Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult
The paper argues that common similarity assumptions still cannot close the async optimization gap.
Alexander Tyurin shows that, for randomized algorithms, widely used first- and second-order similarity assumptions do not improve the pessimistic heterogeneous-case time complexities. The paper also says weak interpolation by itself is not enough. Its positive result needs strong interpolation plus a local Polyak-Lojasiewicz condition, yielding a time bound with the same worker-time dependence as the best known homogeneous result without identical data distributions. ArXiv · AI/CL/LG's note
Alexander Tyurin shows that, for randomized algorithms, widely used first- and second-order similarity assumptions do not improve the pessimistic heterogeneous-case time complexities. The paper also says weak interpolation by itself is not enough. Its positive result needs strong interpolation plus a local Polyak-Lojasiewicz condition, yielding a time bound with the same worker-time dependence as the best known homogeneous result without identical data distributions. ArXiv · AI/CL/LG's note
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