Vyacheslav Kungurtsev

Saeed Vahidian, Mahdi Morafah, Weijia Wang et al.

Clustered federated learning (FL) has been shown to produce promising results by grouping clients into clusters. This is especially effective in scenarios where separate groups of clients have significant differences in the distributions of their local data. Existing clustered FL algorithms are essentially trying to group together clients with similar distributions so that clients in the same cluster can leverage each other's data to better perform federated learning. However, prior clustered FL algorithms attempt to learn these distribution similarities indirectly during training, which can be quite time consuming as many rounds of federated learning may be required until the formation of clusters is stabilized. In this paper, we propose a new approach to federated learning that directly aims to efficiently identify distribution similarities among clients by analyzing the principal angles between the client data subspaces. Each client applies a truncated singular value decomposition (SVD) step on its local data in a single-shot manner to derive a small set of principal vectors, which provides a signature that succinctly captures the main characteristics of the underlying distribution. This small set of principal vectors is provided to the server so that the server can directly identify distribution similarities among the clients to form clusters. This is achieved by comparing the similarities of the principal angles between the client data subspaces spanned by those principal vectors. The approach provides a simple, yet effective clustered FL framework that addresses a broad range of data heterogeneity issues beyond simpler forms of Non-IIDness like label skews. Our clustered FL approach also enables convergence guarantees for non-convex objectives. Our code is available at https://github.com/MMorafah/PACFL.

Jianyang Gu, Saeed Vahidian, Vyacheslav Kungurtsev et al.

Dataset distillation reduces the storage and computational consumption of training a network by generating a small surrogate dataset that encapsulates rich information of the original large-scale one. However, previous distillation methods heavily rely on the sample-wise iterative optimization scheme. As the images-per-class (IPC) setting or image resolution grows larger, the necessary computation will demand overwhelming time and resources. In this work, we intend to incorporate generative diffusion techniques for computing the surrogate dataset. Observing that key factors for constructing an effective surrogate dataset are representativeness and diversity, we design additional minimax criteria in the generative training to enhance these facets for the generated images of diffusion models. We present a theoretical model of the process as hierarchical diffusion control demonstrating the flexibility of the diffusion process to target these criteria without jeopardizing the faithfulness of the sample to the desired distribution. The proposed method achieves state-of-the-art validation performance while demanding much less computational resources. Under the 100-IPC setting on ImageWoof, our method requires less than one-twentieth the distillation time of previous methods, yet yields even better performance. Source code and generated data are available in https://github.com/vimar-gu/MinimaxDiffusion.

Bapi Chatterjee, Vyacheslav Kungurtsev, Dan Alistarh

Powered by the simplicity of lock-free asynchrony, Hogwilld! is a go-to approach to parallelize SGD over a shared-memory setting. Despite its popularity and concomitant extensions, such as PASSM+ wherein concurrent processes update a shared model with partitioned gradients, scaling it to decentralized workers has surprisingly been relatively unexplored. To our knowledge, there is no convergence theory of such methods, nor systematic numerical comparisons evaluating speed-up. In this paper, we propose an algorithm incorporating decentralized distributed memory computing architecture with each node running multiprocessing parallel shared-memory SGD itself. Our scheme is based on the following algorithmic tools and features: (a) asynchronous local gradient updates on the shared-memory of workers, (b) partial backpropagation, and (c) non-blocking in-place averaging of the local models. We prove that our method guarantees ergodic convergence rates for non-convex objectives. On the practical side, we show that the proposed method exhibits improved throughput and competitive accuracy for standard image classification benchmarks on the CIFAR-10, CIFAR-100, and Imagenet datasets. Our code is available at https://github.com/bapi/LPP-SGD.

