arXiv subjects

Ashkan Soleymani

Publications and source records attributed to Ashkan Soleymani.

At least 19 recordsLinked to original sources

arXiv2026

On Lipschitz Explosion in Deep Neural Networks with Normalization: Consequences for Optimization and Adversarial Robustness

Can a network look stable at every layer and still be exponentially unstable as a whole? The Lipschitz constant of a neural network is a basic stability quantity appearing in optimization guarantees, generalization bounds, and robustness certificates. Deep networks naturally admit two such notions, input Lipschitzness, measuring sensitivity to data perturbations, and parameter Lipschitzness, measuring sensitivity to weight perturbations. We prove that, for deep networks with normalization layers, with batch normalization as the canonical example, both Lipschitz constants can grow exponentially with depth and hence with parameter dimension, even under strong per-layer norm control such as $\|W_\ell\|_2\le 1$, and already for linear activations. Thus, a mechanism widely used to stabilize training can create severe worst-case instabilities that are invisible locally, i.e., from layerwise norm bounds alone. Parameter-Lipschitz explosion turns Lipschitz-dependent nonsmooth optimization guarantees into exponential-in-dimension bounds for deep normalized networks, while input-Lipschitz explosion makes worst-case Lipschitz-based generalization and robustness certificates vacuous. The latter also yields a concrete rank-separation mechanism for adversarial vulnerability. The theory predicts that perturbations introducing new singular directions should be amplified much more strongly than perturbations at the same noise level that remain within the input's original singular subspace. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 support this prediction, showing that rank-creating perturbations cause substantially sharper drops in accuracy, confidence, and margins than same-subspace perturbations.

cs.LG↗

arXiv2026

A Quasipolynomial Algorithm for $\ell_\infty$ Contractions

We give an algorithm for computing an $\eps$-approximate fixed point of any $d$-dimensional nonexpansion with respect to the $\ell_\infty$ norm in time $\log(1/\eps)^{O(\log^2 d)}$. At its core, our method uses a boosting argument to geometrically shrink a search region. Among other consequences, our algorithm implies that simple stochastic games can be solved in quasipolynomial time.

cs.GT↗

arXiv2026

Breaking the 1/3 Barrier for Approximate Nash Equilibria in Symmetric Bimatrix Games

We give the first unconditional family of polynomial-time algorithms that breaks the $1/3$ approximation barrier for symmetric bimatrix games. For every fixed $δ>0$, an algorithm in this family computes a symmetric $(1-1/\sqrt{2}+δ)$-approximate Nash equilibrium, improving on the previous best guarantee of $(1/3+δ)$ due to Kontogiannis and Spirakis [2011].

cs.GT↗

arXiv2026

Exact-Form Regret for Gradient Descent, Mirror Descent and Follow-the-Regularized-Leader

Online gradient descent is usually studied through external regret, where the learner competes with fixed alternatives. Recent work shows that first-order methods control richer action-dependent deviations. We ask for a geometric characterization of the deviations with respect to which online gradient descent, mirror descent, and follow-the-regularized-leader (FTRL) achieve no regret. We identify exactness as the common principle. Exactness means that the relevant displacement field is generated by a scalar potential, or equivalently that the associated one-form is exact in the geometry used by the algorithm. This geometry depends on the algorithm. For gradient descent it is Euclidean geometry, for mirror descent it is the geometry induced by the regularizer, and for FTRL it is the cumulative dual state. Under mild regularity conditions, exactness yields sublinear regret, while nonzero circulation provides the complementary obstruction and leads to linear regret. This gives a unified geometric framework for understanding the deviation classes controlled by these algorithms and reveals that different first-order methods can control genuinely different classes of deviations. These deviation classes have direct consequences for learning, particularly in games. We study the equilibrium notions induced by exact-form deviations and introduce conservative correlated equilibrium, reflecting both the conservative geometry of the underlying displacement fields and the restricted family of deviations available to the players. We characterize its relation to correlated equilibrium, determine when the resulting equilibrium notions coincide and when they separate, and show how these relationships depend on the geometry and the learning algorithm. Overall, this work gives a unified geometric account of what first-order online learning algorithms are no-regret with respect to, beyond fixed comparators.

