Slavomír Hanzely's scientific contributions

Publications (5)

Preprint
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In this work, we consider the problem of minimizing the sum of Moreau envelopes of given functions, which has previously appeared in the context of meta-learning and personalized federated learning. In contrast to the existing theory that requires running subsolvers until a certain precision is reached, we only assume that a finite number of gradie...
Preprint
In this paper, we present the first stepsize schedule for Newton method resulting in fast global and local convergence guarantees. In particular, a) we prove an $O\left( \frac 1 {k^2} \right)$ global rate, which matches the state-of-the-art global rate of cubically regularized Newton method of Polyak and Nesterov (2006) and of regularized Newton me...
Preprint
Full-text available
Despite their high computation and communication costs, Newton-type methods remain an appealing option for distributed training due to their robustness against ill-conditioned convex problems. In this work, we study ommunication compression and aggregation mechanisms for curvature information in order to reduce these costs while preserving theoreti...
Preprint
In this work, we consider the optimization formulation of personalized federated learning recently introduced by Hanzely and Richt\'arik (2020) which was shown to give an alternative explanation to the workings of local {\tt SGD} methods. Our first contribution is establishing the first lower bounds for this formulation, for both the communication...
Preprint
Recent advances in the theoretical understandingof SGD (Qian et al., 2019) led to a formula for the optimal mini-batch size minimizing the number of effective data passes, i.e., the number of iterations times the mini-batch size. However, this formula is of no practical value as it depends on the knowledge of the variance of the stochastic gradient...