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Forgetting-Factor Regrets for Online Convex Optimization
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DOI：10.1109/TAC.2023.3340120.png)
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Abstract
En 中文
This article develops a class of novel algo-rithms for online convex optimization. The key constructis a forgetting-factor regret. It introduces weights to theobjective functions at each time instanttand allows theweights of the past objective functions decaying to zero.We establish the forgetting-factor regret bounds of clas-sical algorithms including online gradient descent algo-rithms, online gradient-free algorithms, and online Frank-Wolfe algorithms. In addition, the article introduces onlinegradient descent algorithm with a forgetting factor, andanalyze its performance under the new regret. Sufficientconditions are obtained to guarantee the bounds of theforgetting-factor regret of the above algorithms being of theorder o(1), which guarantees the tracking performance forminimizers of time-varying objective functions. Finally, ourresults are tested through numerical demonstration
Keywords:
Prediction algorithms
Optimization
Linear programming
Heuristic algorithms
Convex functions
Target tracking
Loss measurement
Forgetting-factor regret
iterative optimization algorithm
online convex optimization
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W