Daniel Mastropietro, Vyacheslav Kungurtsev

High intermittent renewable penetration in the energy mix presents challenges in robustness for the management of power systems' operation. If a tail realization of the distribution of weather yields a prolonged period of time during which solar irradiation and wind speed are insufficient for satisfying energy demand, then it becomes critical to ramp up the generation of conventional power plants with adequate foresight. This event trigger is costly, and inaccurate forecasting can either be wasteful or yield catastrophic undersupply. This encourages particular attention to accurate modeling of the noise and the resulting dynamics within the aforementioned scenario. In this work we present a method for rare event-aware control of power systems using multi-stage scenario-based stochastic programming. A Fleming-Viot particle approach is used to bias the scenario generation towards rare realizations of very low wind power, in order to obtain a cost-effective control of conventional power plants that is robust under prolonged renewable energy shortfalls.

Mahdi Morafah, Vyacheslav Kungurtsev, Hojin Chang et al.

Federated Learning has emerged as a promising paradigm for collaborative machine learning, while preserving user data privacy. Despite its potential, standard FL lacks support for diverse heterogeneous device prototypes, which vary significantly in model and dataset sizes -- from small IoT devices to large workstations. This limitation is only partially addressed by existing knowledge distillation techniques, which often fail to transfer knowledge effectively across a broad spectrum of device prototypes with varied capabilities. This failure primarily stems from two issues: the dilution of informative logits from more capable devices by those from less capable ones, and the use of a single integrated logits as the distillation target across all devices, which neglects their individual learning capacities and and the unique contributions of each. To address these challenges, we introduce TAKFL, a novel KD-based framework that treats the knowledge transfer from each device prototype's ensemble as a separate task, independently distilling each to preserve its unique contributions and avoid dilution. TAKFL also incorporates a KD-based self-regularization technique to mitigate the issues related to the noisy and unsupervised ensemble distillation process. To integrate the separately distilled knowledge, we introduce an adaptive task arithmetic knowledge integration process, allowing each student model to customize the knowledge integration for optimal performance. Additionally, we present theoretical results demonstrating the effectiveness of task arithmetic in transferring knowledge across heterogeneous devices with varying capacities. Comprehensive evaluations of our method across both CV and NLP tasks demonstrate that TAKFL achieves SOTA results in a variety of datasets and settings, significantly outperforming existing KD-based methods Code is released at https://github.com/MMorafah/TAKFL

Saeed Vahidian, Sreevatsank Kadaveru, Woonjoon Baek et al.

An oft-cited open problem of federated learning is the existence of data heterogeneity at the clients. One pathway to understanding the drastic accuracy drop in federated learning is by scrutinizing the behavior of the clients' deep models on data with different levels of "difficulty", which has been left unaddressed. In this paper, we investigate a different and rarely studied dimension of FL: ordered learning. Specifically, we aim to investigate how ordered learning principles can contribute to alleviating the heterogeneity effects in FL. We present theoretical analysis and conduct extensive empirical studies on the efficacy of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random curriculum. We find that curriculum learning largely alleviates non-IIDness. Interestingly, the more disparate the data distributions across clients the more they benefit from ordered learning. We provide analysis explaining this phenomenon, specifically indicating how curriculum training appears to make the objective landscape progressively less convex, suggesting fast converging iterations at the beginning of the training procedure. We derive quantitative results of convergence for both convex and nonconvex objectives by modeling the curriculum training on federated devices as local SGD with locally biased stochastic gradients. Also, inspired by ordered learning, we propose a novel client selection technique that benefits from the real-world disparity in the clients. Our proposed approach to client selection has a synergic effect when applied together with ordered learning in FL.

Frank E. Curtis, Vyacheslav Kungurtsev, Daniel P. Robinson et al.

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth nonconvex optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique in its use of inner neighborhoods of the feasible region -- defined by a positive and vanishing neighborhood-parameter sequence -- in which the iterates are forced to remain. It is shown that with a careful balance between the barrier, step-size, and neighborhood sequences, the proposed algorithm satisfies convergence guarantees in both deterministic and stochastic settings. The results of numerical experiments show that in both settings the algorithm can outperform projection-based methods.

