Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and discrete number of subsets is inherently non-differentiable, prohibiting end-to-end gradient-based optimization of parameters. We overcome this limitation by proposing a novel two-step method for inferring partitions, which allows its usage in variational inference tasks. This new approach enables reparameterized gradients with respect to the parameters of the new random partition model. Our method works by inferring the number of elements per subset and, second, by filling these subsets in a learned order. We highlight the versatility of our general-purpose approach on three different challenging experiments: variational clustering, inference of shared and independent generative factors under weak supervision, and multitask learning.

Designing and analyzing model-based RL (MBRL) algorithms with guaranteed monotonic improvement has been challenging, mainly due to the interdependence between policy optimization and model learning. Existing discrepancy bounds generally ignore the impacts of model shifts, and their corresponding algorithms are prone to degrade performance by drastic model updating. In this work, we first propose a novel and general theoretical scheme for a non-decreasing performance guarantee of MBRL. Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. These discoveries encourage us to formulate a constrained lower-bound optimization problem to permit the monotonicity of MBRL. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns. Motivated by these analyses, we design a simple but effective algorithm CMLO (Constrained Model-shift Lower-bound Optimization), by introducing an event-triggered mechanism that flexibly determines when to update the model. Experiments show that CMLO surpasses other state-of-the-art methods and produces a boost when various policy optimization methods are employed.

We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm, called DAGP (Double Averaging and Gradient Projection), based on local gradients, projection onto local constraints, and local averaging. We achieve global optimality through a novel distributed tracking technique we call distributed null projection. Further, we show that DAGP can be used to solve unconstrained problems with non-differentiable objective terms with a problem reduction scheme. Assuming only smoothness of the objective terms, we study the convergence of DAGP and establish sub-linear rates of convergence in terms of feasibility, consensus, and optimality, with no extra assumption (e.g. strong convexity). For the analysis, we forego the difficulties of selecting Lyapunov functions by proposing a new methodology of convergence analysis in optimization problems, which we refer to as aggregate lower-bounding. To demonstrate the generality of this method, we also provide an alternative convergence proof for the standard gradient descent algorithm with smooth functions. Finally, we present numerical results demonstrating the effectiveness of our proposed method in both constrained and unconstrained problems. In particular, we propose a distributed scheme by DAGP for the optimal transport problem with superior performance and speed.

Optimization problems on manifolds are ubiquitous in science and engineering. For instance, lowrank matrix completion and rotational alignment of 3D bodies can be formulated as optimization problems over spaces of matrices that are naturally endowed with manifold structures. These matrix manifolds belong to agreeable families [56] for which Riemannian gradients, geodesics, and other geometric quantities have closed-form expressions that facilitate the use of Riemannian optimization algorithms [19, 1, 9]. In contrast, this paper is motivated by optimization problems where the search space is a manifold that the practitioner can only access through a discrete point cloud representation, preventing direct use of Riemannian optimization algorithms. Moreover, the hidden manifold may not belong to an agreeable family, further hindering the use of classical methods. Illustrative examples where manifolds are represented by point cloud data include computer vision, robotics, and shape analysis of geometric morphometrics [33, 23, 25]. Additionally, across many applications in data science, high-dimensional point cloud data contains low-dimensional structure that can be modeled as a manifold for algorithmic design and theoretical analysis [14, 3, 27]. Motivated by these problems, this paper introduces a Bayesian optimization method with convergence guarantees to optimize an expensive-to-evaluate function on a point cloud of manifold samples.

Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process. Cover-encoding maps were devised to circumvent this problem by transforming the original landscape to one that is free of local minima and enriched in near-optimal solutions. By definition, these involve the mapping of the original (larger) search space into smaller subspaces, by processes that typically amount to a form of coarse-graining. In this paper, we explore the details of this coarse-graining using formal arguments, as well as concrete examples of cover-encoding maps, that are investigated analytically as well as computationally. Our results strongly suggest that the coarse-graining involved in cover-encoding maps bears a strong resemblance to that encountered in renormalisation group schemes. Given the apparently disparate nature of these two formalisms, these strong similarities are rather startling, and suggest deep mathematical underpinnings that await further exploration.

