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H. Milton Stewart School of Industrial and Systems Engineering

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https://hdl.handle.net/1853/70758

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College of Engineering

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Organizational Unit

William M. Keck Virtual Factory Lab (VFL)

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https://finding-aids.library.gatech.edu/agents/corporate_entities/1032

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Publication Search Results

Now showing 1 - 10 of 723

Finding feasible systems with subjective probability constraints with a military application

(Georgia Institute of Technology, 2024-04-29) Kim, Taehoon

We consider the problem of determining feasible systems among a finite set of simulated alternatives with respect to probability constraints, where observations from stochastic simulations are Bernoulli distributed. Most statistically valid procedures for feasibility determination consider constraints on the means of normally distributed observations. When observations are Bernoulli distributed, one can still use the existing procedures by treating batch means of Bernoulli observations as basic observations. However, achieving approximate normality may require a large batch size, which can lead to the unnecessary waste of observations in reaching a decision. This thesis proposes procedures that utilize Bernoulli-distributed observations to determine feasibility. We allow for subjective constraints, meaning that thresholds can be tightened if too many systems are feasible or relaxed if no feasible system exists, and adding thresholds sequentially over multiple passes. We demonstrate that our procedures outperform an existing feasibility determination procedure for subjective constraints, originally developed for normal observations. We also show that the proposed procedure can be used to find a system with the largest or smallest probability. Next, we consider the problem of finding feasible combinations of army aviation assets, specifically attack helicopters and unmanned aerial vehicles, to counter enemy armored units in the presence of constraints on the expected total cost and the mission failure probability. Both performance measures need to be estimated by stochastic simulation of a battlefield. Moreover, the decision maker may be interested in how the feasible combinations change as the threshold values are tightened or loosened, which can help identify the bi-objective optimal solution. We formulate this problem as feasibility determination with subjective constraints and combine two feasibility determination procedures originally designed for mean and probability, respectively. A case study is performed for an imaginary battlefield scenario in the area near the Korean border with an agent-based simulation.
Unifying Strategic Military Force Design and Operational Warfighting: A Stochastic Game Approach

(Georgia Institute of Technology, 2024-04-27) McCarthy, Joseph

Military strategic investment and operational warfighting are necessarily intertwined, yet it is quite challenging to integrate these two levels analytically. In this thesis, we provide a framework to unify these levels through stochastic games and a force design model. We start with the operational level, where we exploit the structure of military games to construct a tractable representation of the large-scale problem. We develop the campaign stochastic game (CSG), a two-player, discounted, zero-sum stochastic game model for dynamic operational planning in military campaigns. Then, at the strategic level, we use this representation to evaluate force designs directly in the operational contexts where they may be employed in a future global landscape. Together, the thesis represents an original methodology to integrate military strategic and operational decision making.
Demand Management and Delivery Optimization for E-Retail Fulfillment

(Georgia Institute of Technology, 2024-04-24) Banerjee, Dipayan

Increased competition and customer expectations in the e-retail sector have led to the proliferation of rapid fulfillment guarantees, such as same-day delivery (SDD) and next-day delivery (NDD). This thesis studies a series of tactical and operational logistics problems that arise in the design and management of rapid e-retail fulfillment systems. In Chapter 2, we study the linked tactical design problems of fleet sizing and partitioning a given service region into vehicle routing zones for SDD systems. Using continuous approximations to capture average-case operational behavior, we first solve the optimization problem of maximizing the area of a single-vehicle delivery zone as a function of the zone’s distance from the depot. We then demonstrate how to derive fleet sizes from these maximum areas and propose an associated Voronoi approach to partition the region into single-vehicle zones. In Chapter 3, we study the tactical problem of choosing the SDD service region itself — allowing the region to vary over the course of the day — with the objective of maximizing the average number of daily orders served. Using a continuous approximation model proposed by Stroh (2021), we first derive new bounds on the optimization model's objective and variables under a variety of conditions. Then, we illustrate how the theoretical model can be applied to real-world road networks by proposing an iterative method for empirically estimating a single Beardwood-Halton-Hammersley routing constant when service regions vary over time. In Chapter 4, we study a system in which a common delivery fleet provides service to both SDD and NDD orders placed by e-retail customers who are sensitive to delivery prices. We develop a continuous approximation model of the system and optimize with respect to customer satisfaction and profit. In Chapter 5, motivated by multichannel retailers using in-store inventory to satisfy both in-store customers and online rapid delivery requests, we study the finite-horizon continuous-time dynamic yield management problem with stationary arrival rates. We analyze a class of linear threshold policies proposed by Hodge (2008), in which each online (i.e., less desirable) customer is accepted if and only if the remaining inventory at the customer's arrival time exceeds a threshold that linearly decreases over the selling horizon, to show that these policies achieve uniformly bounded regret.
Synergizing Machine Learning and Optimization: Scalable Real-Time Risk Assessment in Power Systems

