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The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Since a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need…

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…

The goal of policy gradient approaches is to find a policy in a given class of policies which maximizes the expected return. Given a differentiable model of the policy, we want to apply a gradient-ascent technique to reach a local optimum.…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…

We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…

We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…

We study offline Reinforcement Learning in large infinite-horizon discounted Markov Decision Processes (MDPs) when the reward and transition models are linearly realizable under a known feature map. Starting from the classic linear-program…

Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…

We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider…

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

Rolling forecasts have been almost overlooked in the renewable energy storage literature. In this paper, we provide a new approach for handling uncertainty not just in the accuracy of a forecast, but in the evolution of forecasts over time.…

This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning…

We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize…

In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization…

The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…

This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…