With coocmap, 10-40MB of text data and a few minutes of CPU time is sufficient to achieve unsupervised word translation if the training corpora are in the same domain (e.g. both on

We study the problem of switching-constrained online convex optimization (OCO), where the player has a limited number of opportunities to change her action. While the discrete analog of this online learning task has been studied extensively, previous work in the continuous setting has neither established the minimax rate nor algorithmically achieved it. In this paper, we show that $ T $-round switching-constrained OCO with fewer than $ K $ switches has a minimax regret of $ \Theta(\frac{T}{\sqrt{K}}) $. In particular, it is at least $ \frac{T}{\sqrt{2K}} $ for one dimension and at least $ \frac{T}{\sqrt{K}} $ for higher dimensions. The lower bound in higher dimensions is attained by an orthogonal subspace argument.

We thank the reviewers for their helpful comments. We first provide individual responses to each reviewer's comments For example, one could easily apply this method to the last row of a neural network. We will make the suggested changes to improve the writing. We will make this reference in the text of the paper. The reviewer correctly points out that [19] doesn't estimate individual densities but directly estimates the weight.

With coocmap, 10-40MB of text data and a few minutes of CPU time is sufficient to achieve unsupervised word translation if the training corpora are in the same domain (e.g. both on

We thank the reviewers for their kind and thoughtful comments on our work. Below, we respond to reviewer-specific comments. Our claim that a standard multilayer perceptron "fails to learn high frequencies in theory" is based on the theoretical For example, in the abstract, modifying "a standard MLP fails to learn high frequencies both We directly extend the 1D experiment in Figure 4 to a two-dimensional setting in Section 1.4 of the supplement, and