How do you model the future?

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# How do you model the future? - PowerPoint PPT Presentation

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.

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## How do you model the future?

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Presentation Transcript
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
• 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.
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
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