Publications#
Papers listed by type and year of publication or year of submission if unpublished.
Preprints#
Tighter performance theory of FedExProx
Authors: Wojciech Anyszka, Kaja Gruntkowska, Alexander Tyurin, Peter Richtárik
International Conference on Learning Representations, 2026
Abstract:
We revisit FedExProx — a recently proposed distributed optimization method designed to enhance convergence properties of parallel proximal algorithms via extrapolation. In the process, we uncover a surprising flaw: its known theoretical guarantees on quadratic optimization tasks are no better than those offered by the vanilla Gradient Descent (GD) method. Motivated by this observation, we develop a novel analysis framework, establishing a tighter linear convergence rate for non-strongly convex quadratic problems. By incorporating both computation and communication costs, we demonstrate that FedExProx can indeed provably outperform GD, in stark contrast to the original analysis. Furthermore, we consider partial participation scenarios and analyze two adaptive extrapolation strategies — based on gradient diversity and Polyak stepsizes — again significantly outperforming previous results. Moving beyond quadratics, we extend the applicability of our analysis to general functions satisfying the Polyak-Łojasiewicz condition, outperforming the previous strongly convex analysis while operating under weaker assumptions. Backed by empirical results, our findings point to a new and stronger potential of FedExProx, paving the way for further exploration of the benefits of extrapolation in federated learning.
We revisit FedExProx — a recently proposed distributed optimization method designed to enhance convergence properties of parallel proximal algorithms via extrapolation. In the process, we uncover a surprising flaw: its known theoretical guarantees on quadratic optimization tasks are no better than those offered by the vanilla Gradient Descent (GD) method. Motivated by this observation, we develop a novel analysis framework, establishing a tighter linear convergence rate for non-strongly convex quadratic problems. By incorporating both computation and communication costs, we demonstrate that FedExProx can indeed provably outperform GD, in stark contrast to the original analysis. Furthermore, we consider partial participation scenarios and analyze two adaptive extrapolation strategies — based on gradient diversity and Polyak stepsizes — again significantly outperforming previous results. Moving beyond quadratics, we extend the applicability of our analysis to general functions satisfying the Polyak-Łojasiewicz condition, outperforming the previous strongly convex analysis while operating under weaker assumptions. Backed by empirical results, our findings point to a new and stronger potential of FedExProx, paving the way for further exploration of the benefits of extrapolation in federated learning.
BibTeX:
@inproceedings{anyszka2026tighter,
title = {Tighter Performance Theory of {FedExProx}},
author = {Anyszka, Wojciech and Gruntkowska, Kaja and Tyurin, Alexander and Richt{\'a}rik, Peter},
booktitle = {International Conference on Learning Representations},
volume = {2026},
pages = {57131--57175},
year = {2026}
}Theses#
Investigating Stationarity Properties of the Signature Transform
Type: MSc dissertation (Mathematical Sciences)
Adviser: Zhongmin Qian
Institution: University of Oxford
Abstract:
The signature transform, a mathematical tool rooted in rough path theory, has gained prominence in machine learning due to its ability to extract informative features from time series data. This dissertation investigates the predictive utility of sliding signatures derived from stationary processes. We establish a novel theoretical result: the sliding signature transform preserves stationarity. Empirically, we confirm that log increments of foreign exchange prices are stationary, consistent with the Black–Scholes model, and demonstrate that sliding signatures of these increments retain stationarity in 51.3% of multidimensional cases and 93.0% of individual components. Predictive experiments indicate that models employing sliding signatures of log increments provide marginal improvements over those trained on raw prices. Although these signature-based models achieve low mean squared error and near-perfect R² values, their practical profitability is limited due to minimal returns and high variability. These findings suggest that while signature transforms offer theoretical and statistical advantages, translating these into meaningful practical outcomes remains challenging, highlighting the need for further research into their real-world applicability.
