VoI for adversarial information structures

Transcription

1 ARO ARO MURI MURI on on Value-centered Theory for for Adaptive Learning, Inference, Tracking, and and Exploitation VoI for adversarial information structures Kickf Emre Ertin, Nithin Sugavanam The Ohio State University

2 Research program Resource Exploitation Performance tradefs Distributed algorithms Mission and Objectives Resource Exploitation Kickf Cochran (Lead); Ertin, Hero, How, Moses, Soatto Adversarial Info Structures Complexity Management Actionable Robust Mission Planning Scalable, Actionable VoI measures

3 Design for Adversarial Opponent Sensor systems do not compete against nature but against adversaries with opposing interests. Adversarial action extends to: Countermeasures for avoiding detection Dynamic strategies for avoiding capture Coordinated team actions We focus on sensor control and sensor system design to maximize VoI assessed in adversarial setting Contrast this to differential game Kickf theory literature for pursuer motion control which assumes perfect state observability Our approach combines Design for adversary (target) and Design for uncertainty (Sensor, Noise) Optimal sensor control strategies to maximize information rate Adversary models that attempts to minimize information rate to the observer Omniscient adversary models are employed to provide performance guarantees

4 Goals and Relation to other research thrusts Quantifying VoI in adversarial structures New measures performance for area and barrier coverage Optimal controlled sensing strategies in adversarial setting Sensor system design to maximize VoI controlled sensing systems This will lead to Task specific measures for Kickf fused information (Moses) Computationally tractable, distributed algorithms to manage VoI (Fisher) New insights for developing sensor management and placement strategies (Cochran) Collaborative Project with J. Fisher on VoI past vs current measurements

5 DARPA ExScal Project: 1,200 nodes over 1,200m x 300m Detect, Track and Classify vehicles and personnel to protect a long linear asset from intruders Motivating Scenario Multimodal sensors provide local detections, fusion center computes Kickf global detections and tracks Intruders Long Linear Asset

6 Sensor Selection in Adversarial Setting Surveillance game between two players with opposing objectives. The observer is choosing an open loop randomized strategy to choose sensor observations to maximize probability detection. Sensor 1 (q 1m,p 1 ) The adversary (target) is using an open Kickf loop randomized control strategy over the available evading actions to minimize the probability being detected. Observer Sensor 2 (q 2m,p 2 ) H1 (m) H 0 Min-max composite detection problem Sensor K (q Km,p K ) Focus on asymptotic performance in finite sample size problems

7 Sensor Selection in Adversarial Setting For each observation period The observer chooses among K sensors with observations in finite space X, ( X = J) The target chooses among M evading actions H 0 : P [s k = x j ]=p k j Kickf H 1 : P [s k (m) =x j ]=qj km Observer Sensor 1 (q 1m,p 1 ) Sensor 2 (q 2m,p 2 ) H1 (m) H 0 Observer and Target are employing open loop randomized control strategies r = {r 1,...,r K } ( X r k = 1) k Sensor K (q Km,p K ) s = {s 1,...,s M } ( X m s m = 1)

8 Related Work Controlled Sensing Tsitsiklis(1988) Open loop strategies against random opponent Veeravalli (2012) Closed loop strategies against random opponent Robust Detection Classical treatment classes under each Hypothesis are defined as small neighborhoods the nominal distributions Kickf Huber ( ) Contamination Total Variation Performance and the classes are defined through asymptotical error metrics Dabak and Johnson (2003)

9 Sensor Selection in Adversarial Setting Given sensor observations y collected over N periods using sensors I = {i 1,...,i N } use decision rule given by the partition (U 0, U 1 ) Decide H 0 if (y, I) 2 U 0 Decide H 1 if (y, I) 2 U 1 Sensor 1 (q 1m,p 1 ) Type I and II errors are given by Kickf Observer Sensor 2 (q 2m,p 2 ) H1 (m) H 0 P M N (r, s) = P FA N (r, s) = X NY (y,i)2u 0 n=1 X NY (y,i)2u 1 n=1 r in X m r in p i n yn s m q i nm y n Sensor K (q Km,p K )

