More Optimal Fractional-Order Stochastic Gradient Descent for Non-Convex Optimization Problems
This work addresses optimization challenges in non-convex problems for researchers and practitioners, but it is incremental as it builds on existing FOSGD methods with a novel tuning mechanism.
The paper tackled the problem of tuning and stabilizing fractional exponents in fractional-order stochastic gradient descent (FOSGD) for non-convex optimization by proposing 2SEDFOSGD, which adapts the exponent using a data-driven approach, resulting in faster convergence and more robust parameter estimates in empirical evaluations.
Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We propose 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), which integrates the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to adapt the fractional exponent in a data-driven manner. By tracking model sensitivity and effective dimensionality, 2SEDFOSGD dynamically modulates the exponent to mitigate oscillations and hasten convergence. Theoretically, for onoconvex optimization problems, this approach preserves the advantages of fractional memory without the sluggish or unstable behavior observed in naïve fractional SGD. Empirical evaluations in Gaussian and $α$-stable noise scenarios using an autoregressive (AR) model highlight faster convergence and more robust parameter estimates compared to baseline methods, underscoring the potential of dimension-aware fractional techniques for advanced modeling and estimation tasks.