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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

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Decision Region Determination for Touch Based Localization

In Collaboration with: Yuxin Chen, Amin Karbasi, Andreas Krause, J. Andrew (Drew) Bagnell, and Siddhartha Srinivasa

Shervin Javdani

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Guarded Moves Are Effective

Objective: Generate sequence of moves automatically

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Task: Open the Microwave

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Hypotheses

Possible Object Locations

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Tests

Information Gathering Actions

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

Localize Object

S. Javdani, M. Klingensmith, J. A. D. Bagnell, N. Pollard, and S. Srinivasa.

Efficient touch based localization through submodularity. In IEEE ICRA , 2013.

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The task should affect how information is gathered

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Decisions

Actions to accomplish task
Corresponding hypotheses

Task-Performing Actions

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

Localize Object

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Determine Successful Decision

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

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Hypothesis Decision Region Test

… … … … … …

Decisions affect termination condition and optimization criteria

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Framework is General

Hypotheses Decision Regions Tests

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

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Optimization Bounds

NP-hard to optimize NP-hard to approximate s.t.

Key Insight: Formulate as adaptive submodular maximization

C(π) = E [number tests] C(π) ≤ C(π∗) · o(ln N) [1] C(πG) ≤ (α ln N + 1)C(π∗)

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Method Overview

Our Problem: Overlapping

decision regions

Known algorithm: Disjoint

regions

Extend known algorithm

to solve our problem

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Edge Cutting (EC2) [2]

Edges between

hypotheses in different decision regions

Edge cut if any

hypothesis it connects removed Key Properties:

1. All edges cut iff all hypotheses in one decision region
2. Adaptive submodular

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EC22 EC21 EC23 DiRECt

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EC22 EC21 EC23 DiRECt

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All hypotheses in one region iff All edges in one EC2 instance cut

EC22 EC21 EC23 DiRECt

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Combine EC2 Instances

Combine instances with noisy-OR
Objective maximized iff one EC2 instance complete
Still adaptive submodular
Performance bound and computation time scale

with number of regions

1 − Y (1 − fi)

Can we use fewer EC2 instances?

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EC21 EC22 EC23 DiRECt

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EC21 EC22 EC23 DiRECt

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EC21 EC22 EC23 DiRECt

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2k ln(N) + 1 ˆ k ln(N) + 1 O(kN) O(N

ˆ k)

DiRECt HEC Approximation Runtime 200 400 600 800 1000 2.5 3 3.5 4 4.5 5 Query complexity Number of Tests

EC2 GBS GBS−DRD EC2−DRD VoI DiRECt HEC

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Differences

Non-Adaptive
Motions relative
Complex Tests
Adaptive
Motions Globals
Simple Tests

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[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-
ptimal bayesian active learning for decision making. In AISTATS , 2014.