Optimization

Most machine learning algorithms build an optimization model and learn its parameters from the given data. Thus, developing effective and efficient optimization methods is of the essence.

Area 12. Optimization.svg

Publications

  • Decentralized Optimization with Coupled Constraints

    Optimization
    Demyan Yarmoshik
    Alexander Rogozin
    Nikita Kiselev
    Daniil Dorin
    Alexander Gasnikov
    Dmitry Kovalev
    ICLR, 2025

    We consider the decentralized minimization of a separable objective $\sum_{i=1}^{n} f_i(x_i)$, where the variables are coupled through an affine constraint $\sum_{i=1}^n\left(\mathbf{A}_i x_i - b_i\right) = 0$. We assume that the functions $f_i$, matrices $\mathbf{A}_i$, and vectors $b_i$ are stored locally by the nodes of a computational network, and that the functions $f_i$ are smooth and strongly convex.

    This problem has significant applications in resource allocation and systems control and can also arise in distributed machine learning. We propose lower complexity bounds for decentralized optimization problems with coupled constraints and a first-order algorithm achieving the lower bounds. To the best of our knowledge, our method is also the first linearly convergent first-order decentralized algorithm for problems with general affine coupled constraints.

  • Lower Bounds and Optimal Algorithms for Non-Smooth Convex Decentralized Optimization over Time-Varying Networks

    Optimization
    Dmitry Kovalev
    Ekaterina Borodich
    Alexander Gasnikov
    Dmitrii Feoktistov
    NeurIPS, 2024

    We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or the links of the network are fixed in time, or both. In particular, lower bounds on the number of decentralized communications and (sub)gradient computations required to solve the problem have been established, along with matching optimal algorithms. However, the remaining and most challenging setting of non-smooth decentralized optimization over time-varying networks is largely underexplored, as neither lower bounds nor optimal algorithms are known in the literature. We resolve this fundamental gap with the following contributions: (i) we establish the first lower bounds on the communication and subgradient computation complexities of solving non-smooth convex decentralized optimization problems over time-varying networks; (ii) we develop the first optimal algorithm that matches these lower bounds and offers substantially improved theoretical performance compared to the existing state of the art.

  • The Iterative Optimal Brain Surgeon: Faster Sparse Recovery by Leveraging Second-Order Information

    OptimizationModel compression
    Diyuan Wu
    Ionut-Vlad Modoranu
    Mher Safaryan
    Denis Kuznedelev
    Dan Alistarh
    NeurIPS, 2024

    The rising footprint of machine learning has led to a focus on imposing model sparsity as a means of reducing computational and memory costs. For deep neural networks (DNNs), the state-of-the-art accuracy-vs-sparsity is achieved by heuristics inspired by the classical Optimal Brain Surgeon (OBS) framework [LeCun et al., 1989, Hassibi and Stork, 1992, Hassibi et al., 1993], which leverages loss curvature information to make better pruning decisions. Yet, these results still lack a solid theoretical understanding, and it is unclear whether they can be improved by leveraging connections to the wealth of work on sparse recovery algorithms. In this paper, we draw new connections between these two areas and present new sparse recovery algorithms inspired by the OBS framework that come with theoretical guarantees under reasonable assumptions and have strong practical performance. Specifically, our work starts from the observation that we can leverage curvature information in OBS-like fashion upon the projection step of classic iterative sparse recovery algorithms such as IHT. We show for the first time that this leads both to improved convergence bounds in well-behaved settings and to stronger practical convergence. Furthermore, we present extensions of this approach to training accurate sparse DNNs, and validate it experimentally at scale.