Abstract
We study the prediction with expert advice problem, where in each round, the player selects one of N actions and incurs the corresponding loss according to an N-dimensional linear loss vector, and aim to minimize the regret. In this paper, we consider a new measure of the loss functions, which we call L ∞ -variation. Consider the loss functions with small L ∞ -variation, if the player is allowed to have some information related to the variation in each round, we can obtain an online bandit algorithm for the problem without using the self-concordance methodology, which conditionally answers an open problem in [8]. Another related problem is the combinatorial prediction game, in which the set of actions is a subset of {0,1}d, and the loss function is in [–1,1]d. We provide an online algorithm in the semi-bandit setting when the loss functions have small L ∞ -variation.
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References
Abernethy, J., Hazan, E., Rakhlin, A.: Competing in the dark: An efficient algorithm for bandit linear optimization. In: COLT, pp. 263–274 (2008)
Audibert, J.-Y., Bubeck, S.: Regret Bounds and Minimax Policies under Partial Monitoring. Journal of Machine Learning Research 11, 2635–2686 (2010)
Audibert, J.-Y., Bubeck, S., Lugosi, G.: Minimax Policies for Combinatorial Prediction Games. In: COLT, pp. 107–132 (2011)
Chiang, C.-K., Yang, T., Lee, C.-J., Mahdavi, M., Lu, C.-J., Jin, R., Zhu, S.: Online optimization with gradual variations. In: COLT, pp. 6.1–6.20 (2012)
Dani, V., Hayes, T., Kakade, S.M.: The Price of Bandit Information for Online Optimization. In: NIPS, pp. 345–352 (2008)
Freund, Y., Schapire, R.E.: A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting. J. Comput. Syst. Sci. 55(1), 119–139 (1997)
Hazan, E., Kale, S.: Extracting certainty from uncertainty: Regret bounded by variation in costs. Machine Learning 80(2-3), 165–188 (2010)
Hazan, E., Kale, S.: Better Algorithms for Benign Bandits. Journal of Machine Learning Research 12, 1287–1311 (2011)
Littlestone, N., Warmuth, M.K.: The Weighted Majority Algorithm. Inf. Comput. 108(2), 212–261 (1994)
Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Softw. 11(1), 37–57 (1985)
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Lee, CJ., Tsai, SC., Yang, MC. (2014). Online Prediction Problems with Variation. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_5
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DOI: https://doi.org/10.1007/978-3-319-08783-2_5
Publisher Name: Springer, Cham
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