arXiv subjects

Georgiy A. Bondar

Publications and source records attributed to Georgiy A. Bondar.

8 recordsLinked to original sources

arXiv2026

On the Equivalence of Stochastic Control and Path Space Formulations for Schrödinger Bridges over Compact Connected Lie Groups

We establish the equivalence between the stochastic optimal control and path space formulations of the Schrödinger bridge problem (SBP) for the kinematic equation on a compact connected Lie group. Using the geometric concepts of horizontal lift and stochastic anti-development, we derive a Girsanov-type change-of-measure result, and show that the expected control energy equals the relative entropy of the controlled path law with respect to the reference Wiener measure. Thus, the SBP is equivalently a path space relative entropy minimization problem subject to prescribed endpoint marginals.Our result has three useful implications. From an analytic viewpoint, the shown equivalence helps prove the existence and uniqueness of the SB. From a probabilistic viewpoint, it helps interpret the SB as the most probable deviation of the uncontrolled stochastic dynamics consistent with the endpoint constraints. From a computational viewpoint, it allows using static Sinkhorn recursions to directly solve the relative entropy minimization problem and compute the optimal path measure. We illustrate the equivalence numerically on the torus $\mathbb{T}^2$. The code is publicly available at: https://github.com/gradslab/LargeDeviationSBP

math.OC↗

arXiv2026

Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schrödinger Bridge Problem

Solutions to the Schrödinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approach is the Hopf-Cole transform that recasts the conditions for optimality into a system of boundary-coupled linear PDEs. Recent works pointed out that for the control-affine Schrödinger bridge problem, this exact linearity via Hopf-Cole transform, and thus the standard Sinkhorn recursion, apply only if the control and noise channels are proportional. When the channels do not match, the Hopf-Cole-transformed PDEs remain nonlinear, and no algorithm is available to solve the same. We advance the state-of-the-art by designing a Sinkhorn recursion with memory that leverages the structure of these nonlinear PDEs, and demonstrate how it solves the control-affine Schrödinger bridge problem with input and noise channel mismatch. We prove the local stability of the proposed algorithm.

math.OC↗

arXiv2026

Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocation

Modern real-time systems require accurate characterization of task timing behavior to ensure predictable performance, particularly on complex hardware architectures. Existing methods, such as worst-case execution time analysis, often fail to capture the fine-grained timing behaviors of a task under varying resource contexts (e.g., an allocation of cache, memory bandwidth, and CPU frequency), which is necessary to achieve efficient resource utilization. In this paper, we introduce a novel generative profiling approach that synthesizes context-dependent, fine-grained timing profiles for real-time tasks, including those for unmeasured resource allocations. Our approach leverages a nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation to generate accurate execution profiles for unseen resource contexts, with maximum likelihood guarantees. We demonstrate the efficiency and effectiveness of our approach through real-world benchmarks, and showcase its practical utility in a representative case study of adaptive multicore resource allocation for real-time systems.

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arXiv2025

Optimal Multimarginal Schrödinger Bridge: Minimum Spanning Tree over Measure-valued Vertices

The Multimarginal Schrödinger Bridge (MSB) finds the optimal coupling among a collection of random vectors with known statistics and a known correlation structure. In the MSB formulation, this correlation structure is specified \emph{a priori} as an undirected connected graph with measure-valued vertices. In this work, we formulate and solve the problem of finding the optimal MSB in the sense we seek the optimal coupling over all possible graph structures. We find that computing the optimal MSB amounts to solving the minimum spanning tree problem over measure-valued vertices. We show that the resulting problem can be solved in two steps. The first step constructs a complete graph with edge weight equal to a sum of the optimal value of the corresponding bimarginal SB and the entropies of the endpoints. The second step solves a standard minimum spanning tree problem over that complete weighted graph. Numerical experiments illustrate the proposed solution.

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arXiv2025

Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schrödinger Bridge

We propose to learn the time-varying stochastic computational resource usage of software as a graph structured Schrödinger bridge problem. In general, learning the computational resource usage from data is challenging because resources such as the number of CPU instructions and the number of last level cache requests are both time-varying and statistically correlated. Our proposed method enables learning the joint time-varying stochasticity in computational resource usage from the measured profile snapshots in a nonparametric manner. The method can be used to predict the most-likely time-varying distribution of computational resource availability at a desired time. We provide detailed algorithms for stochastic learning in both single and multi-core cases, discuss the convergence guarantees, computational complexities, and demonstrate their practical use in two case studies: a single-core nonlinear model predictive controller, and a synthetic multi-core software.

math.OC↗

arXiv2025

CORD: Co-design of Resource Allocation and Deadline Decomposition with Generative Profiling

As multicore hardware is becoming increasingly common in real-time systems, traditional scheduling techniques that assume a single worst-case execution time for a task are no longer adequate, since they ignore the impact of shared resources on execution time. When tasks execute concurrently on different cores, their execution times often vary substantially with their allocated budgets of shared resources, such as cache and memory bandwidth. Even under a specific resource allocation, the resource use pattern of a task also changes with time during a job execution. It is therefore important to consider the relationship between multicore resources and execution time in task modeling and scheduling algorithm design. In this paper, we propose a much more precise execution model for DAG-based real-time tasks that captures the time-varying resource use characteristics of a task under different budgets of shared resources. We present a generative resource profiling algorithm that efficiently predicts, from limited measurement data, the resource profile of a task at any time during its execution under a given resource budget. The generative profiles can then be used to construct the execution models for tasks, using which one can make informed resource allocation decisions. We further introduce a multicore resource allocation and deadline decomposition co-design technique for DAG-based tasks that leverages the generated execution models to jointly allocate resources and deadlines to subtasks, to maximize resource efficiency and schedulability. Our evaluation results show that our generative profiling algorithm achieves high accuracy while being efficient, and that our co-allocation technique substantially improves schedulability compared to a state-of-the-art deadline decomposition method.

cs.OS↗

arXiv2024

Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Maps

For a given ground cost, approximating the Monge optimal transport map that pushes forward a given probability measure onto another has become a staple in several modern machine learning algorithms. The fourth-order Ma-Trudinger-Wang (MTW) tensor associated with this ground cost function provides a notion of curvature in optimal transport. The non-negativity of this tensor plays a crucial role for establishing continuity for the Monge optimal transport map. It is, however, generally difficult to analytically verify this condition for any given ground cost. To expand the class of cost functions for which MTW non-negativity can be verified, we propose a provably correct computational approach which provides certificates of non-negativity for the MTW tensor using Sum-of-Squares (SOS) programming. We further show that our SOS technique can also be used to compute an inner approximation of the region where MTW non-negativity holds. We apply our proposed SOS programming method to several practical ground cost functions to approximate the regions of regularity of their corresponding optimal transport maps.

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arXiv2023

Path Structured Multimarginal Schrödinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Software

The solution of the path structured multimarginal Schrödinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent algorithmic advances in solving such structured MSBPs for learning stochastic hardware resource usage by control software. The solution enables predicting the time-varying distribution of hardware resource availability at a desired time with guaranteed linear convergence. We demonstrate the efficacy of our probabilistic learning approach in a model predictive control software execution case study. The method exhibits rapid convergence to an accurate prediction of hardware resource utilization of the controller. The method can be broadly applied to any software to predict cyber-physical context-dependent performance at arbitrary time.

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