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Online Convex Optimization with Unconstrained Domains and Losses

2020-02-05 | |  39 |   42 |   0

Abstract 

We propose an online convex optimization algorithm (RESCALEDEXP) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation between the regret of existing algorithms that require a known bound on the loss functions and any algorithm that does not require such knowledge. RESCALEDEXP matches this lower bound asymptotically in the number of iterations. RESCALEDEXP is naturally hyperparameter-free and we demonstrate empirically that it matches prior optimization algorithms that require hyperparameter optimization.

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