Related papers: Analysis and Optimisation of Bellman Residual Erro…
Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In existing studies on DRE, methods based on Bregman divergence (BD) minimization have been extensively…
We develop a geometric convergence theory for neural-network optimization within the minimizing movement scheme (MMS) framework. Reformulating each neural MMS step as a minimization over the set of increments in a Hilbert space, we show…
Meta-reinforcement learning (meta-RL) aims to learn from multiple training tasks the ability to adapt efficiently to unseen test tasks. Despite the success, existing meta-RL algorithms are known to be sensitive to the task distribution…
We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle:…
Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of…
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove…
Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…
Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of interactions with the MDP.…
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…
One of the most natural approaches to reinforcement learning (RL) with function approximation is value iteration, which inductively generates approximations to the optimal value function by solving a sequence of regression problems. To…
Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for…
This paper presents an evolutionary metaheuristic called Multiple Search Neuroevolution (MSN) to optimize deep neural networks. The algorithm attempts to search multiple promising regions in the search space simultaneously, maintaining…
We present a novel multiscale super-resolution framework (SRLBM) that applies deep learning directly to the mesoscopic density distribution functions of the lattice Boltzmann method for high-fidelity flow reconstruction. Two neural network…
We derive a new margin-based regularization formulation, termed multi-margin regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by principles that were applied in margin analysis of shallow linear classifiers, e.g.,…
Distributed training in deep learning (DL) is common practice as data and models grow. The current practice for distributed training of deep neural networks faces the challenges of communication bottlenecks when operating at scale, and…
This paper aims at the algorithmic/theoretical core of reinforcement learning (RL) by introducing the novel class of proximal Bellman mappings. These mappings are defined in reproducing kernel Hilbert spaces (RKHSs), to benefit from the…
In this article we study fully-connected feedforward deep ReLU ANNs with an arbitrarily large number of hidden layers and we prove convergence of the risk of the GD optimization method with random initializations in the training of such…
With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and…