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We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
In this paper, we propose a robust optimization-based heuristic algorithm for the chance-constrained binary knapsack problem (CKP). We assume that the weights of items are independent normally distributed. By utilizing the properties of the…
We study the problem of structured prediction under test-time budget constraints. We propose a novel approach applicable to a wide range of structured prediction problems in computer vision and natural language processing. Our approach…
We present an adaptive approach for robust learning from corrupted training sets. We identify corrupted and non-corrupted samples with latent Bernoulli variables and thus formulate the learning problem as maximization of the likelihood…
Constrained submodular maximization has been extensively studied in the recent years. In this paper, we study adaptive robust optimization with nearly submodular structure (ARONSS). Our objective is to randomly select a subset of items that…
We consider learning a predictive model to be subsequently used for a given downstream task (described by an algorithm) that requires access to the model evaluation. This task need not be prediction, and this situation is frequently…
Adding constraint support in Machine Learning has the potential to address outstanding issues in data-driven AI systems, such as safety and fairness. Existing approaches typically apply constrained optimization techniques to ML training,…
Learning to optimize is an approach that leverages training data to accelerate the solution of optimization problems. Many approaches use unrolling to parametrize the update step and learn optimal parameters. Although L2O has shown…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data…
There has been significant progress in deep reinforcement learning (RL) in recent years. Nevertheless, finding suitable hyperparameter configurations and reward functions remains challenging even for experts, and performance heavily relies…
Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems…
The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…
This paper presents an interpretable reward design framework for reinforcement learning based constrained optimal control problems with state and terminal constraints. The problem is formalized within a standard partially observable Markov…
We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…
Identifying statistical regularities in solutions to some tasks in multi-task reinforcement learning can accelerate the learning of new tasks. Skill learning offers one way of identifying these regularities by decomposing pre-collected…