Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond
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Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. this paper rigorously characterizes the effect of forgetting factors for a class of online Newton algorithms. objectives, the algorithms achieve a dynamic regret of {O( T),O(√(TV))}, where V is a bound on the path length of the comparison sequence. forgetting factor achieves this dynamic regret bound. obtain a trade-off between static and dynamic regret. how the forgetting factor can be tuned to obtain and dynamic regret. algorithms, our second contribution is a novel gradient descent step size rule for strongly convex functions. regret bounds described above. regret of O(T^1-β) and dynamic regret of O(T^β V^*), where β∈ (0,1) and V^* is the path length of the sequence of minimizers. varying β, we obtain a trade-off between static and dynamic regret.
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