Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work characterizes the benefits of averaging techniques widely used in conjunction with stochastic gradient descent (SGD). In particular, this work sharply analyzes: (1) mini-batching, a method of averaging many samples of the gradient to both reduce the variance of a stochastic gradient estimate and for parallelizing SGD and (2) tail-averaging, a method involving averaging the final few iterates of SGD in order to decrease the variance in SGD's final iterate. This work presents the first tight non-asymptotic generalization error bounds for these schemes for the stochastic approximation problem of least squares regression. #R##N#Furthermore, this work establishes a precise problem-dependent extent to which mini-batching can be used to yield provable near-linear parallelization speedups over SGD with batch size one. These results are utilized in providing a highly parallelizable SGD algorithm that obtains the optimal statistical error rate with nearly the same number of serial updates as batch gradient descent, which improves significantly over existing SGD-style methods. #R##N#Finally, this work sheds light on some fundamental differences in SGD's behavior when dealing with agnostic noise in the (non-realizable) least squares regression problem. In particular, the work shows that the stepsizes that ensure optimal statistical error rates for the agnostic case must be a function of the noise properties. #R##N#The central analysis tools used by this paper are obtained through generalizing the operator view of averaged SGD, introduced by Defossez and Bach (2015) follod by developing a novel analysis in bounding these operators to characterize the generalization error. These techniques may be of broader interest in analyzing various computational aspects of stochastic approximation.
['Prateek Jain', 'Sham M. Kakade', 'Rahul Kidambi', 'Praneeth Netrapalli', 'Aaron Sidford']
I am writing a research paper on a idea Parallelizing Stochastic Approximation Through Mini-Batching and Tail-Averaging
[{"from": "human", "value": "I am writing a research paper on a idea Parallelizing Stochastic Approximation Through Mini-Batching and Tail-Averaging"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work characterizes the benefits of averaging techniques widely used in conjunction with stochastic gradient descent (SGD). In particular, this work sharply analyzes: (1) mini-batching, a method of averaging many samples of the gradient to both reduce the variance of a stochastic gradient estimate and for parallelizing SGD and (2) tail-averaging, a method involving averaging the final few iterates of SGD in order to decrease the variance in SGD's final iterate. This work presents the first tight non-asymptotic generalization error bounds for these schemes for the stochastic approximation problem of least squares regression. #R##N#Furthermore, this work establishes a precise problem-dependent extent to which mini-batching can be used to yield provable near-linear parallelization speedups over SGD with batch size one. These results are utilized in providing a highly parallelizable SGD algorithm that obtains the optimal statistical error rate with nearly the same number of serial updates as batch gradient descent, which improves significantly over existing SGD-style methods. #R##N#Finally, this work sheds light on some fundamental differences in SGD's behavior when dealing with agnostic noise in the (non-realizable) least squares regression problem. In particular, the work shows that the stepsizes that ensure optimal statistical error rates for the agnostic case must be a function of the noise properties. #R##N#The central analysis tools used by this paper are obtained through generalizing the operator view of averaged SGD, introduced by Defossez and Bach (2015) follod by developing a novel analysis in bounding these operators to characterize the generalization error. These techniques may be of broader interest in analyzing various computational aspects of stochastic approximation."}]