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Documents authored by Orecchia, Lorenzo

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.49
Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game

Authors: Antares Chen, Lorenzo Orecchia, and Erasmo Tani

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Despite there being significant work on developing spectral- [Chan et al., 2018; Lau et al., 2023; Kwok et al., 2022], and metric-embedding-based [Louis and Makarychev, 2016] approximation algorithms for hypergraph conductance, little is known regarding the approximability of other hypergraph partitioning objectives. This work proposes algorithms for a general model of hypergraph partitioning that unifies both undirected and directed versions of many well-studied partitioning objectives. The first contribution of this paper introduces polymatroidal cut functions, a large class of cut functions amenable to approximation algorithms via metric embeddings and routing multicommodity flows. We demonstrate a simple O(√{log n})-approximation, where n is the number of vertices in the hypergraph, for these problems by rounding relaxations to metrics of negative-type. The second contribution of this paper generalizes the cut-matching game framework of Khandekar et al. [Khandekar et al., 2007] to tackle polymatroidal cut functions. This yields an almost-linear time O(log n)-approximation algorithm for standard versions of undirected and directed hypergraph partitioning [Kwok et al., 2022]. A technical contribution of our construction is a novel cut-matching game, which greatly relaxes the set of allowed actions by the cut player and allows for the use of approximate s-t maximum flows by the matching player. We believe this to be of independent interest.
Cite as

Antares Chen, Lorenzo Orecchia, and Erasmo Tani. Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.49,
  author =	{Chen, Antares and Orecchia, Lorenzo and Tani, Erasmo},
  title =	{{Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{49:1--49:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.49},
  URN =		{urn:nbn:de:0030-drops-234261},
  doi =		{10.4230/LIPIcs.ICALP.2025.49},
  annote =	{Keywords: Hypergraph Partitioning, Cut Improvement, Cut-Matching Game}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.23
Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Method

Authors: Jelena Diakonikolas and Lorenzo Orecchia

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We provide a novel accelerated first-order method that achieves the asymptotically optimal convergence rate for smooth functions in the first-order oracle model. To this day, Nesterov's Accelerated Gradient Descent (AGD) and variations thereof were the only methods achieving acceleration in this standard blackbox model. In contrast, our algorithm is significantly different from AGD, as it relies on a predictor-corrector approach similar to that used by Mirror-Prox [Nemirovski, 2004] and Extra-Gradient Descent [Korpelevich, 1977] in the solution of convex-concave saddle point problems. For this reason, we dub our algorithm Accelerated Extra-Gradient Descent (AXGD). Its construction is motivated by the discretization of an accelerated continuous-time dynamics [Krichene et al., 2015] using the classical method of implicit Euler discretization. Our analysis explicitly shows the effects of discretization through a conceptually novel primal-dual viewpoint. Moreover, we show that the method is quite general: it attains optimal convergence rates for other classes of objectives (e.g., those with generalized smoothness properties or that are non-smooth and Lipschitz-continuous) using the appropriate choices of step lengths. Finally, we present experiments showing that our algorithm matches the performance of Nesterov's method, while appearing more robust to noise in some cases.
Cite as

Jelena Diakonikolas and Lorenzo Orecchia. Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Method. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{diakonikolas_et_al:LIPIcs.ITCS.2018.23,
  author =	{Diakonikolas, Jelena and Orecchia, Lorenzo},
  title =	{{Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Method}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.23},
  URN =		{urn:nbn:de:0030-drops-83562},
  doi =		{10.4230/LIPIcs.ITCS.2018.23},
  annote =	{Keywords: Acceleration, dynamical systems, discretization, first-order methods}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.3
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent

Authors: Zeyuan Allen-Zhu and Lorenzo Orecchia

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. We observe that the performances of gradient and mirror descent are complementary, so that faster algorithms can be designed by "linearly coupling" the two. We show how to reconstruct Nesterov's accelerated gradient methods using linear coupling, which gives a cleaner interpretation than Nesterov's original proofs. We also discuss the power of linear coupling by extending it to many other settings that Nesterov's methods cannot apply to.
Cite as

Zeyuan Allen-Zhu and Lorenzo Orecchia. Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{allenzhu_et_al:LIPIcs.ITCS.2017.3,
  author =	{Allen-Zhu, Zeyuan and Orecchia, Lorenzo},
  title =	{{Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.3},
  URN =		{urn:nbn:de:0030-drops-81850},
  doi =		{10.4230/LIPIcs.ITCS.2017.3},
  annote =	{Keywords: linear coupling, gradient descent, mirror descent, acceleration}
}
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