Related papers: Learning to optimize with guarantees: a complete c…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper,…
Machine learning algorithms typically rely on optimization subroutines and are well-known to provide very effective outcomes for many types of problems. Here, we flip the reliance and ask the reverse question: can machine learning…
In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of H\'{a}jek and Le Cam for classical statistical problems. We give complementary optimality results,…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
There is a long history in machine learning of model ensembling, beginning with boosting and bagging and continuing to the present day. Much of this history has focused on combining models for classification and regression, but recently…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…
Our work revisits the design of mechanisms via the learning-augmented framework. In this model, the algorithm is enhanced with imperfect (machine-learned) information concerning the input, usually referred to as prediction. The goal is to…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
Learning-augmented algorithms has been extensively studied recently in the computer-science community, due to the potential of using machine learning predictions in order to improve the performance of algorithms. Predictions are especially…
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…