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Submodular optimization problems and greedy strategies: A survey

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

97 MATHEMATICS AND COMPUTING↗

PREEMPT: Scalable Epidemic Interventions Using Submodular Optimization on Multi-GPU Systems

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we make several contributions: First, we present a new approach for intervention via maximizing the influence of vaccinated nodes on the network. We call this method \preempt. Next, we prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for \preempt, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that \preempt{} is able to achieve a significant reduction (up to 6.75$\times$) in the percentage of people infected on a city-scale network. We also show strong scaling results of \preempt{} on 128 nodes of the Summit supercomputer. Our parallel implementation is able to significantly reduce time to solution, from hours to minutes on large networks. This work represents a first-of-its-kind effort in parallelizing greedy hill climbing and applying it toward devising effective interventions for epidemics.

Minutoli, Marco↗

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.

97 MATHEMATICS AND COMPUTING↗

Sampling two-dimensional isometric tensor network states

Sampling a quantum system’s underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently representing states of large quantum systems with limited entanglement. Algorithms for sampling one-dimensional (1D) tensor networks are well-established and utilized in several 1D tensor network methods. In this paper we introduce two novel sampling algorithms for two-dimensional (2D) isometric tensor network states (isoTNS) that generalize existing 1D tensor network sampling algorithms. Our first proposed algorithm performs independent sampling and yields a single configuration together with its associated probability. The second algorithm employs a greedy search strategy to identify high-probability configurations and their corresponding probabilities. Numerical results demonstrate the effectiveness of these algorithms across quantum states with varying entanglement and system size.

Dumitrescu, Eugene [ORNL] (ORCID:0000000158519567)↗

Advanced Shuttle Strategies for Parallel QCCD Architectures

Trapped ions (TIs) are at the forefront of quantum computing implementation, offering unparalleled coherence, fidelity, and connectivity. However, the scalability of TI systems is hampered by the limited capacity of individual ion traps, necessitating intricate ion shuttling for advanced computational tasks. The quantum charge-coupled device (QCCD) framework has emerged as a promising solution, facilitating ion mobility for universal quantum computation. Current QCCD architectures predominantly feature a linear topology, which is increasingly recognized as inefficient for complex quantum operations. Anticipating the shift toward more efficacious designs, this article introduces an innovative quantum scheduling strategy optimized for parallel QCCD topologies. Our strategy proposes a probabilistic formula for ion movement, alongside ingenious methods for local layer generation and layer compression, yielding a significant reduction in ion shuttle times. Through simulations, we demonstrate that our strategy not only substantially outstrips the linear model but also exhibits better performance over other parallel strategies that employ greedy algorithms. This is achieved through our nuanced resolution of complexities, such as traffic blocks and trap capacity limitations. The consequent reduction in shuttle operations leads to lower energy consumption and an enhancement in the quantum computer's fidelity, ultimately accelerating program execution times.

43 PARTICLE ACCELERATORS↗

Feedback Control Approaches for Restoration of Power Grids from Blackouts

The automated restoration of power systems with variable energy resources is a timely problem to tackle. Automated restoration advice can support operators in deciding on strategic actions to restore power grids from a blackout with a mix of conventional and renewable generation resources. To this end, this paper frames the restoration process of power grids with solar resources as a nonlinear dynamic model with algebraic constraints in discrete time which is steered by feedback control loops. We discuss two feedback-control strategies based on greedy and reinforcement learning algorithms, and contrast their performance with restoration plans generated by a mixed-integer linear program. We found that the reinforcement learning algorithm infers restoration actions faster than the greedy one. However, the tuning process of the reinforcement learning parameters is slower than for the greedy one.

machine learning↗

Artificial intelligence driven laser parameter search: Inverse design of photonic surfaces using greedy surrogate-based optimization

Photonic surfaces designed with specific optical characteristics are becoming increasingly crucial for novel energy harvesting and storage systems. The design of these surfaces can be achieved by texturing materials using lasers. The optimal adjustment of laser fabrication parameters to achieve target surface optical properties is an open challenge. Thus, we develop a surrogate-based optimization approach. Our framework employs the Random Forest algorithm to model the forward relationship between the laser fabrication parameters and the resulting optical characteristics. During the optimization process, we use a greedy, prediction-based exploration strategy that iteratively selects batches of laser parameters to be used in experimentation by minimizing the predicted discrepancy between the surrogate model’s outputs and the user-defined target optical characteristics. This strategy allows for efficient identification of optimal fabrication parameters without the need to model the error landscape directly. We demonstrate the efficiency and effectiveness of our approach on two synthetic benchmarks and two specific experimental applications of photonic surface inverse design targets. By calculating the average performance of our algorithm compared to other state of the art optimization methods, we show that our algorithm performs, on average, twice as well across all benchmarks. Additionally, a warm starting inverse design technique for changed target optical characteristics enhances the performance of the introduced approach.

