Related papers: Lipschitz Continuity in Model-based Reinforcement …

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn…

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is…

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of…

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends…

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…

Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…

Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with…

In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…

Improving adversarial robustness of neural networks remains a major challenge. Fundamentally, training a neural network via gradient descent is a parameter estimation problem. In adaptive control, maintaining persistency of excitation (PoE)…

Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert…

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…

Model-Predictive Control (MPC) is a powerful tool for controlling complex, real-world systems that uses a model to make predictions about future behavior. For each state encountered, MPC solves an online optimization problem to choose a…

The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…

Lifelong machine learning (LML) is an area of machine learning research concerned with human-like persistent and cumulative nature of learning. LML system's objective is consolidating new information into an existing machine learning model…

A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these…

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…