Diyuan Wu, Vyacheslav Kungurtsev, Marco Mondelli

The stochastic heavy ball method (SHB), also known as stochastic gradient descent (SGD) with Polyak's momentum, is widely used in training neural networks. However, despite the remarkable success of such algorithm in practice, its theoretical characterization remains limited. In this paper, we focus on neural networks with two and three layers and provide a rigorous understanding of the properties of the solutions found by SHB: \emph{(i)} stability after dropping out part of the neurons, \emph{(ii)} connectivity along a low-loss path, and \emph{(iii)} convergence to the global optimum. To achieve this goal, we take a mean-field view and relate the SHB dynamics to a certain partial differential equation in the limit of large network widths. This mean-field perspective has inspired a recent line of work focusing on SGD while, in contrast, our paper considers an algorithm with momentum. More specifically, after proving existence and uniqueness of the limit differential equations, we show convergence to the global optimum and give a quantitative bound between the mean-field limit and the SHB dynamics of a finite-width network. Armed with this last bound, we are able to establish the dropout-stability and connectivity of SHB solutions.

Fabio V. Difonzo, Vyacheslav Kungurtsev, Jakub Marecek

Stochastic differential equations of Langevin-diffusion form have received significant attention, thanks to their foundational role in both Bayesian sampling algorithms and optimization in machine learning. In the latter, they serve as a conceptual model of the stochastic gradient flow in training over-parameterized models. However, the literature typically assumes smoothness of the potential, whose gradient is the drift term. Nevertheless, there are many problems for which the potential function is not continuously differentiable, and hence the drift is not Lipschitz continuous everywhere. This is exemplified by robust losses and Rectified Linear Units in regression problems. In this paper, we show some foundational results regarding the flow and asymptotic properties of Langevin-type Stochastic Differential Inclusions under assumptions appropriate to the machine-learning settings. In particular, we show strong existence of the solution, as well as an asymptotic minimization of the canonical free-energy functional.

Johannes Aspman, Vyacheslav Kungurtsev, Reza Roohi Seraji

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a geometric category when generalized to manifolds, exhibits some structure that enables theoretical guarantees of expected function decrease and asymptotic convergence for generic stochastic sub-gradient descent. Recent work has shown that this class of functions faithfully model the loss landscape of deep neural network training objectives, and the autograd operation used in deep learning packages implements a variant of subgradient descent with the correct properties for convergence. Riemannian optimization uses geometric properties of a constraint set to perform a minimization procedure while enforcing adherence to the the optimization variable lying on a Riemannian manifold. This paper presents the first study of tame optimization on Riemannian manifolds, highlighting the rich geometric structure of the problem and confirming the appropriateness of the canonical "SGD" for such a problem with the analysis and numerical reports of a simple Retracted SGD algorithm.

Dylan Waldner, Vyacheslav Kungurtsev, Mitchelle Ashimosi

This paper investigates the dynamics of noncooperative interactions between artificial intelligence agents and human decision-makers in strategic environments. In particular, motivated by extensive literature in behavioral Economics, human agents are more faithfully modeled with respect to the state of the art using Prospect Theoretic preferences, while AI agents are modeled with standard expected utility maximization. Prospect Theory incorporates known cognitive heuristics employed by humans, including reference dependence and greater loss aversion relative to utility to relative gains. This paper runs different combinations of expected utility and prospect theoretic agents in a number of classic matrix games as well as examples specialized to tease out distinctions in strategic behavior with respect to preference functions, to explore the emergent behaviors from mixed population (human vs. AI) competition. Extensive numerical simulations are performed across AI, aware humans (those with full knowledge of the game structure and payoffs), and learning Prospect Agents (i.e., for AIs representing humans). A number of interesting observations and patterns show up, spanning barely distinguishable behavior, behavior corroborating Prospect preference anomalies in the theoretical literature, and unexpected surprises. Code can be found at https://github.com/dylanwaldner/noncooperative-human-AI.

