Finite model approximations and asymptotic optimality of quantized policies in decentralized stochastic control
| Autor: | Tamas Linder, Serdar Yüksel, Naci Saldi |
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| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Approximations of π Optimal cost 0211 other engineering and technologies Systems and Control (eess.SY) 02 engineering and technology 020901 industrial engineering & automation Witsenhausen's counterexample Arbitrary-precision arithmetic FOS: Mathematics FOS: Electrical engineering electronic engineering information engineering Applied mathematics Electrical and Electronic Engineering Mathematics - Optimization and Control Mathematics Stochastic control 021103 operations research Stochastic process Action (physics) Computer Science Applications Asymptotically optimal algorithm Control and Systems Engineering Optimization and Control (math.OC) Computer Science - Systems and Control Counterexample |
| Zdroj: | CDC |
| DOI: | 10.1109/cdc.2016.7799063 |
| Popis: | In this paper, we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to Witsenhausen's celebrated counterexample and the Gaussian relay channel problem. For the Witsenhausen's counterexample, our approximation approach provides, to our knowledge, the first rigorously established result that one can construct an $\varepsilon$-optimal strategy for any $\varepsilon > 0$ through a solution of a simpler problem. 13 pages, double column |
| Databáze: | OpenAIRE |
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