To mitigate the bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, underlies the design of fair algorithms. To this end, this paper provides a complete characterization of the inherent tradeoff of demographic parity on classification problems, under the most general multi-group, multi-class, and noisy setting. Specifically, we show that the minimum error rate achievable by randomized and attribute-aware fair classifiers is given by the optimal value of a Wasserstein-barycenter problem. On the practical side, our findings lead to a simple post-processing algorithm that derives fair classifiers from score functions, which yields the optimal fair classifier when the score is Bayes optimal. We provide suboptimality analysis and sample complexity for our algorithm, and demonstrate its effectiveness on benchmark datasets.

We recover the Riemannian gradient of a given function defined on interior points of a Riemannian submanifold in the Euclidean space based on a sample of function evaluations at points in the submanifold. This approach is based on the estimates of the Laplace-Beltrami operator proposed in the diffusion-maps theory. The Riemannian gradient estimates do not involve differential terms. Analytical convergence results of the Riemannian gradient expansion are proved. We apply the Riemannian gradient estimate in a gradient-based algorithm providing a derivative-free optimization method. We test and validate several applications, including tomographic reconstruction from an unknown random angle distribution, and the sphere packing problem in dimensions 2 and 3.

Stochastic multi-level compositional optimization problems cover many new machine learning paradigms, e.g., multi-step model-agnostic meta-learning, which require efficient optimization algorithms for large-scale applications. This paper studies the decentralized stochastic multi-level optimization algorithm, which is challenging because the multi-level structure and decentralized communication scheme may make the number of levels affect the order of the convergence rate. To this end, we develop two novel decentralized optimization algorithms to deal with the multi-level function and its gradient. Our theoretical results show that both algorithms can achieve the level-independent convergence rate for nonconvex problems under much milder conditions compared with existing single-machine algorithms. To the best of our knowledge, this is the first work that achieves the level-independent convergence rate under the decentralized setting. Moreover, extensive experiments confirm the efficacy of our proposed algorithms.

We study the problem of efficiently generating differentially private synthetic data that approximate the statistical properties of an underlying sensitive dataset. In recent years, there has been a growing line of work that approaches this problem using first-order optimization techniques. However, such techniques are restricted to optimizing differentiable objectives only, severely limiting the types of analyses that can be conducted. For example, first-order mechanisms have been primarily successful in approximating statistical queries only in the form of marginals for discrete data domains. In some cases, one can circumvent such issues by relaxing the task's objective to maintain differentiability. However, even when possible, these approaches impose a fundamental limitation in which modifications to the minimization problem become additional sources of error. Therefore, we propose Private-GSD, a private genetic algorithm based on zeroth-order optimization heuristics that do not require modifying the original objective. As a result, it avoids the aforementioned limitations of first-order optimization. We empirically evaluate Private-GSD against baseline algorithms on data derived from the American Community Survey across a variety of statistics--otherwise known as statistical queries--both for discrete and real-valued attributes. We show that Private-GSD outperforms the state-of-the-art methods on non-differential queries while matching accuracy in approximating differentiable ones.

Federated Learning is a collaborative training framework that leverages heterogeneous data distributed across a vast number of clients. Since it is practically infeasible to request and process all clients during the aggregation step, partial participation must be supported. In this setting, the communication between the server and clients poses a major bottleneck. To reduce communication loads, there are two main approaches: compression and local steps. Recent work by Mishchenko et al. [2022] introduced the new ProxSkip method, which achieves an accelerated rate using the local steps technique. Follow-up works successfully combined local steps acceleration with partial participation [Grudzie\'n et al., 2023, Condat et al. 2023] and gradient compression [Condat et al. [2022]. In this paper, we finally present a complete method for Federated Learning that incorporates all necessary ingredients: Local Training, Compression, and Partial Participation. We obtain state-of-the-art convergence guarantees in the considered setting. Moreover, we analyze the general sampling framework for partial participation and derive an importance sampling scheme, which leads to even better performance. We experimentally demonstrate the advantages of the proposed method in practice.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially non-linear in the distribution. Existing methods to optimize nonlinear functions in probability space use the Frechet derivatives, which present both theoretical and computational challenges. Motivated by this, we propose an alternative notion for the derivative and corresponding smoothness based on Gateaux (G)-derivative for generic risk measures. These concepts are explained via three running risk measure examples of variance, entropic risk, and risk on finite support sets. We then propose a G-derivative based Frank-Wolfe (FW) algorithm for generic non-linear optimization problems in probability spaces and establish its convergence under the proposed notion of smoothness in a completely norm-independent manner. We use the set-up of the FW algorithm to devise a methodology to compute a saddle point of the non-linear DRO problem. Finally, for the minimum variance portfolio selection problem we analyze the regularity conditions and compute the FW-oracle in various settings, and validate the theoretical results numerically.

