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Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting
Zhaodong Sun, Thomas Sanchez, Fabian Latorre +1
We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The m…
Regret minimization in stochastic non-convex learning via a proximal-gradient approach
Nadav Hallak, Panayotis Mertikopoulos, Volkan Cevher
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly…
Efficient Proximal Mapping of the 1-path-norm of Shallow Networks
Fabian Latorre, Paul Rolland, Nadav Hallak +1
We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal oper…
Random extrapolation for primal-dual coordinate descent
Ahmet Alacaoglu, Olivier Fercoq, Volkan Cevher
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our me…
Conditional gradient methods for stochastically constrained convex minimization
Maria-Luiza Vladarean, Ahmet Alacaoglu, Ya-Ping Hsieh +1
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this…
Double-Loop Unadjusted Langevin Algorithm
Paul Rolland, Armin Eftekhari, Ali Kavis +1
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size sch…
Robust Inverse Reinforcement Learning under Transition Dynamics Mismatch
Luca Viano, Yu-Ting Huang, Parameswaran Kamalaruban +2
We study the inverse reinforcement learning (IRL) problem under a transition dynamics mismatch between the expert and the learner. Specifically, we consider the Maximum Causal Entr…
Interaction-limited Inverse Reinforcement Learning
Martin Troussard, Emmanuel Pignat, Parameswaran Kamalaruban +2
This paper proposes an inverse reinforcement learning (IRL) framework to accelerate learning when the learner-teacher \textit{interaction} is \textit{limited} during training. Our…
Environment Shaping in Reinforcement Learning using State Abstraction
Parameswaran Kamalaruban, Rati Devidze, Volkan Cevher +1
One of the central challenges faced by a reinforcement learning (RL) agent is to effectively learn a (near-)optimal policy in environments with large state spaces having sparse and…
On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems
Panayotis Mertikopoulos, Nadav Hallak, Ali Kavis +1
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the s…
Convergence of adaptive algorithms for weakly convex constrained optimization
Ahmet Alacaoglu, Yura Malitsky, Volkan Cevher
We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the $\mathcal{\tilde O}(t^…
The limits of min-max optimization algorithms: convergence to spurious non-critical sets
Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenom…
Lipschitz constant estimation of Neural Networks via sparse polynomial optimization
Fabian Latorre, Paul Rolland, Volkan Cevher
We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization p…
A new regret analysis for Adam-type algorithms
Ahmet Alacaoglu, Yura Malitsky, Panayotis Mertikopoulos +1
In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parame…
A Newton Frank-Wolfe Method for Constrained Self-Concordant Minimization
Deyi Liu, Volkan Cevher, Quoc Tran-Dinh
We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the…
Robust Reinforcement Learning via Adversarial training with Langevin Dynamics
Parameswaran Kamalaruban, Yu-Ting Huang, Ya-Ping Hsieh +3
We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynam…