Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization

In this paper, we consider online convex optimization (OCO) with time-varying loss and constraint functions. Specifically, the decision maker chooses sequential decisions based only on past information, meantime the loss and constraint functions are revealed over time. We first develop a class of model-based augmented Lagrangian methods (MALM) for time-varying functional constrained OCO (without feedback delay). Under standard assumptions, we establish sublinear regret and sublinear constraint violation of MALM. Furthermore, we extend MALM to deal with time-varying functional constrained OCO with delayed feedback, in which the feedback information of loss and constraint functions is revealed to decision maker with delays. Without additional assumptions, we also establish sublinear regret and sublinear constraint violation for the delayed version of MALM. Finally, numerical results for several examples of constrained OCO including online network resource allocation, online logistic regression and online quadratically constrained quadratical program are presented to demonstrate the efficiency of the proposed algorithms.

A stochastic linearized proximal method of multipliers for convex stochastic optimization with expectation constraints

This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal method of multipliers, to solve this convex stochastic optimization problem. This algorithm can be roughly viewed as a hybrid of stochastic approximation and the traditional proximal method of multipliers. Under mild conditions, we show that this algorithm exhibits $O(K^{-1/2})$ expected convergence rates for both objective reduction and constraint violation if parameters in the algorithm are properly chosen, where $K$ denotes the number of iterations. Moreover, we show that, with high probability, the algorithm has $O(\log(K)K^{-1/2})$ constraint violation bound and $O(\log^{3/2}(K)K^{-1/2})$ objective bound. Some preliminary numerical results demonstrate the performance of the proposed algorithm.

Synergistic Drug Combination Prediction by Integrating Multi-omics Data in Deep Learning Models

Drug resistance is still a major challenge in cancer therapy. Drug combination is expected to overcome drug resistance. However, the number of possible drug combinations is enormous, and thus it is infeasible to experimentally screen all effective drug combinations considering the limited resources. Therefore, computational models to predict and prioritize effective drug combinations is important for combinatory therapy discovery in cancer. In this study, we proposed a novel deep learning model, AuDNNsynergy, to prediction drug combinations by integrating multi-omics data and chemical structure data. In specific, three autoencoders were trained using the gene expression, copy number and genetic mutation data of all tumor samples from The Cancer Genome Atlas. Then the physicochemical properties of drugs combined with the output of the three autoencoders, characterizing the individual cancer cell-lines, were used as the input of a deep neural network that predicts the synergy value of given pair-wise drug combinations against the specific cancer cell-lines. The comparison results showed the proposed AuDNNsynergy model outperforms four state-of-art approaches, namely DeepSynergy, Gradient Boosting Machines, Random Forests, and Elastic Nets. Moreover, we conducted the interpretation analysis of the deep learning model to investigate potential vital genetic predictors and the underlying mechanism of synergistic drug combinations on specific cancer cell-lines.