Machine learning models can leak information about the data used to train them. Differentially Private (DP) variants of optimization algorithms like Stochastic Gradient Descent (DP-SGD) have been designed to mitigate this, inducing a trade-off between privacy and utility. In this paper, we propose a new method for composite Differentially Private Empirical Risk Minimization (DP-ERM): Differentially Private proximal Coordinate Descent (DP-CD). We analyze its utility through a novel theoretical analysis of inexact coordinate descent, and highlight some regimes where DP-CD outperforms DP-SGD, thanks to the possibility of using larger step sizes. We also prove new lower bounds for composite DP-ERM under coordinate-wise regularity assumptions, that are, in some settings, nearly matched by our algorithm. In practical implementations, the coordinate-wise nature of DP-CD updates demands special care in choosing the clipping thresholds used to bound individual contributions to the gradients. A natural parameterization of these thresholds emerges from our theory, limiting the addition of unnecessarily large noise without requiring coordinate-wise hyperparameter tuning or extra computational cost.

In Bayesian Optimization (BO) we study black-box function optimization with noisy point evaluations and Bayesian priors. Convergence of BO can be greatly sped up by batching, where multiple evaluations of the black-box function are performed in a single round. The main difficulty in this setting is to propose at the same time diverse and informative batches of evaluation points. In this work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO by leveraging the repulsive properties of Determinantal Point Processes (DPP) to naturally diversify the batch sampling procedure. We illustrate this framework by formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to sample from it. We then prove novel Bayesian simple regret bounds for both classical batched TS as well as our counterpart DPP-TS, with the latter bound being tighter. Our real-world, as well as synthetic, experiments demonstrate improved performance of DPP-BBO over classical batching methods with Gaussian process and Cox process models.

Learning from ants: Ant colony optimization algorithms are versatile and useful for several real-world applications. These applications usually center on complex optimization problems. Here are three uses for the algorithm. In a logistics example, perhaps the distance between destinations, traffic conditions, types of packages being delivered, and times of day are important constraints to optimize the operations of the business. ACOs can help with that.

Logic synthesis is a challenging and widely-researched combinatorial optimization problem during integrated circuit (IC) design. It transforms a high-level description of hardware in a programming language like Verilog into an optimized digital circuit netlist, a network of interconnected Boolean logic gates, that implements the function. Spurred by the success of ML in solving combinatorial and graph problems in other domains, there is growing interest in the design of ML-guided logic synthesis tools. Yet, there are no standard datasets or prototypical learning tasks defined for this problem domain. Here, we describe OpenABC-D,a large-scale, labeled dataset produced by synthesizing open source designs with a leading open-source logic synthesis tool and illustrate its use in developing, evaluating and benchmarking ML-guided logic synthesis. OpenABC-D has intermediate and final outputs in the form of 870,000 And-Inverter-Graphs (AIGs) produced from 1500 synthesis runs plus labels such as the optimized node counts, and de-lay. We define a generic learning problem on this dataset and benchmark existing solutions for it. The codes related to dataset creation and benchmark models are available athttps://github.com/NYU-MLDA/OpenABC.git. The dataset generated is available athttps://archive.nyu.edu/handle/2451/63311

In tabular multi-agent reinforcement learning with average-cost criterion, a team of agents sequentially interacts with the environment and observes local incentives. We focus on the case that the global reward is a sum of local rewards, the joint policy factorizes into agents' marginals, and full state observability. To date, few global optimality guarantees exist even for this simple setting, as most results yield convergence to stationarity for parameterized policies in large/possibly continuous spaces. To solidify the foundations of MARL, we build upon linear programming (LP) reformulations, for which stochastic primal-dual methods yields a model-free approach to achieve \emph{optimal sample complexity} in the centralized case. We develop multi-agent extensions, whereby agents solve their local saddle point problems and then perform local weighted averaging. We establish that the sample complexity to obtain near-globally optimal solutions matches tight dependencies on the cardinality of the state and action spaces, and exhibits classical scalings with respect to the network in accordance with multi-agent optimization. Experiments corroborate these results in practice.

