Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast Convergence
This provides an adaptive learning rate method for training over-parameterized models in machine learning, offering a practical improvement over existing optimization techniques.
The authors tackled the problem of setting learning rates in stochastic gradient descent (SGD) by proposing a stochastic Polyak step-size (SPS), which adapts without needing problem-dependent constants, and showed it enables fast convergence to the true solution in over-parameterized models, outperforming state-of-the-art methods in experiments.
We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing the Polyak step-size requires knowledge of the optimal function values, this information is readily available for typical modern machine learning applications. Consequently, the proposed stochastic Polyak step-size (SPS) is an attractive choice for setting the learning rate for stochastic gradient descent (SGD). We provide theoretical convergence guarantees for SGD equipped with SPS in different settings, including strongly convex, convex and non-convex functions. Furthermore, our analysis results in novel convergence guarantees for SGD with a constant step-size. We show that SPS is particularly effective when training over-parameterized models capable of interpolating the training data. In this setting, we prove that SPS enables SGD to converge to the true solution at a fast rate without requiring the knowledge of any problem-dependent constants or additional computational overhead. We experimentally validate our theoretical results via extensive experiments on synthetic and real datasets. We demonstrate the strong performance of SGD with SPS compared to state-of-the-art optimization methods when training over-parameterized models.