1. Geometry of Online Packing Linear Programs Marco Molinaro and R. Ravi Carnegie Mellon University

2. Packing Integer Programs (PIPs) A x ≤ b m n

3. A Online Packing Integer Programs Adversary chooses values for c, A, b …but columns are presented in random order …when column comes, set variable to 0/1 irrevocably b and n are known upfront x ≤ b c A A A A n A A 1 0

4. Online Packing Integer Programs

5. Previous Results do not depend on n depends on n

6. Main Question and Result Q: Do general PIPs become more difficult for larger n? A: No!

7. High-level Idea 1.Online PIP as learning 2.Improving learning error using tailored covering bounds 3.Geometry of PIPs that allow good covering bounds 4.Reduce general PIP to above

8. Online PIP as Learning 1 1 1 1 0 0 0

9. 1 1 1 1 0 0 0

12. 2)Solving PIP via learning

13. Online PIP as Learning 2)Solving PIP via learning

14. Online PIP as Learning 2)Solving PIP via learning Improve this…

16. Improved Learning Error Idea 1: Covering bounds via witnesses (handling multiple bad classifiers at a time)

17. Geometry of PIPs with Small Witness Set

23. Conclusion

24. Thank you!