cs.LG↗

arXiv2026

Multiplicative Optimism for Constant Regret in Games

We introduce Multiplicatively Optimistic Regret Matching (MORM), an uncoupled learning rule for finite general-sum games. Under simultaneous full-information self-play, every player achieves external regret $O(\sqrt n\log d)$ uniformly over all horizons, using only one-step optimism. The analysis combines a potential-based regret-matching argument with multiplicative stability and Hellinger control of strategy movement. A learning-rate safeguard additionally gives $O(\sqrt{T\log d})$ regret in the face of adversarial utilities.

cs.GT↗

arXiv2026

Efficient Learning and Symmetry Discovery under Exact Invariances

Learning with group invariances is central to many scientific and geometric learning problems, yet its computational foundations remain poorly understood. Even for classical supervised regression settings, it has been unclear whether one can efficiently compute a regression function that is exactly invariant to a given group action. Recent work showed that exact invariance can be enforced in polynomial time when the underlying group is finite and known, but left open the cases of infinite groups and unknown symmetries. In this paper, we resolve both challenges. First, we present the first polynomial-time algorithm for learning with exact group invariances that applies uniformly to finite and infinite groups. The runtime is polynomial in the data dimension and sample size, and independent of the group, while achieving strong generalization guarantees. This provides a computational explanation for the empirical success of invariant and equivariant methods in geometric machine learning and partially answers a recent open question in the literature. Second, we study learning in the symmetry discovery setting, where the invariance group is unknown. Focusing on the subgroup lattice of a finite group, we show that exact symmetries can be identified from data and exploited for learning in polynomial time. For regression over finite-dimensional feature spaces, our algorithm provably recovers the underlying symmetry, matches the minimax-optimal sample complexity of the known-symmetry setting, and runs in time polynomial in the data dimension and sample size. Our analysis relies on tools from random Cayley graphs and expander theory, which may be of independent interest.

cs.LG↗

arXiv2026

Algorithmic Optimality Guarantees for Nonsmooth $H_\infty$ Output-Feedback Policy Search

We study continuous-time full-order dynamic output-feedback $H_\infty$ policy search, a nonconvex and nonsmooth problem. Direct policy search is a central paradigm in reinforcement learning and continuous control, but rigorous guarantees remain scarce in robust output-feedback settings. The $H_\infty$ problem is a canonical benchmark because it captures disturbance attenuation and robustness while exposing the hard nonsmooth geometry of policy-space optimization. We prove that on the exact identity-gauge slice of the extended convex lift, $\varepsilon$-stationarity yields $O(\varepsilon)$-suboptimality on compact exact slices, which in turn yields convergence-rate guarantees for nonsmooth policy-search methods. This result addresses the finite-time optimality-gap question raised by Guo and Hu [2022] in the more general dynamic output-feedback $H_\infty$ policy-search setting. We further use the established value equivalence supplied by extended convex lifting to formulate a nonstrict-feasibility bisection method with one final strict-feasibility recovery step, yielding an explicit $\varepsilon$-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth $H_\infty$ policy search.

math.OC↗

arXiv2025

Cautious Optimism: A Meta-Algorithm for Near-Constant Regret in General Games

We introduce Cautious Optimism, a framework for substantially faster regularized learning in general games. Cautious Optimism, as a variant of Optimism, adaptively controls the learning pace in a dynamic, non-monotone manner to accelerate no-regret learning dynamics. Cautious Optimism takes as input any instance of Follow-the-Regularized-Leader (FTRL) and outputs an accelerated no-regret learning algorithm (COFTRL) by pacing the underlying FTRL with minimal computational overhead. Importantly, it retains uncoupledness, that is, learners do not need to know other players' utilities. Cautious Optimistic FTRL (COFTRL) achieves near-optimal $O_T(\log T)$ regret in diverse self-play (mixing and matching regularizers) while preserving the optimal $O_T(\sqrt{T})$ regret in adversarial scenarios. In contrast to prior works (e.g., Syrgkanis et al. [2015], Daskalakis et al. [2021]), our analysis does not rely on monotonic step sizes, showcasing a novel route for fast learning in general games. Moreover, instances of COFTRL achieve new state-of-the-art regret minimization guarantees in general convex games, exponentially improving the dependence on the dimension of the action space $d$ over previous works [Farina et al., 2022a].