Sagnik Chatterjee, Vyacheslav Kungurtsev

In this work, we propose a novel architecture (and several variants thereof) based on quantum cryptographic primitives with provable privacy and security guarantees regarding membership inference attacks on generative models. Our architecture can be used on top of any existing classical or quantum generative models. We argue that the use of quantum gates associated with unitary operators provides inherent advantages compared to standard Differential Privacy based techniques for establishing guaranteed security from all polynomial-time adversaries.

Saeed Vahidian, Mingyu Wang, Jianyang Gu et al.

Dataset distillation (DD) has emerged as a widely adopted technique for crafting a synthetic dataset that captures the essential information of a training dataset, facilitating the training of accurate neural models. Its applications span various domains, including transfer learning, federated learning, and neural architecture search. The most popular methods for constructing the synthetic data rely on matching the convergence properties of training the model with the synthetic dataset and the training dataset. However, using the empirical loss as the criterion must be thought of as auxiliary in the same sense that the training set is an approximate substitute for the population distribution, and the latter is the data of interest. Yet despite its popularity, an aspect that remains unexplored is the relationship of DD to its generalization, particularly across uncommon subgroups. That is, how can we ensure that a model trained on the synthetic dataset performs well when faced with samples from regions with low population density? Here, the representativeness and coverage of the dataset become salient over the guaranteed training error at inference. Drawing inspiration from distributionally robust optimization, we introduce an algorithm that combines clustering with the minimization of a risk measure on the loss to conduct DD. We provide a theoretical rationale for our approach and demonstrate its effective generalization and robustness across subgroups through numerical experiments. The source code is available at https://github.com/Mming11/RobustDatasetDistillation.

Vyacheslav Kungurtsev, Giovanni Russo

Fully Probabilistic design (FPD) is a powerful framework offering an elegant and unifying account of stochastic control, learning and decision-making. Here we introduce a generalized FPD framework, which we term as Tsallis FPD. Tsallis FPD uses Tsallis divergence in place of the Kullback-Leibler divergence that defines the standard FPD cost term. Tsallis divergence is a natural generalization of the KL divergence, rooted in non-extensive statistical mechanics and providing flexibility towards modeling stochastic processes with non-Gaussian tail behavior. After formulating Tsallis FPD, we develop a constructive proof of convergence by formulating a fixed point iteration. The construction takes the form of a double iteration scheme that performs a sequence of backwards inductions, rather than a single pass down the stages that constitutes the proven approach for classical FPD. We prove that this construction asymptotically converges to a fixed point and that this fixed point is an optimal solution to Tsallis FPD.

Vyacheslav Kungurtsev, Yuanfang Peng, Jianyang Gu et al.

Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter. While DD has a wide range of applications, the theory supporting it is less well evolved. New methods of DD are compared on a common set of benchmarks, rather than oriented towards any particular learning task. In this work, we present a formal model of DD, arguing that a precise characterization of the underlying optimization problem must specify the inference task associated with the application of interest. Without this task-specific focus, the DD problem is under-specified, and the selection of a DD algorithm for a particular task is merely heuristic. Our formalization reveals novel applications of DD across different modeling environments. We analyze existing DD methods through this broader lens, highlighting their strengths and limitations in terms of accuracy and faithfulness to optimal DD operation. Finally, we present numerical results for two case studies important in contemporary settings. Firstly, we address a critical challenge in medical data analysis: merging the knowledge from different datasets composed of intersecting, but not identical, sets of features, in order to construct a larger dataset in what is usually a small sample setting. Secondly, we consider out-of-distribution error across boundary conditions for physics-informed neural networks (PINNs), showing the potential for DD to provide more physically faithful data. By establishing this general formulation of DD, we aim to establish a new research paradigm by which DD can be understood and from which new DD techniques can arise.

Matteo Bergamaschi, Andrea Cristofari, Vyacheslav Kungurtsev et al.

