Adaptive Alternating Minimization Algorithms
Adaptive Alternating Minimization Algorithms
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DOI：
10.1109/tit.2008.2011442
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发表时间：
2007-01
影响因子：
2.5
通讯作者：
Urs Niesen;Devavrat Shah;G. Wornell
中科院分区：
文献类型：
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作者：
Urs Niesen;Devavrat Shah;G. Wornell
在解决两个变量上的优化问题的背景下，经典的交替最小化（或投影）算法已成功。算法的迭代性质和简单性导致其在许多领域的应用，例如信号处理，信息理论，控制和金融。当固定基础问题参数时，已知一组足够的条件，以实现算法的收敛性和正确性。但是，在许多实际情况下，潜在的问题参数随着时间的推移而发生变化，并且使用自适应算法更合适。在本文中，我们研究了这种自适应版本的交替最小化算法。更确切地说，我们考虑具有最小化发生时变化的域缓慢变化的域的影响。作为本文的主要结果，我们为自适应算法的收敛性和正确性提供了一组足够的条件。也许有些令人惊讶的是，这些条件似乎是人们在这种适应性环境中期望的最小情况。我们介绍了结果的应用，以自适应混合物的自适应分解，自适应对数最佳的投资组合选择和自适应滤波器设计。
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm are known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. More precisely, we consider the impact of having a slowly time-varying domain over which the minimization takes place. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps somewhat surprisingly, these conditions seem to be the minimal ones one would expect in such an adaptive setting. We present applications of our results to adaptive decomposition of mixtures, adaptive log-optimal portfolio selection, and adaptive filter design.