A local search algorithm for the Witsenhausen's counterexample
| Autor: | Shih-Hao Tseng, Ao Tang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
030213 general clinical medicine
0209 industrial biotechnology State variable Computer science Approximation algorithm 02 engineering and technology Function (mathematics) Upper and lower bounds 03 medical and health sciences Nonlinear system Range (mathematics) 020901 industrial engineering & automation 0302 clinical medicine Witsenhausen's counterexample Algorithm design Algorithm Counterexample |
| Zdroj: | CDC |
| DOI: | 10.1109/cdc.2017.8264401 |
| Popis: | We propose a local search algorithm to find an optimal controller of the Witsenhausen's counterexample, which still remains unknown. Via variational analysis, a few necessary conditions are derived, and the algorithm is guided by the conditions. The analysis does not require preliminary knowledge about the property of the target cost function, nor does it make any assumption about the functional form of the controller. As such, our method is applicable for a wide range of problems with similar structures as the Witsenhausen's counterexample. Through numerical simulations, we demonstrate that our algorithm outperforms all previous results on the benchmark case. Our results also manifest some structural properties of the first-stage state variable, including that it is not piecewise affine but nonlinear within each step, and that its shape changes from picewise continuous to sigmoid-like as the first-stage cost coefficient increases. Furthermore, a variety of parameter settings are fed to the algorithm, and the generated results can serve as the best upper bounds known thus far under those parameter settings. |
| Databáze: | OpenAIRE |
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