This work proposes a novel generative design tool for passive grippers -- robot end effectors that have no additional actuation and instead leverage the existing degrees of freedom in a robotic arm to perform grasping tasks. Passive grippers are used because they offer interesting trade-offs between cost and capabilities. However, existing designs are limited in the types of shapes that can be grasped. This work proposes to use rapid-manufacturing and design optimization to expand the space of shapes that can be passively grasped. Our novel generative design algorithm takes in an object and its positioning with respect to a robotic arm and generates a 3D printable passive gripper that can stably pick the object up. To achieve this, we address the key challenge of jointly optimizing the shape and the insert trajectory to ensure a passively stable grasp. We evaluate our method on a testing suite of 22 objects (23 experiments), all of which were evaluated with physical experiments to bridge the virtual-to-real gap. Code and data are at https://homes.cs.washington.edu/~milink/passive-gripper/

Federated edge learning (FEEL) enables privacy-preserving model training through periodic communication between edge devices and the server. Unmanned Aerial Vehicle (UAV)-mounted edge devices are particularly advantageous for FEEL due to their flexibility and mobility in efficient data collection. In UAV-assisted FEEL, sensing, computation, and communication are coupled and compete for limited onboard resources, and UAV deployment also affects sensing and communication performance. Therefore, the joint design of UAV deployment and resource allocation is crucial to achieving the optimal training performance. In this paper, we address the problem of joint UAV deployment design and resource allocation for FEEL via a concrete case study of human motion recognition based on wireless sensing. We first analyze the impact of UAV deployment on the sensing quality and identify a threshold value for the sensing elevation angle that guarantees a satisfactory quality of data samples. Due to the non-ideal sensing channels, we consider the probabilistic sensing model, where the successful sensing probability of each UAV is determined by its position. Then, we derive the upper bound of the FEEL training loss as a function of the sensing probability. Theoretical results suggest that the convergence rate can be improved if UAVs have a uniform successful sensing probability. Based on this analysis, we formulate a training time minimization problem by jointly optimizing UAV deployment, integrated sensing, computation, and communication (ISCC) resources under a desirable optimality gap constraint. To solve this challenging mixed-integer non-convex problem, we apply the alternating optimization technique, and propose the bandwidth, batch size, and position optimization (BBPO) scheme to optimize these three decision variables alternately.

This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs (MM-DAGs), which are commonly observed in complex systems, e.g., traffic, manufacturing, and weather systems, whose variables are multi-modal with scalars, vectors, and functions. This paper takes the traffic congestion analysis as a concrete case, where a traffic intersection is usually regarded as a DAG. In a road network of multiple intersections, different intersections can only have some overlapping and distinct variables observed. For example, a signalized intersection has traffic light-related variables, whereas unsignalized ones do not. This encourages the multi-task design: with each DAG as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their consensus and consistency are maximized. To this end, we innovatively propose a multi-modal regression for linear causal relationship description of different variables. Then we develop a novel Causality Difference (CD) measure and its differentiable approximator. Compared with existing SOTA measures, CD can penalize the causal structural difference among DAGs with distinct nodes and can better consider the uncertainty of causal orders. We rigidly prove our design's topological interpretation and consistency properties. We conduct thorough simulations and one case study to show the effectiveness of our MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG