Online Algorithms for Incremental and Robust Inference

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Online Algorithms forIncremental and Robust
Inference

• Sandy Irani
• Information and Computer Science
• UC Irvine

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Incremental and Robust Inference

• Probabilistic model estimates future events
• How to design a plan or give advice which will be
  robust to changes in the distribution?
• How well can a given query be answered as a
  function of how much the predicted actions and
  actual actions of an opponent differ?
• How to adapt the system as the model for the
  future changes over time?

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Online Algorithms

• Input is revealed to the algorithm incrementally
• Output is produced incrementally
• Some output must be produced before the entire
  input is known to the algorithm

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Online Algorithms

• Decision making under partial information
• Unknown information the future

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Applications

• Resource Allocation
• Scheduling
• Memory Management
• Robot Motion Planning
• Exploring an unknown terrain
• Finding a destination
• Computational Finance

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Methods of Analysis

• Worst Case Analysis
• For any input, the cost of our online algorithm
  is never worse than x times the cost of the
  optimal offline algorithm.
• Probabilistic Analysis
• Assume a distribution generating the input
• Find an algorithm which minimizes the expected
  cost of the algorithm.

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Example

• Delivery person planning a route
• Requests for service arrive through day
• Goal
• Reach as many requests as possible by their
  deadline
• OR
• Minimize time or cost in reaching all requests

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Worst Case Analysis

• Seen as a game between the online algorithm and
  an adversary.
• Adversary tries to devise each new piece of the
  input which will cause the algorithm to incur a
  high cost.
• Algorithm tries to minimize cost.
• Often results are very pessimistic.

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Probabilistic Analysis

• Need to accurately determine the true
  distribution generating the request sequence
• Probability distribution generating input
  sequence is non-adaptive (i.e. determined in
  advance and is independent of the choices made by
  the algorithm).

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Adaptive Distributions

• The distribution governing the next move of the
  opponent(s) depends on the current configuration
  of the game, including the previous choices made
  by the algorithm.
• Game-like features of worst-case analysis
• Probabilistic distribution governing choices

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Incremental and Robust Inference

• Model for future actions only an estimate
• How to make decisions which will robust to
  changes in the distribution?
• How well can an algorithm perform as a function
  of how much the predicted actions and actual
  actions of an opponent differ?