cs.LG↗

arXiv2025

Double Machine Learning Based Structure Identification from Temporal Data

Learning the causes of time-series data is a fundamental task in many applications, spanning from finance to earth sciences or bio-medical applications. Common approaches for this task are based on vector auto-regression, and they do not take into account unknown confounding between potential causes. However, in settings with many potential causes and noisy data, these approaches may be substantially biased. Furthermore, potential causes may be correlated in practical applications or even contain cycles. To address these challenges, we propose a new double machine learning based method for structure identification from temporal data (DR-SIT). We provide theoretical guarantees, showing that our method asymptotically recovers the true underlying causal structure. Our analysis extends to cases where the potential causes have cycles, and they may even be confounded. We further perform extensive experiments to showcase the superior performance of our method. Code: https://github.com/sdi1100041/TMLR_submission_DR_SIT

cs.LG↗

arXiv2025

Data Generation without Function Estimation

Estimating the score function (or other population-density-dependent functions) is a fundamental component of most generative models. However, such function estimation is computationally and statistically challenging. Can we avoid function estimation for data generation? We propose an estimation-free generative method: A set of points whose locations are deterministically updated with (inverse) gradient descent can transport a uniform distribution to arbitrary data distribution, in the mean field regime, without function estimation, training neural networks, and even noise injection. The proposed method is built upon recent advances in the physics of interacting particles. We show, both theoretically and experimentally, that these advances can be leveraged to develop novel generative methods.

cs.LG↗

arXiv2025

Double Machine Learning for Conditional Moment Restrictions: IV Regression, Proximal Causal Learning and Beyond

Solving conditional moment restrictions (CMRs) is a key problem considered in statistics, causal inference, and econometrics, where the aim is to solve for a function of interest that satisfies some conditional moment equalities. Specifically, many techniques for causal inference, such as instrumental variable (IV) regression and proximal causal learning (PCL), are CMR problems. Most CMR estimators use a two-stage approach, where the first-stage estimation is directly plugged into the second stage to estimate the function of interest. However, naively plugging in the first-stage estimator can cause heavy bias in the second stage. This is particularly the case for recently proposed CMR estimators that use deep neural network (DNN) estimators for both stages, where regularisation and overfitting bias is present. We propose DML-CMR, a two-stage CMR estimator that provides an unbiased estimate with fast convergence rate guarantees. We derive a novel learning objective to reduce bias and develop the DML-CMR algorithm following the double/debiased machine learning (DML) framework. We show that our DML-CMR estimator can achieve the minimax optimal convergence rate of $O(N^{-1/2})$ under parameterisation and mild regularity conditions, where $N$ is the sample size. We apply DML-CMR to a range of problems using DNN estimators, including IV regression and proximal causal learning on real-world datasets, demonstrating state-of-the-art performance against existing CMR estimators and algorithms tailored to those problems.

stat.ML↗

arXiv2025

Faster Rates for No-Regret Learning in General Games via Cautious Optimism

We establish the first uncoupled learning algorithm that attains $O(n \log^2 d \log T)$ per-player regret in multi-player general-sum games, where $n$ is the number of players, $d$ is the number of actions available to each player, and $T$ is the number of repetitions of the game. Our results exponentially improve the dependence on $d$ compared to the $O(n\, d \log T)$ regret attainable by Log-Regularized Lifted Optimistic FTRL [Far+22c], and also reduce the dependence on the number of iterations $T$ from $\log^4 T$ to $\log T$ compared to Optimistic Hedge, the previously well-studied algorithm with $O(n \log d \log^4 T)$ regret [DFG21]. Our algorithm is obtained by combining the classic Optimistic Multiplicative Weights Update (OMWU) with an adaptive, non-monotonic learning rate that paces the learning process of the players, making them more cautious when their regret becomes too negative.

cs.GT↗

arXiv2025

Learning with Exact Invariances in Polynomial Time

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either fail to provide a polynomial-time solution or are not applicable in the kernel setting. However, with oracle access to the geometric properties of the input space, we propose a polynomial-time algorithm that learns a classifier with \emph{exact} invariances. Moreover, our approach achieves the same excess population risk (or generalization error) as the original kernel regression problem. To the best of our knowledge, this is the first polynomial-time algorithm to achieve exact (not approximate) invariances in this context. Our proof leverages tools from differential geometry, spectral theory, and optimization. A key result in our development is a new reformulation of the problem of learning under invariances as optimizing an infinite number of linearly constrained convex quadratic programs, which may be of independent interest.

cs.LG↗

arXiv2024

Learning Decision Policies with Instrumental Variables through Double Machine Learning

