Decades of exponential scaling in high performance computing (HPC) efficiency is coming to an end. Transistor based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further miniaturization will be impossible. Future HPC efficiency gains will necessarily rely on new technologies and paradigms of compute. The Ising model shows particular promise as a future framework for highly energy efficient computation. Ising systems are able to operate at energies approaching thermodynamic limits for energy consumption of computation. Ising systems can function as both logic and memory. Thus, they have the potential to significantly reduce energy costs inherent to CMOS computing by eliminating costly data movement. The challenge in creating Ising-based hardware is in optimizing useful circuits that produce correct results on fundamentally nondeterministic hardware. The contribution of this paper is a novel machine learning approach, a combination of deep neural networks and random forests, for efficiently solving optimization problems that minimize sources of error in the Ising model. In addition, we provide a process to express a Boltzmann probability optimization problem as a supervised machine learning problem.

Secure two-party computation with homomorphic encryption (HE) protects data privacy with a formal security guarantee but suffers from high communication overhead. While previous works, e.g., Cheetah, Iron, etc, have proposed efficient HE-based protocols for different neural network (NN) operations, they still assume high precision, e.g., fixed point 37 bit, for the NN operations and ignore NNs' native robustness against quantization error. In this paper, we propose HEQuant, which features low-precision-quantization-aware optimization for the HE-based protocols. We observe the benefit of a naive combination of quantization and HE quickly saturates as bit precision goes down. Hence, to further improve communication efficiency, we propose a series of optimizations, including an intra-coefficient packing algorithm and a quantization-aware tiling algorithm, to simultaneously reduce the number and precision of the transferred data. Compared with prior-art HE-based protocols, e.g., CrypTFlow2, Cheetah, Iron, etc, HEQuant achieves $3.5\sim 23.4\times$ communication reduction and $3.0\sim 9.3\times$ latency reduction. Meanwhile, when compared with prior-art network optimization frameworks, e.g., SENet, SNL, etc, HEQuant also achieves $3.1\sim 3.6\times$ communication reduction.

The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to test--or stress--their behavior, to adversarially improve their training, and to embed them in optimization models leveraging their predictive power. Many of these MILP models rely on activation bounds. That is, bounds on the input values of each neuron. In this work, we explore the tradeoff between the tightness of these bounds and the computational effort of solving the resulting MILP models. We provide guidelines for implementing these models based on the impact of network structure, regularization, and rounding.

Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear programming-based) OT estimators when comparing probability measures in high-dimensions~\citep{Vacher-2021-Dimension}. Unfortunately, that statistical benefit comes at a very steep computational price: because their computation relies on the short-step interior-point method (SSIPM), which comes with a large iteration count in practice, these estimators quickly become intractable w.r.t. sample size $n$. To scale these estimators to larger $n$, we propose a nonsmooth fixed-point model for the kernel-based OT problem, and show that it can be efficiently solved via a specialized semismooth Newton (SSN) method: We show, exploring the problem's structure, that the per-iteration cost of performing one SSN step can be significantly reduced in practice. We prove that our SSN method achieves a global convergence rate of $O(1/\sqrt{k})$, and a local quadratic convergence rate under standard regularity conditions. We show substantial speedups over SSIPM on both synthetic and real datasets.

We introduce new algorithms rooted in scattered data approximation that rely on a random exploration step to ensure that the fill-distance of query points decays at a near-optimal rate. Our algorithms retain the ease of implementation of the classical GP-UCB algorithm and satisfy cumulative regret bounds that nearly match those conjectured in [Vak22], hence solving a COLT open problem. Furthermore, the new algorithms outperform GP-UCB and other popular Bayesian optimization strategies in several examples.

We propose a novel algorithm for online resource allocation with non-stationary customer arrivals and unknown click-through rates. We assume multiple types of customers arrive in a nonstationary stochastic fashion, with unknown arrival rates in each period, and that customers' click-through rates are unknown and can only be learned online. By leveraging results from the stochastic contextual bandit with knapsack and online matching with adversarial arrivals, we develop an online scheme to allocate the resources to nonstationary customers. We prove that under mild conditions, our scheme achieves a ``best-of-both-world'' result: the scheme has a sublinear regret when the customer arrivals are near-stationary, and enjoys an optimal competitive ratio under general (non-stationary) customer arrival distributions. Finally, we conduct extensive numerical experiments to show our approach generates near-optimal revenues for all different customer scenarios.

This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock price movements to select a subset of topologically similar (different) assets for a sparse index tracking (Markowitz) portfolio. We introduce new distance measures, which serve as an input to the clustering algorithm, on the space of persistence diagrams and landscapes that consider the time component of a time series. We conduct an empirical analysis on the S\&P index from 2009 to 2020, including a study on the COVID-19 data to validate the robustness of our methodology. Our strategy to integrate TDA with the clustering algorithm significantly enhanced the performance of sparse portfolios across various performance measures in diverse market scenarios.

The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.

Congestion pricing, while adopted by many cities to alleviate traffic congestion, raises concerns about widening socioeconomic disparities due to its disproportionate impact on low-income travelers. In this study, we address this concern by proposing a new class of congestion pricing schemes that not only minimize congestion levels but also incorporate an equity objective to reduce cost disparities among travelers with different willingness-to-pay. Our analysis builds on a congestion game model with heterogeneous traveler populations. We present four pricing schemes that account for practical considerations, such as the ability to charge differentiated tolls to various traveler populations and the option to toll all or only a subset of edges in the network. We evaluate our pricing schemes in the calibrated freeway network of the San Francisco Bay Area. We demonstrate that the proposed congestion pricing schemes improve both efficiency (in terms of reduced average travel time) and equity (the disparities of travel costs experienced by different populations) compared to the current pricing scheme. Moreover, our pricing schemes also generate a total revenue comparable to the current pricing scheme. Our results further show that pricing schemes charging differentiated prices to traveler populations with varying willingness-to-pay lead to a more equitable distribution of travel costs compared to those that charge a homogeneous price to all.

Robotic arms are highly common in various automation processes such as manufacturing lines. However, these highly capable robots are usually degraded to simple repetitive tasks such as pick-and-place. On the other hand, designing an optimal robot for one specific task consumes large resources of engineering time and costs. In this paper, we propose a novel concept for optimizing the fitness of a robotic arm to perform a specific task based on human demonstration. Fitness of a robot arm is a measure of its ability to follow recorded human arm and hand paths. The optimization is conducted using a modified variant of the Particle Swarm Optimization for the robot design problem. In the proposed approach, we generate an optimal robot design along with the required path to complete the task. The approach could reduce the time-to-market of robotic arms and enable the standardization of modular robotic parts. Novice users could easily apply a minimal robot arm to various tasks. Two test cases of common manufacturing tasks are presented yielding optimal designs and reduced computational effort by up to 92%.