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Ioannis Mitliagkas

Ioannis Mitliagkas contributes to research discovery and scholarly infrastructure.

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Machine Learning math.OC Artificial Intelligence Computer Science and Game Theory Computer Vision Cryptography and Security

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preprint2026arXiv

Navigating Potholes with Geometry-Aware Sharpness Minimization

Sharpness-aware minimization (SAM) encourages flat minima by perturbing parameters along directions of high loss curvature, but treats all parameter directions uniformly, ignoring the underlying loss geometry. We introduce LLQR+SAM, which combines SAM with a learned preconditioner obtained from the recently proposed LLQR framework, a second-order method that recasts steepest descent as a layerwise linear-quadratic regulator problem. The preconditioner is updated sparsely and maintained as a slow exponential moving average, so it captures a smoothed, low-resolution picture of the loss landscape geometry. The SAM perturbation then operates on top of this learned geometry, probing curvature at a faster timescale. We show that this two-timescale structure is not merely a computational convenience: theoretically, the preconditioner amplifies the SAM escape signal in directions that are flat under the average geometry but locally sharp (potholes). Wide, flat basins, by contrast, remain stable. Empirically, LLQR+SAM gives consistent gains over both SAM and LLQR alone across standard vision and sequence modeling benchmarks, supporting the view that slow learned geometry and fast sharpness correction are genuinely complementary.

preprint2026arXiv

Orth-Dion: Eliminating Geometric Mismatch in Distributed Low-Rank Spectral Optimization

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of power iteration followed by column normalization (rescaling each column of the right factor to unit length). This makes it compatible with fully sharded data parallel training, but it converges more slowly than full-rank spectral methods. We show that this gap is geometric: column normalization does not yield the rank-$r$ polar factor that Muon implicitly targets, so the resulting direction violates the dual-norm constraint of the low-rank spectral geometry, and the rate picks up an extra factor of $\sqrt{r}$ even though the low-rank approximation of the gradient itself is accurate. The same mismatch enters the smoothness term and the error-feedback recursion in the analysis, which has a knock-on effect on empirical performance. We propose Orth-Dion, which replaces column normalization with QR orthogonalization of the right factor. Under non-Euclidean smoothness, with $L_r$ the curvature constant along rank-$r$ directions, Orth-Dion attains rate $O(\sqrt{L_r/T})$, matching exact spectral methods at the same per-step communication cost as Dion. The proof removes the bounded-drift assumption common in prior error-feedback analyses via a self-consistent fixed-point argument, and uses a time-averaged contraction that only requires the error sequence to contract on average rather than at every step. Experiments on large-scale language model pre-training validate the predicted $\sqrt{r}$ scaling and show that Orth-Dion closes the convergence gap to Muon at Dion's communication cost.

preprint2026arXiv

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data

Noise-based certified machine unlearning currently faces a hard ceiling: the noise magnitude required to certify unlearning typically destroys model utility, particularly for large-scale deletion requests. While leveraging public data is a standard technique in differential privacy to relax this tension, its role in unlearning remains unexplored. We address this gap by introducing Asymmetric Langevin Unlearning (ALU), a framework that uses public data to mitigate privacy costs. We prove that public data injection suppresses the unlearning cost by a factor of $O(1/n_{\mathrm{pub}}^2)$, guaranteeing a strict computational advantage over retraining. This establishes a new control mechanism: practitioners can mitigate the need for high noise-and the associated utility loss-by increasing the volume of public data. Crucially, we analyze the realistic setting of distribution mismatch, explicitly characterizing how shifts between public and private sources impact utility. We show that ALU enables mass unlearning of constant dataset fractions -- a regime where standard symmetric methods become impractical -- while maintaining high utility. Empirical evaluations using variational Rényi divergence and membership inference attacks confirm that ALU effectively thwarts privacy attacks while preserving utility under reasonable distribution shifts.

preprint2022arXiv

Optimal transport meets noisy label robust loss and MixUp regularization for domain adaptation

It is common in computer vision to be confronted with domain shift: images which have the same class but different acquisition conditions. In domain adaptation (DA), one wants to classify unlabeled target images using source labeled images. Unfortunately, deep neural networks trained on a source training set perform poorly on target images which do not belong to the training domain. One strategy to improve these performances is to align the source and target image distributions in an embedded space using optimal transport (OT). However OT can cause negative transfer, i.e. aligning samples with different labels, which leads to overfitting especially in the presence of label shift between domains. In this work, we mitigate negative alignment by explaining it as a noisy label assignment to target images. We then mitigate its effect by appropriate regularization. We propose to couple the MixUp regularization \citep{zhang2018mixup} with a loss that is robust to noisy labels in order to improve domain adaptation performance. We show in an extensive ablation study that a combination of the two techniques is critical to achieve improved performance. Finally, we evaluate our method, called \textsc{mixunbot}, on several benchmarks and real-world DA problems.

