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In deep learning tasks, the learning rate determines the update step size ineach iteration, which plays a critical role in gradient-based optimization.However, the determination of the appropriate learning rate in practicetypically replies on subjective judgement. In this work, we propose a noveloptimization method based on local quadratic approximation (LQA). In eachupdate step, given the gradient direction, we locally approximate the lossfunction by a standard quadratic function of the learning rate. Then, wepropose an approximation step to obtain a nearly optimal learning rate in acomputationally efficient way. The proposed LQA method has three importantfeatures. First, the learning rate is automatically determined in each updatestep. Second, it is dynamically adjusted according to the current loss functionvalue and the parameter estimates. Third, with the gradient direction fixed,the proposed method leads to nearly the greatest reduction in terms of the lossfunction. Extensive experiments have been conducted to prove the strengths ofthe proposed LQA method.

Automatic, Dynamic, and Nearly Optimal Learning Rate Specification by Local Quadratic Approximation