10 papers
Two Answers on Heavy-Ball Dynamics
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We determine the worst-case behavior of the heavy-ball method on smooth strongly convex functions, first for Polyak's quadratic-optimal parameters and then for arbitrary constant p…
Chebyshev-Exact Acceleration under Hessian Variation, II: Computer-Assisted Variational Lower Bound
Dmitry Pasechnyuk-Vilensky, Martin Takáč, Takáč
We study two-step recurrences with positive step sizes and nonnegative momentum coefficients whose terminal residual is the Chebyshev minimax polynomial on a prescribed spectral in…
Chebyshev-Exact Acceleration under Hessian Variation, I: Sine-Jacobi Method
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We study finite-horizon one-gradient realizations with the Chebyshev minimax terminal residual on . Under time-dependent Hessian perturbations, the terminal first variation…
Order-Sensitive Sequential Interventions on Ideal Lattices
Dmitry Pasechnyuk-Vilensky
We study sequential interventions under prerequisite constraints. In this setting, admissible intervention sequences are paths in the ideal lattice of a finite prerequisite poset r…
Heterogeneous-Horizon Exact-Weight Local SGD
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We study adaptive aggregation for heterogeneous local SGD in convex finite-sum optimization, allowing heterogeneous local horizons, minibatch sizes, gradient noise, and participati…
Ethic Duality: A Homological Framework for Primal-Dual Problems
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We develop a homological duality framework based on a contravariant functor with dualizing object . A morphism is called ethic when it satisfies th…
Moduli space of optimization algorithms
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded b…
Cubic Regularized Newton Method with Variance Reduction for Finite-sum Non-convex Problems
Dmitry Pasechnyuk-Vilensky, Dmitry Kamzolov, Martin Takáč
We study finite-sum non-convex optimization and analyze a variance-reduced cubic Newton method based on EMA-smoo…
Learning Latent Graph Geometry via Fixed-Point Schrödinger-Type Activation: A Theoretical Study
Dmitry Pasechnyuk-Vilensky, Martin Takáč
We study neural architectures in which each hidden layer is defined by the stationary state of a dissipative Schrödinger-type dynamics on a learned latent graph. On stable branches…
Information-Theoretic Upper Bounds for Deterministic Noise in Zeroth-Order Convex Optimization
Dmitry Pasechnyuk-Vilensky, Igor Pavlov, Martin Takáč +1
We study zeroth-order convex optimization on Euclidean balls with function values corrupted by a fixed, uniformly bounded deterministic perturbation. For a query budget , the ma…