The evolution of wireless mobile networks towards cloudification, where Radio Access Network (RAN) functions can be hosted at either a central or distributed locations, offers many benefits like low cost deployment, higher capacity, and improved hardware utilization. Nevertheless, the flexibility in the functional deployment comes at the cost of stringent fronthaul (FH) capacity and latency requirements. One possible approach to deal with these rigorous constraints is to use FH compression techniques. To ensure that FH capacity and latency requirements are met, more FH compression is applied during high load, while less compression is applied during medium and low load to improve FH utilization and air interface performance. In this paper, a model-free deep reinforcement learning (DRL) based FH compression (DRL-FC) framework is proposed that dynamically controls FH compression through various configuration parameters such as modulation order, precoder granularity, and precoder weight quantization that affect both FH load and air interface performance. Simulation results show that DRL-FC exhibits significantly higher FH utilization (68.7% on average) and air interface throughput than a reference scheme (i.e. with no applied compression) across different FH load levels. At the same time, the proposed DRL-FC framework is able to meet the predefined FH latency constraints (in our case set to 260 $\mu$s) under various FH loads.

Robot-assisted dressing could profoundly enhance the quality of life of adults with physical disabilities. To achieve this, a robot can benefit from both visual and force sensing. The former enables the robot to ascertain human body pose and garment deformations, while the latter helps maintain safety and comfort during the dressing process. In this paper, we introduce a new technique that leverages both vision and force modalities for this assistive task. Our approach first trains a vision-based dressing policy using reinforcement learning in simulation with varying body sizes, poses, and types of garments. We then learn a force dynamics model for action planning to ensure safety. Due to limitations of simulating accurate force data when deformable garments interact with the human body, we learn a force dynamics model directly from real-world data. Our proposed method combines the vision-based policy, trained in simulation, with the force dynamics model, learned in the real world, by solving a constrained optimization problem to infer actions that facilitate the dressing process without applying excessive force on the person. We evaluate our system in simulation and in a real-world human study with 10 participants across 240 dressing trials, showing it greatly outperforms prior baselines. Video demonstrations are available on our project website\footnote{\url{https://sites.google.com/view/dressing-fcvp}}.

The conventional federated learning (FedL) architecture distributes machine learning (ML) across worker devices by having them train local models that are periodically aggregated by a server. FedL ignores two important characteristics of contemporary wireless networks, however: (i) the network may contain heterogeneous communication/computation resources, and (ii) there may be significant overlaps in devices' local data distributions. In this work, we develop a novel optimization methodology that jointly accounts for these factors via intelligent device sampling complemented by device-to-device (D2D) offloading. Our optimization methodology aims to select the best combination of sampled nodes and data offloading configuration to maximize FedL training accuracy while minimizing data processing and D2D communication resource consumption subject to realistic constraints on the network topology and device capabilities. Theoretical analysis of the D2D offloading subproblem leads to new FedL convergence bounds and an efficient sequential convex optimizer. Using these results, we develop a sampling methodology based on graph convolutional networks (GCNs) which learns the relationship between network attributes, sampled nodes, and D2D data offloading to maximize FedL accuracy. Through evaluation on popular datasets and real-world network measurements from our edge testbed, we find that our methodology outperforms popular device sampling methodologies from literature in terms of ML model performance, data processing overhead, and energy consumption.

To reduce the heavy computational burden of reactive power optimization of distribution networks, machine learning models are receiving increasing attention. However, most machine learning models (e.g., neural networks) are usually considered as black boxes, making it challenging for power system operators to identify and comprehend potential biases or errors in the decision-making process of machine learning models. To address this issue, an explainable machine-learning framework is proposed to optimize the reactive power in distribution networks. Firstly, a Shapley additive explanation framework is presented to measure the contribution of each input feature to the solution of reactive power optimizations generated from machine learning models. Secondly, a model-agnostic approximation method is developed to estimate Shapley values, so as to avoid the heavy computational burden associated with direct calculations of Shapley values. The simulation results show that the proposed explainable framework can accurately explain the solution of the machine learning model-based reactive power optimization by using visual analytics, from both global and instance perspectives. Moreover, the proposed explainable framework is model-agnostic, and thus applicable to various models (e.g., neural networks).

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster structure or the fact that the data is known to lie along a tree- or graph-structured topology. However, generic methods to ensure such structure is salient in the low-dimensional representations are lacking. This negatively impacts the interpretability of low-dimensional embeddings, and plausibly downstream learning tasks. To address this issue, we introduce topological regularization: a generic approach based on algebraic topology to incorporate topological prior knowledge into low-dimensional embeddings. We introduce a class of topological loss functions, and show that jointly optimizing an embedding loss with such a topological loss function as a regularizer yields embeddings that reflect not only local proximities but also the desired topological structure. We include a self-contained overview of the required foundational concepts in algebraic topology, and provide intuitive guidance on how to design topological loss functions for a variety of shapes, such as clusters, cycles, and bifurcations. We empirically evaluate the proposed approach on computational efficiency, robustness, and versatility in combination with linear and non-linear dimensionality reduction and graph embedding methods.