A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded variable known as the instrument, is a standard technique for learning causal relationships between confounded action, outcome, and context variables. Most recent IV regression algorithms use a two-stage approach, where a deep neural network (DNN) estimator learnt in the first stage is directly plugged into the second stage, in which another DNN is used to estimate the causal effect. Naively plugging the estimator can cause heavy bias in the second stage, especially when regularisation bias is present in the first stage estimator. We propose DML-IV, a non-linear IV regression method that reduces the bias in two-stage IV regressions and effectively learns high-performing policies. We derive a novel learning objective to reduce bias and design the DML-IV algorithm following the double/debiased machine learning (DML) framework. The learnt DML-IV estimator has strong convergence rate and $O(N^{-1/2})$ suboptimality guarantees that match those when the dataset is unconfounded. DML-IV outperforms state-of-the-art IV regression methods on IV regression benchmarks and learns high-performing policies in the presence of instruments.

cs.LG↗

arXiv2024

A Universal Class of Sharpness-Aware Minimization Algorithms

Recently, there has been a surge in interest in developing optimization algorithms for overparameterized models as achieving generalization is believed to require algorithms with suitable biases. This interest centers on minimizing sharpness of the original loss function; the Sharpness-Aware Minimization (SAM) algorithm has proven effective. However, most literature only considers a few sharpness measures, such as the maximum eigenvalue or trace of the training loss Hessian, which may not yield meaningful insights for non-convex optimization scenarios like neural networks. Additionally, many sharpness measures are sensitive to parameter invariances in neural networks, magnifying significantly under rescaling parameters. Motivated by these challenges, we introduce a new class of sharpness measures in this paper, leading to new sharpness-aware objective functions. We prove that these measures are \textit{universally expressive}, allowing any function of the training loss Hessian matrix to be represented by appropriate hyperparameters. Furthermore, we show that the proposed objective functions explicitly bias towards minimizing their corresponding sharpness measures, and how they allow meaningful applications to models with parameter invariances (such as scale-invariances). Finally, as instances of our proposed general framework, we present \textit{Frob-SAM} and \textit{Det-SAM}, which are specifically designed to minimize the Frobenius norm and the determinant of the Hessian of the training loss, respectively. We also demonstrate the advantages of our general framework through extensive experiments.

cs.LG↗

arXiv2023

DRCFS: Doubly Robust Causal Feature Selection

Knowing the features of a complex system that are highly relevant to a particular target variable is of fundamental interest in many areas of science. Existing approaches are often limited to linear settings, sometimes lack guarantees, and in most cases, do not scale to the problem at hand, in particular to images. We propose DRCFS, a doubly robust feature selection method for identifying the causal features even in nonlinear and high dimensional settings. We provide theoretical guarantees, illustrate necessary conditions for our assumptions, and perform extensive experiments across a wide range of simulated and semi-synthetic datasets. DRCFS significantly outperforms existing state-of-the-art methods, selecting robust features even in challenging highly non-linear and high-dimensional problems.

cs.LG↗

arXiv2022

Causal Feature Selection via Orthogonal Search

The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. However, established approaches often scale at least exponentially with the number of explanatory variables, are difficult to extend to nonlinear relationships, and are difficult to extend to cyclic data. Inspired by {\em Debiased} machine learning methods, we study a one-vs.-the-rest feature selection approach to discover the direct causal parent of the response. We propose an algorithm that works for purely observational data while also offering theoretical guarantees, including the case of partially nonlinear relationships possibly under the presence of cycles. As it requires only one estimation for each variable, our approach is applicable even to large graphs. We demonstrate significant improvements compared to established approaches.

stat.ML↗

arXiv2022

Federated Learning in Multi-Center Critical Care Research: A Systematic Case Study using the eICU Database

Federated learning (FL) has been proposed as a method to train a model on different units without exchanging data. This offers great opportunities in the healthcare sector, where large datasets are available but cannot be shared to ensure patient privacy. We systematically investigate the effectiveness of FL on the publicly available eICU dataset for predicting the survival of each ICU stay. We employ Federated Averaging as the main practical algorithm for FL and show how its performance changes by altering three key hyper-parameters, taking into account that clients can significantly vary in size. We find that in many settings, a large number of local training epochs improves the performance while at the same time reducing communication costs. Furthermore, we outline in which settings it is possible to have only a low number of hospitals participating in each federated update round. When many hospitals with low patient counts are involved, the effect of overfitting can be avoided by decreasing the batchsize. This study thus contributes toward identifying suitable settings for running distributed algorithms such as FL on clinical datasets.

cs.LG↗