For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called "l0 norm" which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing sparsity when incorporated into an optimization problem for minimizing the fit of a given model to a set of observations. However, in big data settings wherein noisy estimates of the gradient must be evaluated out of computational necessity, the literature is scant on methods that reliably converge. In this paper we present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying stochastic process, and demonstrate the performance on two Machine Learning problems.

Jianyang Gu, Haonan Wang, Ruoxi Jia et al.

Dataset distillation (DD) has witnessed significant progress in creating small datasets that encapsulate rich information from large original ones. Particularly, methods based on generative priors show promising performance, while maintaining computational efficiency and cross-architecture generalization. However, the generation process lacks explicit controllability for each sample. Previous distillation methods primarily match the real distribution from the perspective of the entire dataset, whereas overlooking concept completeness at the instance level. The missing or incorrectly represented object details cannot be efficiently compensated due to the constrained sample amount typical in DD settings. To this end, we propose incorporating the concept understanding of large language models (LLMs) to perform Concept-Informed Diffusion (CONCORD) for dataset distillation. Specifically, distinguishable and fine-grained concepts are retrieved based on category labels to inform the denoising process and refine essential object details. By integrating these concepts, the proposed method significantly enhances both the controllability and interpretability of the distilled image generation, without relying on pre-trained classifiers. We demonstrate the efficacy of CONCORD by achieving state-of-the-art performance on ImageNet-1K and its subsets. The code implementation is released in https://github.com/vimar-gu/CONCORD.

Harsh Choudhary, Chandan Gupta, Vyacheslav Kungurtsev et al.

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and in particular Hamiltonian Neural Networks have emerged as a mechanism to incorporate structural inductive bias into the NN model. By ensuring physical invariances are conserved, the models exhibit significantly better sample complexity and out-of-distribution accuracy than standard NNs. Learning the Hamiltonian as a function of its canonical variables, typically position and velocity, from sample observations of the system thus becomes a critical task in system identification and long-term prediction of system behavior. However, to truly preserve the long-run physical conservation properties of Hamiltonian systems, one must use symplectic integrators for a forward pass of the system's simulation. While symplectic schemes have been used in the literature, they are thus far limited to situations when they reduce to explicit algorithms, which include the case of separable Hamiltonians or augmented non-separable Hamiltonians. We extend it to generalized non-separable Hamiltonians, and noting the self-adjoint property of symplectic integrators, we bypass computationally intensive backpropagation through an ODE solver. We show that the method is robust to noise and provides a good approximation of the system Hamiltonian when the state variables are sampled from a noisy observation. In the numerical results, we show the performance of the method concerning Hamiltonian reconstruction and conservation, indicating its particular advantage for non-separable systems.

Kemboi Cheruiyot, Nickson Kiprotich, Vyacheslav Kungurtsev et al.

The increasing interest in research and innovation towards the development of autonomous agents presents a number of complex yet important scenarios of multiple AI Agents interacting with each other in an environment. The particular setting can be understood as exhibiting three possibly topologies of interaction - centrally coordinated cooperation, ad-hoc interaction and cooperation, and settings with noncooperative incentive structures. This article presents a comprehensive survey of all three domains, defined under the formalism of Federal Reinforcement Learning (RL), Decentralized RL, and Noncooperative RL, respectively. Highlighting the structural similarities and distinctions, we review the state of the art in these subjects, primarily explored and developed only recently in the literature. We include the formulations as well as known theoretical guarantees and highlights and limitations of numerical performance.

Vyacheslav Kungurtsev, Leonardo Christov Moore, Gustav Sir et al.

Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of important domains. In this paper we consider the epistemology of recognizing true cause and effect phenomena. We apply the Ordinary Language method of engaging on the customary use of the word 'cause' to investigate valid semantics of reasoning about cause and effect. We recognize that the grammars of cause and effect are fundamentally distinct in form across scientific domains, yet they maintain a consistent and central function. This function can best be described as the mechanism underlying fundamental forces of influence as considered prominent in the respective scientific domain. We demarcate 1) physics and engineering as domains wherein mathematical models are sufficient to comprehensively describe causality, 2) biology as introducing challenges of emergence while providing opportunities for showing consistent mechanisms across scale, and 3) the social sciences as introducing grander difficulties for establishing models of low prediction error but providing, through Hermeneutics, the potential for findings that are still instrumentally useful to individuals. We posit that definitive causal claims regarding a given phenomenon (writ large) can only come through an agglomeration of consistent evidence across multiple domains. This presents important methodological questions as far as harmonizing between language games and emergence across scales. Given the role of epistemic hubris in the contemporary crisis of credibility in the sciences, exercising greater caution as far as communicating precision as to the real degree of certainty certain evidence provides for rich collections of open problems in optimizing integration of different findings.

Farid Bozorgnia, Vyacheslav Kungurtsev, Shirali Kadyrov et al.

In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the physics of parabolic evolution equations. We integrate the fractional heat kernel into Graph Neural Network architectures such as Graph Convolutional Networks and Graph Attention, enhancing their expressiveness through adaptive, multi-hop diffusion. By applying Chebyshev polynomial approximations, large graphs become computationally feasible. Motivating variational formulations demonstrate that by extending the classical diffusion model to fractional powers of the Laplacian, nonlocal interactions deliver more globally diffusing labels. The particular balance between supervision of known labels and diffusion across the graph is particularly advantageous in the case where only a small number of labeled training examples are present. We demonstrate the effectiveness of this approach on standard datasets.

Morteza Kimiaei, Vyacheslav Kungurtsev

Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods -- line search, direct search, and model-based solvers such as Bayesian optimization -- form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to enhance BBO: ML provides expressive surrogates, adaptive updates, meta-learning portfolios, and generative models, while RL enables dynamic operator configuration, robustness, and meta-optimization across tasks. This paper surveys these developments, covering representative algorithms such as NNs with the modular model-based optimization framework (mlrMBO), zeroth-order adaptive momentum methods (ZO-AdaMM), automated BBO (ABBO), distributed block-wise optimization (DiBB), partition-based Bayesian optimization (SPBOpt), the transformer-based optimizer (B2Opt), diffusion-model-based BBO, surrogate-assisted RL for differential evolution (Surr-RLDE), robust BBO (RBO), coordinate-ascent model-based optimization with relative entropy (CAS-MORE), log-barrier stochastic gradient descent (LB-SGD), policy improvement with black-box (PIBB), and offline Q-learning with Mamba backbones (Q-Mamba). We also review benchmark efforts such as the NeurIPS 2020 BBO Challenge and the MetaBox framework. Overall, we highlight how ML and RL transform classical inexact solvers into more scalable, robust, and adaptive frameworks for real-world optimization.

Morteza Kimiaei, Vyacheslav Kungurtsev, Brian Olimba

Integer and mixed-integer nonlinear programming (INLP, MINLP) are central to logistics, energy, and scheduling, but remain computationally challenging. This survey examines how machine learning and reinforcement learning can enhance exact optimization methods-particularly branch-and-bound (BB)-without compromising global optimality. We cover discrete, continuous, and mixed-integer formulations, and highlight applications such as vehicle routing, hydropower planning, and crew scheduling. We introduce a unified BB framework that embeds learning-based strategies into branching, cut selection, node ordering, and parameter control. Classical algorithms are augmented using supervised, imitation, and reinforcement learning models to accelerate convergence while maintaining correctness. We conclude with a taxonomy of learning methods by solver class and learning paradigm, and outline open challenges in generalization, hybridization, and scaling intelligent solvers.

Martin Krutský, Gustav Šír, Vyacheslav Kungurtsev et al.

Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between the problem's variables. While the framework has yielded promising results in various combinatorial problems, we show that the performance of PI-GNNs systematically plummets with an increasing density of the combinatorial problem graphs. Our analysis reveals an interesting phase transition in the PI-GNNs' training dynamics, associated with degenerate solutions for the denser problems, highlighting a discrepancy between the relaxed, real-valued model outputs and the binary-valued problem solutions. To address the discrepancy, we propose principled alternatives to the naive strategy used in PI-GNNs by building on insights from fuzzy logic and binarized neural networks. Our experiments demonstrate that the portfolio of proposed methods significantly improves the performance of PI-GNNs in increasingly dense settings.

Vyacheslav Kungurtsev, Gustav Sir, Akhil Anand et al.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

Jeremy Kulcsar, Vyacheslav Kungurtsev, Georgios Korpas et al.

In this work we investigate the potential of solving the discrete Optimal Transport (OT) problem with entropy regularization in a federated learning setting. Recall that the celebrated Sinkhorn algorithm transforms the classical OT linear program into strongly convex constrained optimization, facilitating first order methods for otherwise intractably large problems. A common contemporary setting that remains an open problem as far as the application of Sinkhorn is the presence of data spread across clients with distributed inter-communication, either due to clients whose privacy is a concern, or simply by necessity of processing and memory hardware limitations. In this work we investigate various natural procedures, which we refer to as Federated Sinkhorn, that handle distributed environments where data is partitioned across multiple clients. We formulate the problem as minimizing the transport cost with an entropy regularization term, subject to marginal constraints, where block components of the source and target distribution vectors are locally known to clients corresponding to each block. We consider both synchronous and asynchronous variants as well as all-to-all and server-client communication topology protocols. Each procedure allows clients to compute local operations on their data partition while periodically exchanging information with others. We provide theoretical guarantees on convergence for the different variants under different possible conditions. We empirically demonstrate the algorithms performance on synthetic datasets and a real-world financial risk assessment application. The investigation highlights the subtle tradeoffs associated with computation and communication time in different settings and how they depend on problem size and sparsity.

Vyacheslav Kungurtsev, Apaar, Aarya Khandelwal et al.

In this work, we demonstrate the Empirical Bayes approach to learning a Dynamic Bayesian Network. By starting with several point estimates of structure and weights, we can use a data-driven prior to subsequently obtain a model to quantify uncertainty. This approach uses a recent development of Generalized Variational Inference, and indicates the potential of sampling the uncertainty of a mixture of DAG structures as well as a parameter posterior.

Vyacheslav Kungurtsev, Fadwa Idlahcen, Petr Rysavy et al.

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

Alberto Schiabel, Vyacheslav Kungurtsev, Jakub Marecek

Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer lattice. In this work, we consider the problem of maximizing a monotone submodular function on the bounded integer lattice subject to a cardinality constraint. In particular, we focus on maximizing DR-submodular functions, i.e., functions defined on the integer lattice that exhibit the diminishing returns property. Given any epsilon > 0, we present a randomized algorithm with probabilistic guarantees of O(1 - 1/e - epsilon) approximation, using a framework inspired by a Stochastic Greedy algorithm developed for set submodular functions by Mirzasoleiman et al. We then show that, on synthetic DR-submodular functions, applying our proposed algorithm on the integer lattice is faster than the alternatives, including reducing a target problem to the set domain and then applying the fastest known set submodular maximization algorithm.

Alexander Shevchenko, Vyacheslav Kungurtsev, Marco Mondelli

Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via SGD for a univariate regularized regression problem. Our main result is that SGD is biased towards a simple solution: at convergence, the ReLU network implements a piecewise linear map of the inputs, and the number of "knot" points - i.e., points where the tangent of the ReLU network estimator changes - between two consecutive training inputs is at most three. In particular, as the number of neurons of the network grows, the SGD dynamics is captured by the solution of a gradient flow and, at convergence, the distribution of the weights approaches the unique minimizer of a related free energy, which has a Gibbs form. Our key technical contribution consists in the analysis of the estimator resulting from this minimizer: we show that its second derivative vanishes everywhere, except at some specific locations which represent the "knot" points. We also provide empirical evidence that knots at locations distinct from the data points might occur, as predicted by our theory.