Requirements driven search-based testing (also known as falsification) has proven to be a practical and effective method for discovering erroneous behaviors in Cyber-Physical Systems. Despite the constant improvements on the performance and applicability of falsification methods, they all share a common characteristic. Namely, they are best-effort methods which do not provide any guarantees on the absence of erroneous behaviors (falsifiers) when the testing budget is exhausted. The absence of finite time guarantees is a major limitation which prevents falsification methods from being utilized in certification procedures. In this paper, we address the finite-time guarantees problem by developing a new stochastic algorithm. Our proposed algorithm not only estimates (bounds) the probability that falsifying behaviors exist, but also it identifies the regions where these falsifying behaviors may occur. We demonstrate the applicability of our approach on standard benchmark functions from the optimization literature and on the F16 benchmark problem.

Federated Learning (FL) decouples model training from the need for direct access to the data and allows organizations to collaborate with industry partners to reach a satisfying level of performance without sharing vulnerable business information. The performance of a machine learning algorithm is highly sensitive to the choice of its hyperparameters. In an FL setting, hyperparameter optimization poses new challenges. In this work, we investigated the impact of different hyperparameter optimization approaches in an FL system. In an effort to reduce communication costs, a critical bottleneck in FL, we investigated a local hyperparameter optimization approach that -- in contrast to a global hyperparameter optimization approach -- allows every client to have its own hyperparameter configuration. We implemented these approaches based on grid search and Bayesian optimization and evaluated the algorithms on the MNIST data set using an i.i.d. partition and on an Internet of Things (IoT) sensor based industrial data set using a non-i.i.d. partition.

Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter ansatz. We find that in combinatorial optimization problems, since the solutions are described by bit strings, one can trade the expressiveness of the ansatz for high trainability. To be specific, by focusing on the max-cut problem we introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA). The quantum circuits are comprised with single-qubit rotation gates implementing on each qubit. The rotation angles of the gates can be trained free of barren plateaus. Thus, the approximate solution of the max-cut problem can be obtained with probability close to 1. To illustrate the effectiveness of QQRA, we compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.

Recent advances in mobile health (mHealth) technology provide an effective way to monitor individuals' health statuses and deliver just-in-time personalized interventions. However, the practical use of mHealth technology raises unique challenges to existing methodologies on learning an optimal dynamic treatment regime. Many mHealth applications involve decision-making with large numbers of intervention options and under an infinite time horizon setting where the number of decision stages diverges to infinity. In addition, temporary medication shortages may cause optimal treatments to be unavailable, while it is unclear what alternatives can be used. To address these challenges, we propose a Proximal Temporal consistency Learning (pT-Learning) framework to estimate an optimal regime that is adaptively adjusted between deterministic and stochastic sparse policy models. The resulting minimax estimator avoids the double sampling issue in the existing algorithms. It can be further simplified and can easily incorporate off-policy data without mismatched distribution corrections. We study theoretical properties of the sparse policy and establish finite-sample bounds on the excess risk and performance error. The proposed method is implemented by our proximalDTR package and is evaluated through extensive simulation studies and the OhioT1DM mHealth dataset.

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices. We explore the generalization of the BW geometry in three different ways: 1) by generalizing the Lyapunov operator in the metric, 2) by generalizing the orthogonal Procrustes distance, and 3) by generalizing the Wasserstein distance between the Gaussians. We show that they all lead to the same geometry. The proposed generalization is parameterized by a symmetric positive definite matrix $\mathbf{M}$ such that when $\mathbf{M} = \mathbf{I}$, we recover the BW geometry. We derive expressions for the distance, geodesic, exponential/logarithm maps, Levi-Civita connection, and sectional curvature under the generalized BW geometry. We also present applications and experiments that illustrate the efficacy of the proposed geometry.