The signature transform, a mathematical tool rooted in rough path theory, has gained prominence in machine learning due to its ability to extract informative features from time series data. This dissertation investigates the predictive utility of sliding signatures derived from stationary processes. We establish a novel theoretical result: the sliding signature transform preserves stationarity. Empirically, we confirm that log increments of foreign exchange prices are stationary, consistent with the Black–Scholes model, and demonstrate that sliding signatures of these increments retain stationarity in 51.3% of multidimensional cases and 93.0% of individual components. Predictive experiments indicate that models employing sliding signatures of log increments provide marginal improvements over those trained on raw prices. Although these signature-based models achieve low mean squared error and near-perfect R² values, their practical profitability is limited due to minimal returns and high variability. These findings suggest that while signature transforms offer theoretical and statistical advantages, translating these into meaningful practical outcomes remains challenging, highlighting the need for further research into their real-world applicability.
BibTeX:
@mastersthesis{anyszka_signature_stationarity,
title = {Investigating Stationarity Properties of the Signature Transform},
author = {Anyszka, Wojciech},
school = {University of Oxford},
type = {MSc Dissertation in Mathematical Sciences},
advisor = {Qian, Zhongmin}
}The Kepler Problem and Its Relation to Extremal Black Holes
Type: Joint BSc thesis (Mathematics & Physics)
Advisers: Marcello Seri
and Diederik Roest
Institution: University of Groningen
Abstract:
This thesis explores the unique properties of the classical Kepler problem, including Bertrand's theorem, the connection between Kepler and harmonic oscillator potentials, and the existence of an additional conserved quantity — the Laplace–Runge–Lenz (LRL) vector. The role of symmetries in this context is explored. A comprehensive proof of Moser's construction is presented, establishing the correspondence between nonconstant geodesics on an n-dimensional sphere and Kepler orbits with negative energies. Relativistic corrections to two-body problems are investigated, with particular focus on an extremal test particle near an oppositely charged extremal Einstein–Maxwell–dilaton black hole. Notably, the absence of perihelion precession occurs only for a specific dilaton coupling, a = √3. Away from this value, the system corresponds to a perturbed Kepler problem.
This thesis explores the unique properties of the classical Kepler problem, including Bertrand's theorem, the connection between Kepler and harmonic oscillator potentials, and the existence of an additional conserved quantity — the Laplace–Runge–Lenz (LRL) vector. The role of symmetries in this context is explored. A comprehensive proof of Moser's construction is presented, establishing the correspondence between nonconstant geodesics on an n-dimensional sphere and Kepler orbits with negative energies. Relativistic corrections to two-body problems are investigated, with particular focus on an extremal test particle near an oppositely charged extremal Einstein–Maxwell–dilaton black hole. Notably, the absence of perihelion precession occurs only for a specific dilaton coupling, a = √3. Away from this value, the system corresponds to a perturbed Kepler problem.
BibTeX:
@bachelorsthesis{anyszka_kepler_black_holes,
title = {The Kepler Problem and Its Relation to Extremal Black Holes},
author = {Anyszka, Wojciech},
school = {University of Groningen},
type = {BSc Thesis},
url = {https://fse.studenttheses.ub.rug.nl/31614/}
}Towards an Approximation Theory of Observable Operator Models
Type: BSc thesis (Artificial Intelligence)
Adviser: Herbert Jaeger
Institution: University of Groningen
Abstract:
Observable operator models (OOMs) provide a powerful framework for modelling stochastic processes beyond hidden Markov models. This thesis develops a rigorous approximation theory for OOMs of infinite-dimensional processes. An inner product structure on the space of future distributions is established, and continuity of observable operators with respect to the induced 2-norm is proven. A fundamental obstruction to turning this space into a Hilbert space is identified, and a potential remedy is proposed, laying groundwork for future research on approximating infinite-dimensional observable operators.
Observable operator models (OOMs) provide a powerful framework for modelling stochastic processes beyond hidden Markov models. This thesis develops a rigorous approximation theory for OOMs of infinite-dimensional processes. An inner product structure on the space of future distributions is established, and continuity of observable operators with respect to the induced 2-norm is proven. A fundamental obstruction to turning this space into a Hilbert space is identified, and a potential remedy is proposed, laying groundwork for future research on approximating infinite-dimensional observable operators.
BibTeX:
@bachelorsthesis{anyszka_oom_approximation,
title = {Towards an Approximation Theory of Observable Operator Models},
author = {Anyszka, Wojciech},
school = {University of Groningen},
type = {BSc Thesis},
eprint = {2404.12070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.12070}
}