10 Random Opponent with known random strategy Start with observer against random opponent problem with known strategy s Consider all decision rules P FA N (r, s) < Observer chooses sensors to maximize asymptotic error exponent Kickf J (r s) = lim N!1 X Optimal strategy is non-randomized 1 inf {U:PN FA(r,s)< } N log(p N M (r s)) k = arg max k D p k q k (s) J. N. Tsitsiklis, Decentralized detection by a large number sensors, Mathematics Control, Signals, and Systems, vol. 1, no. 2, pp , Closed Loop: Veeravalli 2012

11 Adversarial Target This time we assume an intelligent adversary Again consider all decision rules P FA N (r, s) < Observer (Target) chooses strategies to maximize (minimize) asymptotic error exponent Kickf 1 J (r, s) = lim inf N!1 {U:PN FA(r,s)< } N log(p N M (r, s)) Decision rule for the Observer has to be optimized jointly with the sensing strategy r. We cannot form the likelihood-ratio test without the knowledge s.

12 Detection against an unknown strategy Hoeffding test: Perform a test using distance the empirical histogram from U1 H = {y : D p k ˆp(y) > } The type I and type II error exponent the Hoeffding test is given by 1 FA lim log PN = N!1 N Kickf 1 lim N!1 N log P N M = X r k D p k q k (s) ( ) k For fixed false alarm constraint, we can drive the type II error to zero at the clairvoyant rate J (r, s) = X k r k D p k q k (s)

13 Surveillance Game Looking for equilibrium strategies satisfying the saddle point property J (r, s ) apple J (r,s ) apple J (r,s) At the Nash equilibrium min-max inequality is satisfied V (J )=J (r,s ) = max r min Kickf J (r, s) =min s s max r J (r, s) In this case the strategy spaces are compact and the objectives are convex/ concave functions the strategy space so a fixed point equilibrium strategies exists

14 Searching for Optimal Strategies The equilibrium can be computed using an interior method, using log barrier terms to express inequality constraints The solution corresponds to the saddle point the Lagrangian Kickf Convergence as, exit criteria can be based on the duality gap

15 Example 1: Pruning Tripline Sensors Network K Sensors randomly deployed (Energy Detector-Tripline) Target employs open loop control between locations to evade detection, Generically with K sensors and M locations K>M, target occupies all M locations with M positive probability, M out K sensors can be selected to support the optimal min-max equilibrium K=40 sensors shown with 0dB SNR contours M=9 locations for target Kickf

16 Example 1: Pruning Tripline Sensors Network K Sensors randomly deployed (Energy Detector-Tripline) Target employs open loop control between locations to evade detection, Generically with K sensors and M locations K>M, target occupies all M locations with M positive probability, M out K sensors can be selected to support the optimal min-max equilibrium x 10 3 Kickf 0.7 Duality Gap Number Iterations in Saddle Point Search

17 Optimizing Sensor Placement Given the sensor locations define the value the game x = {x k } K k=1,optimal strategies (r (x),s (x)) V(x) =J (r (x),s (x),x) Sensor locations can be optimized for maximizing the observer advantage in the surveillance game Kickf x = arg max J x (r (x),s (x),x) Envelope theorem provides an efficient way to compute the gradient dj (r (x),s (x),x) dx k s,, k = r k X j p k j q k j (s ) r,s, X k j k s m

18 Example 2: Optimal Sensor Placement For 16 target positions Locations the 4 tripwire sensors are chosen to maximize the value the surveillance game for the observer. Value Game Kickf 250 Y Target Sensors Number Iterations X

19 Value Example 2: Optimal Sensor Placement Sensor Placement and Control in the presence Obstacles Propagation Model [Vecherin 2009] Z r e = (r) dr E(r) = S(r) r st Y 14 Kickf X Simulation Model with Obstructions Random Initialization Optimization trajectory Optimal Placement 1st year review. UCLA 2012

20 Summary and Future Work Value for sensors has to be computed in a task specific context Insight into competitive sensing problems can be obtained through adversarial modeling. Problems Area and Barrier Coverage, Asset Protection Optimizing open-loop control strategies in adversarial setting for fixed sensor locations Kickf Optimize sensor placement to maximize advantage in the surveillance game Future work: Closed loop control in adversarial setting Design for Barrier coverage versus Area Coverage