Noisy Optimization with CE
In this chapter we show how the CE method optimizes noisy objective functions, that is, objective functions corrupted with noise. Noisy optimization, also called stochastic optimization, can arise in various ways. For example, in the analysis of data networks , a well-known problem is to find a routing table that minimizes the congestion in the network. Typically this problem is solved under deterministic assumptions. In particular, the stream of data is represented by a constant “flow,” and the congestion at a link is measured in terms of a constant arrival rate to the link, which is assumed to depend on the routing table only. These assumptions are reasonable only when the arrival process changes very slowly relative to the average time required to empty the queues in the network. In a more realistic setting however, using random arrival and queueing processes, the optimization problem becomes noisy. Other examples of noisy optimization include stochastic scheduling and stochastic shortest/longest path problems. References on noisy optimization include [9, 26, 36, 37, 60, 78].
KeywordsDeterministic Case Repair Rate Buffer Space Buffer Allocation Noisy Version
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