arXiv research

Proposes a method for obtaining interval bounds in off-policy evaluation.

We prove the existence and uniqueness of solutions of SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. The main tool in our reasoning is Picard's iterative procedure and a model-free version of the Burkholder-Davis-Gundy inequality for integrals driven by model-free, continuous martingale…

Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.

We prove some epsilon regularity results for n-dimensional minimal two-valued Lipschitz graphs. The main theorems imply uniqueness of tangent cones and regularity of the singular set in a neighbourhood of any point at which at least one tangent cone is equal to a pair of transversely intersecting multiplicity one n-dim…

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arisi…

Paper defines and studies measures related to earthquakes and best Lipschitz maps.

LiST improves neural network robustness and calibration without manual tuning.

Study shows singular set of certain graphs has codimension 1.

A new one-point feedback scheme improves ZO algorithms for black-box optimization.

Develops new strategy for Hessian estimates in Lagrangian mean curvature equation.

Study Q-learning with averaging for reinforcement learning, proving efficient inference and error bounds.

We characterize locally Lipschitz mappings and existence of Lipschitz extensions through a first order nonlinear system of PDEs. We extend this study to graded group-valued Lipschitz mappings defined on compact Riemannian manifolds. Through a simple application, we emphasize the connection between these PDEs and the Ru…

Two accelerated extragradient methods converge at $O(1/k)$ rate for co-hypomonotone inclusions.

This work addresses the convergence of SGD's final iterate without restrictive assumptions.

New privacy bounds for DP-SGD's last iterate, even with cyclic sampling.

In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization problems. We extend some existing iterative reweighted $l_1$ (IRL1) a…

Optimistic method adapted for faster convex-concave min-max problems.

New PG methods tackle nonconvex optimization with auto-conditioned stepsizes.

Extends Lipschitz functions while preserving local constants.

New framework improves robustness of implicit neural networks.

Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.

Study Lipschitz regularity for manifold-constrained ROF model on curved surfaces.

We compute the local Lipschitz constant of ReLU networks precisely.

A new algorithm solves minimax problems without needing parameters.

New method improves optimization algorithms without Lipschitz smoothness.

A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…

This paper investigates analytic properties of maps between hyperbolic surfaces, focusing on best Lipschitz maps and geodesic laminations.

New method tightens Lipschitz bounds for CNNs efficiently.

New method for differentially private optimization with general Lipschitz conditions.

Consider the problem of minimizing functions that are Lipschitz and strongly convex, but not necessarily differentiable. We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with high probability. We also construct a function from this class for which the error …

Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the paper, we introduce a notion of simple augmented tree which is a Gromov hyperbolic graph. By generalizing a combinatorial device of rearrangeable matrix, we show tha…

Alternative proof and extension of curvature estimates for minimal immersions.

New bounds for online portfolio selection without smoothness assumptions.

We consider the problem of knowledge transfer when an agent is facing a series of Reinforcement Learning (RL) tasks. We introduce a novel metric between Markov Decision Processes (MDPs) and establish that close MDPs have close optimal value functions. Formally, the optimal value functions are Lipschitz continuous with …

Full-batch GD achieves generalization close to any stationary point with fewer assumptions.

New bounds on SGD's final iterate convergence rate in constant dimension.

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore …

Sparse Polyak improves high-dimensional statistical estimation.

Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system identification and learning-based control. They utilise presupposed Lipschitz p…

Study robust learning of Lipschitz functions under corrupted binary signals.

Study on GEPs with generative priors, showing optimal statistical rates and proposing an iterative algorithm.

Researchers find the optimal exercise time for American options using a specific type of diffusion process.

Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.

We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds with respect to {\em any} distribution on the unit ball in $n$ …

The Piyavskii-Shubert algorithm is analyzed for global optimization of Lipschitz functions.

This work improves the convergence theory of diffusion models for generating samples from complex distributions.

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays exponentially in the distance form the boundary of the convex core for points in the th…

Langevin MCMC samples efficiently from Riemannian manifolds with geometric Euler-Murayama analysis.