Dynamic Optimization and Learning for Renewal Systems

Details Dynamic Optimization and Learning for Renewal Systems Dynamic Optimization and Learning for Renewal Systems

2010-11-27

arxiv.org/abs/1011.5942v1

Mathematics

Optimization and Control

This was presented in part at the Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, 2010

Scientific paper

We consider the problem of optimizing time averages in systems with independent and identically distributed behavior over renewal frames. This includes scheduling and task processing to maximize utility in stochastic networks with variable length scheduling modes. Every frame, a new policy is implemented that affects the frame size and that creates a vector of attributes. An algorithm is developed for choosing policies on each frame in order to maximize a concave function of the time average attribute vector, subject to additional time average constraints. The algorithm is based on Lyapunov optimization concepts and involves minimizing a ``drift-plus-penalty'' ratio over each frame. The algorithm can learn efficient behavior without a-priori statistical knowledge by sampling from the past. Our framework is applicable to a large class of problems, including Markov decision problems.

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