preprint2021arXiv

In Search of Robust Measures of Generalization

One of the principal scientific challenges in deep learning is explaining generalization, i.e., why the particular way the community now trains networks to achieve small training error also leads to small error on held-out data from the same population. It is widely appreciated that some worst-case theories -- such as those based on the VC dimension of the class of predictors induced by modern neural network architectures -- are unable to explain empirical performance. A large volume of work aims to close this gap, primarily by developing bounds on generalization error, optimization error, and excess risk. When evaluated empirically, however, most of these bounds are numerically vacuous. Focusing on generalization bounds, this work addresses the question of how to evaluate such bounds empirically. Jiang et al. (2020) recently described a large-scale empirical study aimed at uncovering potential causal relationships between bounds/measures and generalization. Building on their study, we highlight where their proposed methods can obscure failures and successes of generalization measures in explaining generalization. We argue that generalization measures should instead be evaluated within the framework of distributional robustness.

preprint2020arXiv

A Tight and Unified Analysis of Gradient-Based Methods for a Whole Spectrum of Games

We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient method (OG) and consensus optimization (CO), which enjoy linear convergence in cases like bilinear games, where the standard GD fails. The full benefits of theses relatively new methods are not known as there is no unified analysis for both strongly monotone and bilinear games. We provide new analyses of the EG's local and global convergence properties and use is to get a tighter global convergence rate for OG and CO. Our analysis covers the whole range of settings between bilinear and strongly monotone games. It reveals that these methods converge via different mechanisms at these extremes; in between, it exploits the most favorable mechanism for the given problem. We then prove that EG achieves the optimal rate for a wide class of algorithms with any number of extrapolations. Our tight analysis of EG's convergence rate in games shows that, unlike in convex minimization, EG may be much faster than GD.

preprint2020arXiv

Accelerating Smooth Games by Manipulating Spectral Shapes

We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes restricted to the real line represent well-understood classes of problems, like minimization. Shapes spanning the complex plane capture the added numerical challenges in solving smooth games. In this framework, we describe gradient-based methods, such as extragradient, as transformations on the spectral shape. Using this perspective, we propose an optimal algorithm for bilinear games. For smooth and strongly monotone operators, we identify a continuum between convex minimization, where acceleration is possible using Polyak's momentum, and the worst case where gradient descent is optimal. Finally, going beyond first-order methods, we propose an accelerated version of consensus optimization.

preprint2020arXiv

Linear Lower Bounds and Conditioning of Differentiable Games

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower bounds to complement the linear (i.e. geometric) upper bounds observed in the literature on a wide class of problems. We cast saddle-point and min-max problems as 2-player games. We leverage tools from single-objective convex optimisation to propose new linear lower bounds for convex-concave games. Notably, we give a linear lower bound for $n$-player differentiable games, by using the spectral properties of the update operator. We then propose a new definition of the condition number arising from our lower bound analysis. Unlike past definitions, our condition number captures the fact that linear rates are possible in games, even in the absence of strong convexity or strong concavity in the variables.

preprint2020arXiv

Negative Momentum for Improved Game Dynamics

Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial networks (GANs) and actor-critic systems. However, compared to single-objective optimization, game dynamics are more complex and less understood. In this paper, we analyze gradient-based methods with momentum on simple games. We prove that alternating updates are more stable than simultaneous updates. Next, we show both theoretically and empirically that alternating gradient updates with a negative momentum term achieves convergence in a difficult toy adversarial problem, but also on the notoriously difficult to train saturating GANs.

preprint2020arXiv

Stochastic Hamiltonian Gradient Methods for Smooth Games

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain classes of stochastic smooth games. We propose a novel unbiased estimator for the stochastic Hamiltonian gradient descent (SHGD) and highlight its benefits. Using tools from the optimization literature we show that SHGD converges linearly to the neighbourhood of a stationary point. To guarantee convergence to the exact solution, we analyze SHGD with a decreasing step-size and we also present the first stochastic variance reduced Hamiltonian method. Our results provide the first global non-asymptotic last-iterate convergence guarantees for the class of stochastic unconstrained bilinear games and for the more general class of stochastic games that satisfy a "sufficiently bilinear" condition, notably including some non-convex non-concave problems. We supplement our analysis with experiments on stochastic bilinear and sufficiently bilinear games, where our theory is shown to be tight, and on simple adversarial machine learning formulations.

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