Download presentation

Presentation is loading. Please wait.

Published byHamza Root Modified over 2 years ago

1
How do you model the future? Stochastic approach: The future can be modeled as a distribution over possible events. Very successful in many contexts. Alternative: Think of the future as an adversary, do well against all possible future outcomes.

2
Toy Example: Ski Optimization I decide to take up skiing. Should I rent or buy skis? Uncertainty: Will I like skiing? Will there be snow? Will I break my leg? Will the government outlaw skiing? I want to have a good strategy against all possible outcomes In this case an outcome is the number of times I wind up going skiing.

3
Ski Rental A pair of skis (and boots) costs $300. A ski rental costs $50. What should you do? How do you evaluate if you did the right thing? You give a strategy (algorithm) You compare against how well someone who knows that future could do. You take the worst case and call that the competitive ratio

4
Ski Rental Let A be my algorithm. Let OPT be the behavior of someone who knows the future Consider any realization of the future I (number of times I actually ski) Competetive ratio We want a strategy with a small competitive ratio

5
Optimal Strategy Times skiing 12345678lots StrategyRRRRRBBBB Cost50100150200250300300300300

6
Algorithm 1: Buy Times skiing 12345678lots Cost of A 300300300300300300300300300 Opt Cost 50100150200250300300300300 Ratio6321.51.21111 Competitive ratio = 6

7
Algorithm 2: Rent Times skiing 12345678lots Cost of A 50100150200250300350400lots Opt Cost 50100150200250300300300300 Ratio6321.51.211.21.33lots Competitive ratio = lots

8
Algorithm 3: Rent 6 times and then buy Times skiing 12345678lots Cost of A 50100150200250300600600600 Opt Cost 50100150200250300300300300 Ratio111111222 Competitive ratio = 2

9
Lessons Without knowing the future, you can guarantee that no matter what happens, you will never spend more than twice what anyone could have spent. A good algorithm balances different bad outcomes If you allow randomization, you can decrease the competetive ratio to e/(e-1), around 1.58.

Similar presentations

OK

Online Oblivious Routing Nikhil Bansal, Avrim Blum, Shuchi Chawla & Adam Meyerson Carnegie Mellon University 6/7/2003.

Online Oblivious Routing Nikhil Bansal, Avrim Blum, Shuchi Chawla & Adam Meyerson Carnegie Mellon University 6/7/2003.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on major domains of the earth Heat energy for kids ppt on batteries Ppt on online library management Ppt on bluetooth technology downloads Download ppt on foundry technology Ppt on online banking system in java Ppt on fdi in retail sector 2012 Ppt on differential aptitude test Ppt on market friendly state political cartoon Ppt on statistics and probability tutorial