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We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…
We study the problem of meta-learning through the lens of online convex optimization, developing a meta-algorithm bridging the gap between popular gradient-based meta-learning and classical regularization-based multi-task transfer methods.…
This work adopts the very successful distributional perspective on reinforcement learning and adapts it to the continuous control setting. We combine this within a distributed framework for off-policy learning in order to develop what we…
We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…
Off-policy algorithms, in which a behavior policy differs from the target policy and is used to gain experience for learning, have proven to be of great practical value in reinforcement learning. However, even for simple convex problems…
We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning…
In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible…
Training a sparse neural network from scratch requires optimizing connections at the same time as the weights themselves. Typically, the weights are redistributed after a predefined number of weight updates, removing a fraction of the…
This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a…
We consider the problem of learning from observation (LfO), in which the agent aims to mimic the expert's behavior from the state-only demonstrations by experts. We additionally assume that the agent cannot interact with the environment but…
We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…
Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy…
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…
We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…
Improving the sample efficiency of reinforcement learning algorithms requires effective exploration. Following the principle of $\textit{optimism in the face of uncertainty}$ (OFU), we train a separate exploration policy to maximize the…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…