14 citations · 41 across the 14 of their papers we have counts for
15 papers
Globally Optimal Training of Neural Networks with Threshold Activation Functions
Tolga Ergen, Halil Ibrahim Gulluk, Jonathan Lacotte +1
Threshold activation functions are highly preferable in neural networks due to their efficiency in hardware implementations. Moreover, their mode of operation is more interpretable…
Newton-LESS: Sparsification without Trade-offs for the Sketched Newton Update
Michał Dereziński, Jonathan Lacotte, Mert Pilanci +1
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerfu…
Adaptive Newton Sketch: Linear-time Optimization with Quadratic Convergence and Effective Hessian Dimensionality
Jonathan Lacotte, Yifei Wang, Mert Pilanci
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method…
Fast Convex Quadratic Optimization Solvers with Adaptive Sketching-based Preconditioners
Jonathan Lacotte, Mert Pilanci
We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small a…
Adaptive and Oblivious Randomized Subspace Methods for High-Dimensional Optimization: Sharp Analysis and Lower Bounds
Jonathan Lacotte, Mert Pilanci
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptiv…
The Hidden Convex Optimization Landscape of Two-Layer ReLU Neural Networks: an Exact Characterization of the Optimal Solutions
Yifei Wang, Jonathan Lacotte, Mert Pilanci
We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, ch…
Effective Dimension Adaptive Sketching Methods for Faster Regularized Least-Squares Optimization
Jonathan Lacotte, Mert Pilanci
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian…
Optimal Randomized First-Order Methods for Least-Squares Problems
Jonathan Lacotte, Mert Pilanci
We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-con…
Optimal Iterative Sketching with the Subsampled Randomized Hadamard Transform
Jonathan Lacotte, Sifan Liu, Edgar Dobriban +1
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By…
Faster Least Squares Optimization
Jonathan Lacotte, Mert Pilanci
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the…
Risk-sensitive safety specifications for stochastic systems using Conditional Value-at-Risk
Margaret P. Chapman, Jonathan P. Lacotte, Kevin M. Smith +4
This paper proposes a safety analysis method that facilitates a tunable balance between the worst-case and risk-neutral perspectives. First, we define a risk-sensitive safe set to…
High-Dimensional Optimization in Adaptive Random Subspaces
Jonathan Lacotte, Mert Pilanci, Marco Pavone
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adapt…
A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
Margaret P. Chapman, Jonathan Lacotte, Aviv Tamar +7
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint…
Risk-Sensitive Generative Adversarial Imitation Learning
Jonathan Lacotte, Mohammad Ghavamzadeh, Yinlam Chow +1
We study risk-sensitive imitation learning where the agent's goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imi…
Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods
Sumeet Singh, Jonathan Lacotte, Anirudha Majumdar +1
The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are…