Machine Learning and Optimization For Traffic and Emergency Resource Management. Milos Hauskrecht Department of Computer Science University of Pittsburgh Students: Branislav Kveton, Tomas Singliar UPitt 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

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 ? ? ? ? ? ? ? ? ? ?

Solving the problem A 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 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 spikesOccupancy falls

Incident detection algorithms Machine Learning approach (ICML 2006) Use a set of simple feature detectors and learn the classifier from the data Improved performance 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 spaces Goals: hundreds of state and action variables

Thank you Questions