Decision Region Determination for Touch Based Localization Shervin - PowerPoint PPT Presentation

Decision Region Determination for Touch Based Localization Shervin Javdani In Collaboration with: Yuxin Chen, Amin Karbasi, Andreas Krause, J. Andrew (Drew) Bagnell, and Siddhartha Srinivasa

Guarded Moves Are E ff ective Objective: Generate sequence of moves automatically

Task: Open the Microwave

Hypotheses Possible Object Locations

Tests Information Gathering Actions

Localize Object Hypotheses Tests Goal: Determine object location (with fewest tests) S. Javdani, M. Klingensmith, J. A. D. Bagnell, N. Pollard, and S. Srinivasa. Efficient touch based localization through submodularity. In IEEE ICRA , 2013.

The task should a ff ect how information is gathered

Decisions Task-Performing Actions • Actions to accomplish task • Corresponding hypotheses

Localize Object Hypotheses Tests Goal: Determine object location (with fewest tests)

Determine Successful Decision Hypotheses Tests Decisions Goal: Determine which decision will succeed (with fewest tests)

Decision Region Hypothesis Test … … … … … … Decisions a ff ect termination condition and optimization criteria

Framework is General Hypotheses Tests Decision Regions Movie Risky Choice Application Bird Conservation Recommendation Selection Hypothesis Cause of nest failure Target Movie Theory Pair of lottery Test Monitoring Action Pair of Movies choices Decision Conservation Recommendation Theory adoption

Optimization Bounds C ( π ) = E [number tests] NP-hard to optimize NP-hard to approximate s.t. C ( π ) ≤ C ( π ∗ ) · o (ln N ) [1] Key Insight: Formulate as adaptive submodular maximization C ( π G ) ≤ ( α ln N + 1) C ( π ∗ )

Method Overview • Our Problem: Overlapping decision regions • Known algorithm: Disjoint regions • Extend known algorithm to solve our problem

Edge Cutting (EC 2 ) [2] • Edges between hypotheses in di ff erent decision regions • Edge cut if any hypothesis it connects removed Key Properties: 1. All edges cut i ff all hypotheses in one decision region 2. Adaptive submodular

EC 21 EC 22 DiRECt EC 23

EC 21 EC 22 DiRECt EC 23

EC 21 All hypotheses in one region i ff All edges in one EC 2 instance cut EC 22 DiRECt EC 23

Combine EC 2 Instances Y • Combine instances with noisy-OR 1 − (1 − f i ) • Objective maximized i ff one EC2 instance complete • Still adaptive submodular • Performance bound and computation time scale with number of regions Can we use fewer EC 2 instances?

EC 21 EC 22 DiRECt EC 23

EC 21 EC 22 DiRECt EC 23

EC 21 EC 22 DiRECt EC 23

DiRECt HEC ˆ 2 k ln( N ) + 1 k ln( N ) + 1 Approximation ˆ O ( kN ) k ) O ( N Runtime 5 4.5 Query complexity GBS 4 EC2 EC2 − DRD GBS − DRD 3.5 VoI 3 DiRECt HEC 2.5 0 200 400 600 800 1000 Number of Tests

Di ff erences • Non-Adaptive • Adaptive • Motions relative • Motions Globals • Complex Tests • Simple Tests

[1] V. T. Chakaravarthy, V. Pandit, S. Roy, P. Awasthi, and M. Mohania. Decision trees for entity identification: Approximation algorithms and hardness results. In ACM-SIGMOD PODS, 2007. � [2] D. Golovin, A. Krause, and D. Ray. Near-optimal bayesian active learning with noisy observations. In NIPS, 2010. � [3] S. Javdani, Y. Chen, A. Karbasi, A. Krause, D. Bagnell, and S. Srinivasa. Near- optimal bayesian active learning for decision making. In AISTATS , 2014.