1 / 9

How do you model the future?

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. Toy Example: Ski Optimization.

paul
Download Presentation

How do you model the future?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  6. Algorithm 1: Buy Competitive ratio = 6

  7. Algorithm 2: Rent Competitive ratio = lots

  8. Algorithm 3: Rent 6 times and then buy 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.

More Related