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Motivated by the study of $Q$-learning algorithms in reinforcement learning, we study a class of stochastic approximation procedures based on operators that satisfy monotonicity and quasi-contractivity conditions with respect to an…

Optimization models used to make discrete decisions often contain uncertain parameters that are context-dependent and estimated through prediction. To account for the quality of the decision made based on the prediction, decision-focused…

In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. However, existing regret analyses, including those of…

In this paper, we develop upon the emerging topic of loss function learning, which aims to learn loss functions that significantly improve the performance of the models trained under them. Specifically, we propose a new meta-learning…

We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can…

Policy learning is a quickly growing area. As robotics and computers control day-to-day life, their error rate needs to be minimized and controlled. There are many policy learning methods and bandit methods with provable error rates that…

We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show that adversarial risk is equivalent to the risk induced by a distributional adversarial…

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower…

Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy…

In this work, we explore online convex optimization (OCO) and introduce a new condition and analysis that provides fast rates by exploiting the curvature of feasible sets. In online linear optimization, it is known that if the average…

We propose a new loss function for supervised and physics-informed training of neural networks and operators that incorporates a posteriori error estimate. More specifically, during the training stage, the neural network learns additional…

We revisit the so-called sampling and discarding approach used to quantify the probability of constraint violation of a solution to convex scenario programs when some of the original samples are allowed to be discarded. Motivated by two…

Estimating the value function for a fixed policy is a fundamental problem in reinforcement learning. Policy evaluation algorithms---to estimate value functions---continue to be developed, to improve convergence rates, improve stability and…

In order to develop practical and efficient algorithms while circumventing overly pessimistic computational lower bounds, recent work has been interested in developing oracle-efficient algorithms in a variety of learning settings. Two such…

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…

Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and…

We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…

This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…