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Optimal anytime regret with two experts
In the fixed-time setting, where the time horizon is known in advance, algorithms that achieve the optimal regret are known when there are two, three, or four experts or when the number of experts is large.
Simple and optimal high-probability bounds for strongly-convex stochastic gradient descent
We consider a simple, non-uniform averaging strategy of Lacoste-Julien et al. (2011) and prove that it achieves the optimal $O(1/T)$ convergence rate with high probability.
Tight Analyses for Non-Smooth Stochastic Gradient Descent
We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with high probability.
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