I am interested in finding references that develop high probability suboptimality bounds for stochastic gradient descent (SGD) for **general** convex functions in the case where we return the average of the last $\alpha T$ iterates (suffix-averaging) where $\alpha\in(0,1)$ and $T$ denotes the total number of iterations. I have found [this](https://arxiv.org/pdf/1909.00843.pdf) source on suffix-averaging in the case of strongly-convex functions, but that's about it.



High probability bounds of SGD for general convex functions with suffix averaging
I didn't look very carefully. I found [this](https://www.cs.ubc.ca/%7Enickhar/papers/GradientDescent/GradientDescent.pdf) paper by Harvey et al (2018) demonstrating the result for general convex, 1-Lipschitz $f(\cdot)$.


