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Fractional order online gradient descent algorithm with constraints
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DOI：10.1080/23307706.2025.2556341.png)
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This paper introduces a novel fractional constrained online gradient descent algorithm for online optimisation problems, addressing both convex and strongly convex objective functions. Distinguishes from traditional integer-order online gradient descent methods, the algorithm introduces the fractional-order parameter alpha, which effectively increases the algorithm's degrees of freedom, enabling finer control over the optimisation process and improving convergence performance. For convex objective functions, the proposed algorithm achieves a sublinear regret bound, which is consistent with traditional online gradient descent methods but with improved convergence properties due to the fractional order. For strongly convex objective functions, the regret bound is tighter compared to the convex case, demonstrating the algorithm's enhanced performance in this setting. Finally, several numerical examples are given, it is shown that by tuning alpha the algorithm can achieve faster convergence or higher accuracy.
Keyword:
Fractional calculus
convex optimisation
online optimisation
gradient descent algorithm
期刊
IF:
1.8
论文数:
160
被引数:
724
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