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1. ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees.

   Chen, K. L. ; Lee, C. H. ; Garudadri, H. ; Rao, B. D. ( December 2021 , Advances in neural information processing systems)

   Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that widemore »ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special = architectural re-design.« less
2. Asynchronous Adaptive Sampling and Reduced-Order Modeling of Dynamic Processes by Robot Teams via Intermittently Connected Networks

   https://doi.org/10.1109/IROS45743.2020.9341636  

   Rovina, Hannes ; Salam, Tahiya ; Kantaros, Yiannis ; Ani Hsieh, M. ( October 2020 , 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   This work presents an asynchronous multi-robot adaptive sampling strategy through the synthesis of an intermittently connected mobile robot communication network. The objective is to enable a team of robots to adaptively sample and model a nonlinear dynamic spatiotemporal process. By employing an intermittently connected communication network, the team is not required to maintain an all-time connected network enabling them to cover larger areas, especially when the team size is small. The approach first determines the next meeting locations for data exchange and as the robots move towards these predetermined locations, they take measurements along the way. The data is thenmore »shared with other team members at the designated meeting locations and a reducedorder-model (ROM) of the process is obtained in a distributed fashion. The ROM is used to estimate field values in areas without sensor measurements, which informs the path planning algorithm when determining a new meeting location for the team. The main contribution of this work is an intermittent communication framework for asynchronous adaptive sampling of dynamic spatiotemporal processes. We demonstrate the framework in simulation and compare different reduced-order models under full, all-time and intermittent connectivity.« less
3. Probing to Minimize

   https://doi.org/10.4230/LIPIcs.ITCS.2022.120  

   Wang, Weina ; Gupta, Anupam ; Williams, Jalani K. ( January 2022 , 13th Innovations in Theoretical Computer Science Conference (ITCS 2022))

   Braverman, Mark (Ed.)

   We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing problems are well-studied. On the other hand, few techniques are known for minimizing the objective, especially in the adaptive setting, where information about the random objective is revealed during the set-selection process and allowed to influence it. For minimization problems in particular, incorporating adaptivity can have a considerable effect on performance. In this work, we seek approximation algorithms that compare well to the optimal adaptive policy. We develop new techniquesmore »for adaptive minimization, applying them to a few problems of interest. The core technique we develop here is an approximate reduction from an adaptive expectation minimization problem to a set of adaptive probability minimization problems which we call threshold problems. By providing near-optimal solutions to these threshold problems, we obtain bicriteria adaptive policies. We apply this method to obtain an adaptive approximation algorithm for the Min-Element problem, where the goal is to adaptively pick random variables to minimize the expected minimum value seen among them, subject to a knapsack constraint. This partially resolves an open problem raised in [Goel et al., 2010]. We further consider three extensions on the Min-Element problem, where our objective is the sum of the smallest k element-weights, or the weight of the min-weight basis of a given matroid, or where the constraint is not given by a knapsack but by a matroid constraint. For all three of the variations we explore, we develop adaptive approximation algorithms for their corresponding threshold problems, and prove their near-optimality via coupling arguments.« less
4. CoNICE: Consensus in Intermittently-Connected Environments by Exploiting Naming with Application to Emergency Response

   https://doi.org/10.1109/ICNP49622.2020.9259370  

   Jahanian, Mohammad ; Ramakrishnan, K. K. ( October 2020 , 2020 IEEE 28th International Conference on Network Protocols (ICNP))

   In many scenarios, information must be disseminated over intermittently-connected environments when network infrastructure becomes unavailable. Example scenarios include disasters in which first responders need to send updates about their critical tasks. If such updates pertain to a shared data set (e.g., pins on a map), their consistent dissemination is important. We can achieve this through causal ordering and consensus. Popular consensus algorithms, such as Paxos and Raft, are most suited for connected environments with reliable links. While some work has been done on designing consensus algorithms for intermittently-connected environments, such as the One-Third Rule (OTR) algorithm, there is need tomore »improve their efficiency and timely completion. We propose CoNICE, a framework to ensure consistent dissemination of updates among users in intermittently-connected, infrastructure-less environments. It achieves efficiency by exploiting hierarchical namespaces for faster convergence, and lower communication overhead. CoNICE provides three levels of consistency to users' views, namely replication, causality and agreement. It uses epidemic propagation to provide adequate replication ratios, and optimizes and extends Vector Clocks to provide causality. To ensure agreement, CoNICE extends basic OTR to support long-term fragmentation and critical decision invalidation scenarios. We integrate the multilevel consistency schema of CoNICE, with a naming schema that follows a topic hierarchy-based dissemination framework, to improve functionality and performance. Performing city-scale simulation experiments, we demonstrate that CoNICE is effective in achieving its consistency goals, and is efficient and scalable in the time for convergence and utilized network resources.« less
5. Strong Metric (Sub)regularity of Karush–Kuhn–Tucker Mappings for Piecewise Linear-Quadratic Convex-Composite Optimization and the Quadratic Convergence of Newton’s Method

   https://doi.org/10.1287/moor.2019.1027  

   Burke, James V. ; Engle, Abraham ( August 2020 , Mathematics of Operations Research)

   This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: where one minimizes an objective that can be written as the composition of a convex function with one that is continuiously differentiable. We focus on the case in which the convex function is a potentially infinite-valued piecewise linear-quadratic function. Such problems include nonlinear programming, mini-max optimization, and estimation of nonlinear dynamics with non-Gaussian noise as well as many modern approaches to large-scale data analysis and machine learning. Our approach embeds the optimality conditions for convex-composite optimization problems into a generalized equation. We establish conditions formore »strong metric subregularity and strong metric regularity of the corresponding set-valued mappings. This allows us to extend classical convergence of Newton and quasi-Newton methods to the broader class of nonfinite valued piecewise linear-quadratic convex-composite optimization problems. In particular, we establish local quadratic convergence of the Newton method under conditions that parallel those in nonlinear programming.« less