Machine Learning and Optimization For Traffic and Emergency Resource Management.

Milos HauskrechtDepartment of Computer Science

University of Pittsburgh

Students: Branislav Kveton, Tomas SingliarUPitt collaborators: Louise Comfort, JS Lin External: Eli Upfal (Brown), Carlos Guestrin (CMU)

S-CITI related projects Modeling multivariate distributions of traffic

variables Optimization of (emergency) resources over

unreliable transportation network Traffic monitoring and traffic incident detection Optimization of distributed systems with

discrete and continuous variables: Traffic light control

S-CITI related projects Modeling multivariate distributions of traffic

variables Optimization of (emergency) resources over

unreliable transportation network Traffic monitoring and traffic incident detection Optimization of control of distributed systems

with discrete and continuous variables: Traffic light control

Traffic network

PITTSBURGH

Traffic network systems are stochastic (things happen at random) distributed (at many places concurrently)

Modeling and computational challenges Very complex structure Involved interactions High dimensionality

Challenges Modeling the behavior of a large stochastic system

Represent relations between traffic variables Inference (Answer queries about model)

Estimate congestion in unobserved area using limited information

Useful for a variety of optimization tasks Learning (Discovering the model automatically)

Interaction patterns not known Expert knowledge difficult to elicit Use Data

Our solutions: probabilistic graphical models, statistical Machine learning methods

Road traffic data We use PennDOT sensor network

155 sensors for volume and speed every 5 minutes

LegendSensors

State & InterstateLocalTownRd

Twonship

2.5 0 2.51.25 Miles

¯

Models of traffic data Local interactions Markov random

field Effects are circular

Solution:Break the cycles

The all-independent assumption

Unrealistic!

Mixture of trees A tree structure

retains many dependencies but still loses some

Have many trees to represent interactions

Latent variable model A combination

of latent factors represent interactions

Four projects Modeling multivariate distributions of traffic

variables Optimization of (emergency) resources over

unreliable transportation network Traffic monitoring and traffic incident detection Optimization of distributed systems with

discrete and continuous variables: Traffic light control

Optimizations in unreliable transportation networks Unreliable network – connections (or nodes) may fail

E.g. traffic congestion, power line failure

Optimizations in unreliable transportation networks Unreliable network – connections (nodes) may fail

more than one connection may go down to

Optimizations in unreliable transportation networks Unreliable network – connections (nodes) may fail

many connections may go down together

Optimizations in unreliable transportation networks Unreliable network – connections (nodes) may fail

parts of the network may become disconnected

Optimizations of resources in unreliable transportation networks Example: emergency system. Emergency vehicles

use the network system to get from one location to the other

Optimizations of resources in unreliable transportation networks One failure here won’t prevent us from reaching the

target, though the path taken can be longer

Optimizations of resources in unreliable transportation networks Two failures can get the two nodes disconnected

Optimizations of resources in unreliable transportation networks Emergencies can occur at different locations and they

can come with different priorities

Optimizations of resources in unreliable transportation networks … considering all possible emergencies, it may be better

to change the initial location of the vehicle to get a better coverage

Optimizations of resources in unreliable transportation networks … If emergencies are concurrent and/or some

connections are very unreliable it may be better to use two vehicles …

Optimizations of resources in unreliable transportation networks where to place the vehicles and how many of them to

achieve the coverage with the best expected cost-benefit tradeoff

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Solving the problemA two stage stochastic program with recourse Problem stages:1. Find optimal allocations of resources (em. vehicles)2. Match (repeatedly) emergency demands with

allocated vehicles after failures occur

Curse of dimensionality: many possible failure configurations in the second stage

Our solution: Stochastic (MC) approximations (UAI-2001, UAI-2003)Current: adapt to continuous random quantities (congestion

rates,traffic flows and their relations)

Four projects Modeling multivariate distributions of traffic

variables Optimization of (emergency) resources over

unreliable transportation network Traffic monitoring and traffic incident

detection Optimization of distributed systems with

discrete and continuous variables: Traffic light control

Incident detection on dynamic data

incident

incident no incident

Incident detection algorithms Incidents detected indirectly through caused congestion State of the art: California 2 algorithm

If OCC(up) – OCC(down) > T1, next step If [OCC(up) – OCC(down)]/ OCC(up) > T2, next step If [OCC(up) – OCC(down)]/ OCC(down) > T3, possible accident If previous condition persists for another time step, sound

alarm Hand-calibrated for the specific section of the road

Occupancy spikes Occupancy falls

Incident detection algorithmsMachine Learning approach (ICML 2006) Use a set of simple feature detectors and learn the

classifier from the data Improved performance

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AUC: 0.642187

PE - TSC2, T1 = 13.00, T2 = 0.75, T3 = 2.00 - 13:8:9

False positive rate

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AUC: 0.939690

PE - SVM usingDiff(s1up_spd-s1up_spd(t-5)),Prop(s1up_spd/s1up_spd(t-5)),Diff(s1up_occ-s1up_occ(t-5))... - 8:52:24

False positive rate

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California 2 SVM based model

Four projects Modeling multivariate distributions of traffic

variables Optimization of (emergency) resources over

unreliable transportation network Traffic monitoring and traffic incident detection Optimization of control of distributed systems

with discrete and continuous variables: Traffic light control

Dynamic traffic management A set of intersections A set of connection (roads)

in between intersections Traffic lights regulating the

traffic flow on roads Traffic lights are controlled

independently

Objective: coordinate traffic lights to minimize congestions and maximize the throughput

Solutions Problems:

how to model the dynamic behavior of the system how to optimize the plans

Our solutions (NIPS 03,ICAPS 04, UAI 04, IJCAI 05, ICAPS 06, AAAI 06) Model: Factored hybrid Markov decision processes

continuous and discrete variables Optimization:

Hybrid Approximate Linear Programming optimizations over 30 dimensional continuous state

spaces and 25 dimensional action spacesGoals: hundreds of state and action variables

Thank you

Questions