Results

M

= 50,

N

= 10,

N

test

= 500

Upper bound

!

31Slide32

Results

Conservation Reservoir

Initial population

M

= 50,

N

= 10,

N

test

= 500

Upper bound

!

32Slide33

Conservation Strategies

33

Both

approaches build outward from source

Greedy buys best patches next to currently-owned patchesOptimal solution builds toward areas of high conservation potentialIn this case, the two strategies are very similar

Conservation Reservoir

Source populationSlide34

A Harder Instance

Move the conservation reservoir so it is more remote.

34Slide35

Conservation Strategies

Greedy Baseline

SAA Optimum

(our approach)

$150M

$260M

$320M

Build outward from sources

Path-building (goal-setting)

35Slide36

Shortcomings of the Method

All parcels are purchased at time

Reality: money arrives incrementally

All parcels are assumed to be for sale at

Reality: parcel availability and price can vary from year to yearHow about an MDP? Each year we can see where the birds actually spread to and then update our purchase plans accordinglyThis is a very hard MDP, no known solution methodCurrent method is very slow

36Slide37

Status

The Conservation Fund is making purchasing decisions based (partially) on the plans computed using this modelAlan Fern, Shan

Xue

, and Dan Sheldon have developed an extension that proposes a schedule for purchasing

the parcels37