Vyacheslav Kungurtsev, Adam Cobb, Tara Javidi et al.

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as to the uncertainty of a random quantity, and Langevin and Hamiltonian methods are effective at realizing sampling from an uncertain distribution with large parameter dimensions. Such methods have only recently appeared in the decentralized setting, and either exclusively use stochastic gradient Langevin and Hamiltonian Monte Carlo approaches that require a diminishing stepsize to asymptotically sample from the posterior and are known in practice to characterize uncertainty less faithfully than constant step-size methods with a Metropolis adjustment, or assume strong convexity properties of the potential function. We present the first approach to incorporating constant stepsize Metropolis-adjusted HMC in the decentralized sampling framework, show theoretical guarantees for consensus and probability distance to the posterior stationary distribution, and demonstrate their effectiveness numerically on standard real world problems, including decentralized learning of neural networks which is known to be highly non-convex.

Allahkaram Shafiei, Vyacheslav Kungurtsev, Jakub Marecek

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.

Vyacheslav Kungurtsev, Bapi Chatterjee, Dan Alistarh

Stochastic Gradient Langevin Dynamics (SGLD) ensures strong guarantees with regards to convergence in measure for sampling log-concave posterior distributions by adding noise to stochastic gradient iterates. Given the size of many practical problems, parallelizing across several asynchronously running processors is a popular strategy for reducing the end-to-end computation time of stochastic optimization algorithms. In this paper, we are the first to investigate the effect of asynchronous computation, in particular, the evaluation of stochastic Langevin gradients at delayed iterates, on the convergence in measure. For this, we exploit recent results modeling Langevin dynamics as solving a convex optimization problem on the space of measures. We show that the rate of convergence in measure is not significantly affected by the error caused by the delayed gradient information used for computation, suggesting significant potential for speedup in wall clock time. We confirm our theoretical results with numerical experiments on some practical problems.

Giorgi Nadiradze, Ilia Markov, Bapi Chatterjee et al.

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to train machine learning models in large-scale distributed shared-memory and message-passing environments. Many of these models are trained employing variants of stochastic gradient descent (SGD) based optimization. In this paper, we introduce a general consistency condition covering communication-reduced and asynchronous distributed SGD implementations. Our framework, called elastic consistency enables us to derive convergence bounds for a variety of distributed SGD methods used in practice to train large-scale machine learning models. The proposed framework de-clutters the implementation-specific convergence analysis and provides an abstraction to derive convergence bounds. We utilize the framework to analyze a sparsification scheme for distributed SGD methods in an asynchronous setting for convex and non-convex objectives. We implement the distributed SGD variant to train deep CNN models in an asynchronous shared-memory setting. Empirical results show that error-feedback may not necessarily help in improving the convergence of sparsified asynchronous distributed SGD, which corroborates an insight suggested by our convergence analysis.

Ondrej Kuzelka, Vyacheslav Kungurtsev

We study lifted weight learning of Markov logic networks. We show that there is an algorithm for maximum-likelihood learning of 2-variable Markov logic networks which runs in time polynomial in the domain size. Our results are based on existing lifted-inference algorithms and recent algorithmic results on computing maximum entropy distributions.

Vyacheslav Kungurtsev, Tomas Pevny

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonconvex. This alone presents a challenge to application and development of appropriate optimization algorithms for solving the problem. However, in addition, there are a number of interesting problems for which the objective function is non- smooth and nonseparable. In this paper, we summarize the primary challenges involved, the state of the art, and present some numerical results on an interesting and representative class of problems.

Vyacheslav Kungurtsev, Tomas Pevny

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonlinear. This presents a challenge to application and development of appropriate optimization algorithms for solving the problem. In this paper, we summarize the primary challenges involved and present the case for a Newton-based method incorporating directions of negative curvature, including promising numerical results on data arising from security anomally deetection.