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Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
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 adaptive sampling strategy for the random subspace significantly…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
A Task Decomposition method for iterative learning Model Predictive Control (TDMPC) for linear time-varying systems is presented. We consider the availability of state-input trajectories which solve an original task T1, and design a…
Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…
Existing work on data-driven optimization focuses on problems in static environments, but little attention has been paid to problems in dynamic environments. This paper proposes a data-driven optimization algorithm to deal with the…
Data is often generated in streams, with new observations arriving over time. A key challenge for learning models from data streams is capturing relevant information while keeping computational costs manageable. We explore intelligent data…
For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
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…
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…
In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…
The need to estimate a positive definite solution to an overdetermined linear system of equations with multiple right hand side vectors arises in several process control contexts. The coefficient and the right hand side matrices are…
In this paper we consider a novel partitioned framework for distributed optimization in peer-to-peer networks. In several important applications the agents of a network have to solve an optimization problem with two key features: (i) the…