_:n21f71838e43942f38d198d09f388ebdexb30
<http://schema.org/description>
"We introduce online learning with vector costs () where in each time\nstep t ∈{1,…, T}, we need to play an action i ∈{1,…,n}\nthat incurs an unknown vector cost in [0,1]^d. The goal of the online\nalgorithm is to minimize the ℓ_p norm of the sum of its cost vectors. This\ncaptures the classical online learning setting for d=1, and is interesting\nfor general d because of applications like online scheduling where we want to\nbalance the load between different machines (dimensions).\n  We study in both stochastic and adversarial arrival settings, and give\na general procedure to reduce the problem from d dimensions to a single\ndimension. This allows us to use classical online learning algorithms in both\nfull and bandit feedback models to obtain (near) optimal results. In\nparticular, we obtain a single algorithm (up to the choice of learning rate)\nthat gives sublinear regret for stochastic arrivals and a tight O(min{p,\nlog d}) competitive ratio for adversarial arrivals.\n  The problem also occurs as a natural subproblem when trying to solve\nthe popular Bandits with Knapsacks () problem. This connection allows us to\nuse our techniques to obtain (near) optimal results for in both\nstochastic and adversarial settings. In particular, we obtain a tight O(log d\n·log T) competitive ratio algorithm for adversarial , which improves\nover the O(d ·log T) competitive ratio algorithm of Immorlica et al.\n[FOCS'19]."
<https://api.deepai.org/profile/thomas-kesselheim>