We theoretically establish that our algorithms almost surely converge to locally optimal policies of our safe optimization framework.

Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question.

Recent advances in constrained reinforcement learning (RL) have endowed reinforcement learning with certain safety guarantees.

However,the criteria by which the prediction model is trained are often inconsistent with the goal of the downstream optimization problem. Recently, decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. However, they cannot directly handle the soft constraints with the max operator required in many real-world objectives.

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraintsislarge.

We study convex resource allocation problems with $m$ hard constraints under $(\varepsilon,\delta)$-joint differential privacy (Joint-DP or JDP) in an offline setting. To approximately solve the problem, we propose a generic algorithm called Noisy Dual Mirror Descent. The algorithm applies noisy Mirror Descent to a dual problem from relaxing the hard constraints for private shadow prices, and then uses the shadow prices to coordinate allocations in the primal problem.

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation.Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior.This approach results in a superior latent representation and allows each encoding to preserve information better from its uncompressed original features. In extensive experiments on multiple benchmark datasets and two challenging real-world datasets, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.