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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence

Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond

February 1, 2023

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Authors

Jianjun Yuan

University of Minnesota


Andrew Lamperski

University of Minnesota


DOI:

10.1609/aaai.v34i04.6149


Abstract:

Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a class of online Newton algorithms. For exp-concave and strongly convex objectives, the algorithms achieve the dynamic regret of max{O(log T),O(√TV)}, where V is a bound on the path length of the comparison sequence. In particular, we show how classic recursive least-squares with a forgetting factor achieves this dynamic regret bound. By varying V, we obtain a trade-off between static and dynamic regret. In order to obtain more computationally efficient algorithms, our second contribution is a novel gradient descent step size rule for strongly convex functions. Our gradient descent rule recovers the order optimal dynamic regret bounds described above. For smooth problems, we can also obtain static regret of O(T1-β) and dynamic regret of O(TβV*), where β ∈ (0,1) and V* is the path length of the sequence of minimizers. By varying β, we obtain a trade-off between static and dynamic regret.

Topics: AAAI

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Jianjun Yuan||Andrew Lamperski Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond Proceedings of the AAAI Conference on Artificial Intelligence (2020) 6712-6719.

Jianjun Yuan||Andrew Lamperski Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond AAAI 2020, 6712-6719.

Jianjun Yuan||Andrew Lamperski (2020). Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond. Proceedings of the AAAI Conference on Artificial Intelligence, 6712-6719.

Jianjun Yuan||Andrew Lamperski. Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond. Proceedings of the AAAI Conference on Artificial Intelligence 2020 p.6712-6719.

Jianjun Yuan||Andrew Lamperski. 2020. Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond. "Proceedings of the AAAI Conference on Artificial Intelligence". 6712-6719.

Jianjun Yuan||Andrew Lamperski. (2020) "Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond", Proceedings of the AAAI Conference on Artificial Intelligence, p.6712-6719

Jianjun Yuan||Andrew Lamperski, "Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond", AAAI, p.6712-6719, 2020.

Jianjun Yuan||Andrew Lamperski. "Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond". Proceedings of the AAAI Conference on Artificial Intelligence, 2020, p.6712-6719.

Jianjun Yuan||Andrew Lamperski. "Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond". Proceedings of the AAAI Conference on Artificial Intelligence, (2020): 6712-6719.

Jianjun Yuan||Andrew Lamperski. Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond. AAAI[Internet]. 2020[cited 2023]; 6712-6719.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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