97 MATHEMATICS AND COMPUTING↗

Molecular dynamics on quantum annealers

Abstract In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.

74 ATOMIC AND MOLECULAR PHYSICS↗

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗

A Comprehensive Investigation of Active Learning Strategies for Conducting Anti-Cancer Drug Screening

It is well-known that cancers of the same histology type can respond differently to a treatment. Thus, computational drug response prediction is of paramount importance for both preclinical drug screening studies and clinical treatment design. To build drug response prediction models, treatment response data need to be generated through screening experiments and used as input to train the prediction models. In this study, we investigate various active learning strategies of selecting experiments to generate response data for the purposes of (1) improving the performance of drug response prediction models built on the data and (2) identifying effective treatments. Here, we focus on constructing drug-specific response prediction models for cancer cell lines. Various approaches have been designed and applied to select cell lines for screening, including a random, greedy, uncertainty, diversity, combination of greedy and uncertainty, sampling-based hybrid, and iteration-based hybrid approach. All of these approaches are evaluated and compared using two criteria: (1) the number of identified hits that are selected experiments validated to be responsive, and (2) the performance of the response prediction model trained on the data of selected experiments. The analysis was conducted for 57 drugs and the results show a significant improvement on identifying hits using active learning approaches compared with the random and greedy sampling method. Active learning approaches also show an improvement on response prediction performance for some of the drugs and analysis runs compared with the greedy sampling method.

60 APPLIED LIFE SCIENCES↗

FLEET: Flexible Efficient Ensemble Training for Heterogeneous Deep Neural Networks

Parallel training of an ensemble of Deep Neural Networks (DNN) on a cluster of nodes is an effective approach to shorten the process of neural network architecture search and hyper-parameter tuning for a given learning task. Prior efforts have shown that data sharing, where the common preprocessing operation is shared across the DNN training pipelines, saves computational resources and improves pipeline efficiency. Data sharing strategy, however, performs poorly for a heterogeneous set of DNNs where each DNN has varying computational needs and thus different training rate and convergence speed. This paper proposes FLEET, a flexible ensemble DNN training framework for efficiently training a heterogeneous set of DNNs. We build FLEET via several technical innovations. We theoretically prove that an optimal resource allocation is NP-hard and propose a greedy algorithm to efficiently allocate resources for training each DNN with data sharing. We integrate data-parallel DNN training into ensemble training to mitigate the differences in training rates and introduce checkpointing into this context to address the issue of different convergence speeds. Experiments show that FLEET significantly improves the training efficiency of DNN ensembles without compromising the quality of the result.

Guan, Hui↗

Optimizing the location and configuration of disaster resilience hubs under transportation and electric power network failures

Natural disasters often result in failures of transportation network components and blackouts that imperil the wellbeing of vulnerable populations. In response to these events, resilience hubs have been proposed as a pre-disaster planning strategy to improve access to critical services. This paper introduces an optimization-based approach to locate and configure electric power-generating resilience hubs considering the possibility of failures in transportation and electric power systems. The model's objective is to identify hub locations and configurations that maximize transportation accessibility to the hubs and maximize the satisfaction of basic energy needs through hub-generated electric power. Besides a budget constraint, the model accounts for limits on the levels of hub energy generation vis-à-vis community energy demands, and on the transportation network distance of communities to hubs. Three heuristics are presented for the proposed planning problem. The first heuristic is a genetic algorithm (GA) with problem-specific solution generation procedures. The other two heuristics implement greedy search techniques. Numerical experiments were conducted, using data from rural Puerto Rico, to illustrate the application of the proposed model and heuristics, and examine their performance. In the numerical experiments, the GA heuristic found better solutions than the greedy heuristics. Additionally, design solutions consisting of spatially dispersed hubs with low energy generation capacity were better than solutions with spatially concentrated high-capacity hubs. Lastly, across a wide range of hub demand scenarios, only a small number of candidate hub locations consistently ranked among the best locations for establishing a hub.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