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Support vector machines regression (SVMR) is an important tool in many machine learning applications. In this paper, we focus on the theoretical understanding of SVMR based on the insensitive loss. For fixed ??≥?0 and general data generating distributions, we show that the minimizer of the expected risk for insensitive loss used in SVMR is a set-valued function called conditional median. We then establish a calibration inequality of insensitive loss under a noise condition on the conditional distributions. This inequality also ensures us to present a nontrivial variance-expectation bound for insensitive loss, and which is known to be important in statistical analysis of the regularized learning algorithms. With the help of the calibration inequality and variance-expectation bound, we finally derive an explicit learning rate for SVMR in some space. 相似文献
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This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary environment, where a set of agents aim to cooperatively minimize the sum of locally time-varying cost functions when the communication graphs are time-changing connected and unbalanced. Based on dual decomposition, we propose a distributed online dual push-sum learning algorithm by incorporating the push-sum protocol into dual gradient method. We then show that the regret bound has a sublinear growth of O(Tp) and the constraint violation is also sublinear with order of where T is the time horizon and 0 < p ≤ 1/2. Finally, simulation experiments on a plug-in electric vehicle charging problem are utilized to verify the performance of the proposed algorithm. The proposed algorithm is adaptive without knowing the total number of iterations T in advance. The convergence results are established on more general unbalanced graphs without the boundedness assumption on dual variables. In addition, more privacy concerns are guaranteed since only dual variables related with coupled constraints are exchanged among agents. 相似文献
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