(Georgia Institute of Technology, 2024-04-24) Chen, Wenbo

The integration of renewable energy introduces increased uncertainties in power systems. These uncertainties bring new types of risk and motivate the Independent System Operators (ISOs) in the US to perform risk analysis in real-time. However, traditional optimization-based risk assessment is not practical given the tight time budget of real-time operation as it requires systematically solving a sequence of large-scale optimization instances for thousands of load and renewable scenarios. Additionally, day-to-day operations often involve numerous instances. This cumulates a large dataset and gives the opportunity to shift the computational burden from online to offline through machine learning. These challenges and opportunities have motivated the thesis to develop optimization proxies, differentiable programs to learn the input-output mapping of underlying optimization, to enable real-time risk assessment by the principled integration of Machine Learning (ML) and optimization. First, this thesis focuses on the practicality of developing optimization proxies for industrial-size Security-Constrained Economic Dispatch (SCED) problems, a foundational building block in US energy market clearing. Motivated by a principled analysis of the market-clearing optimization and simulation process in a realistic US energy market pipeline, the thesis proposes a novel just-in-time ML pipeline that addresses the main challenges incurred by the variability in load, renewable output, and production costs, as well as the combinatorial structure of commitment decisions. Second, the thesis presents a novel End-to-End Learning and Repair (E2ELR) architecture to unifiedly improve the feasibility and scalability. E2ELR combines deep learning with closed-form, differentiable optimization layers, thereby integrating learning and feasibility in an end-to-end fashion. The results demonstrate that the E2ELR achieves state-of-the-art performance, with optimality gaps that outperform other baselines by at least an order of magnitude. Finally, the thesis presents the first real-time risk assessment framework for large-scale power systems with high granularity e.g., at the level of generators and transmission lines.
Sparse and Low-rank Constrained Optimization: Formulations, Theory, and Algorithms

(Georgia Institute of Technology, 2024-04-24) Li, Yongchun

Sparsity and low rank are fundamental concepts in data reduction. Sparse and low-rank constrained optimization has benefited various application areas by effectively managing the rapid growth of big data, including machine learning, finance, cloud computing, and healthcare. Despite its versatility, sparse and low-rank constrained optimization is known to be NP-hard. This thesis aims to mitigate this challenge by developing novel formulations, theory, and algorithms. This thesis's first part focuses on two classic sparse constrained optimization problems within the domains of optimization and interpretable machine learning. Both problems involve selecting a fixed-size subset of matrix rows and/or columns to maximize metrics like entropy or accuracy, aiming to minimize the gap relative to their non-sparse counterparts. The submatrix selection problem can be naturally formulated as discrete optimization since whether to select each candidate element corresponds to a binary variable. This motivates us to explore discrete algorithms and methods. First, we derive equivalent mixed-integer convex programming formulations for both sparse constrained optimization problems, which pave the way for designing efficient branch-and-cut algorithms to achieve optimality. In addition, we develop scalable approximation algorithms, analyze their first-known theoretical guarantees, and provide their efficient implementations for approximately solving sparse constrained optimization problems. In the second part of this thesis, we propose a general low-rank optimization framework. We show that various problems in optimization and machine learning fall into our framework, including quadratically constrained quadratic program, fair machine learning, and recommendation systems. The low-rank constrained optimization is generally NP-hard and not even mixed-integer convex representable. Hence, we leverage partial convexification to obtain a tractable convex relaxation of low-rank constrained optimization. While partial convexification is often practical, its solution quality lacks theoretical guarantees. We fill this gap by developing a new theory in convex geometry, which offers a geometric perspective to analyze the performance of partial convexification. Specifically, (i) we establish the necessary and sufficient condition under which partial convexification matches the original low-rank constrained optimization, and (ii) we derive an upper bound on the minimum rank among all the optimal solutions of partial convexification and prove its tightness. To efficiently solve partial convexification, we develop a column generation algorithm combined with a rank-reduction algorithm. This combination ensures that the output solution satisfies the theoretical guarantees.
Data-driven stochastic optimization in the presence of distributional uncertainty

(Georgia Institute of Technology, 2024-04-09) Lin, Yifan

Stochastic optimization is a mathematical framework that models decision making under uncertainty. It usually assumes that the decision maker has full knowledge about the underlying uncertainty through a known probability distribution and minimizes (or maximizes) a functional of the cost (or reward) function. However, the probability distribution of the randomness in the system is rarely known in practice and is often estimated from historical data. The goal of the decision maker is therefore to select the optimal decision under this distributional uncertainty. This thesis aims to address the distributional uncertainty in the context of stochastic optimization by proposing new formulations and devising new approaches. In Chapter 2, we consider stochastic optimization under distributional uncertainty, where the unknown distributional parameter is estimated from streaming data that arrive sequentially over time. Moreover, data may depend on the decision of the time when they are generated. For both decision-independent and decision-dependent uncertainties, we propose an approach to jointly estimate the distributional parameter via Bayesian posterior distribution and update the decision by applying stochastic gradient descent (SGD) on the Bayesian average of the objective function. Our approach converges asymptotically over time and achieves the convergence rates of classical SGD in the decision-independent case. In Chapter 3, we deviate from the static stochastic optimization studied in the previous chapters and instead focus on a multistage setting. Specifically, we consider a class of sequential decision making problem called multi-armed bandit (MAB). MAB is an online decision-making problem with limited feedback. It is a class of reinforcement learning (RL) problems, where there is no state transition and the action is just a single choice from a fixed and finite set of choices. In certain situations, the decision maker may also be provided with contexts (also known as covariates or side information). We consider the contextual MAB with linear payoffs under a risk-averse criterion. At each round, contexts are revealed for each arm, and the decision maker chooses one arm to pull and receives the corresponding reward. In particular, we consider mean-variance as the risk criterion, and the best arm is the one with the largest mean-variance reward. We apply the Thompson Sampling algorithm and provide a comprehensive regret analysis for a variant of the proposed algorithm. In Chapter 4, we consider the multistage stochastic optimization problem in the context of Markov decision processes (MDPs). MDP a paradigm for modeling sequential decision making under distributional uncertainty. In the first half of the chapter, we consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the distributional uncertainty can sometimes be overly conservative. We propose a new formulation, Bayesian risk Markov Decision Process (BR-MDP), to address distributional uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distributions of the unknown parameters. The proposed formulation provides more flexible risk attitudes towards distributional uncertainty and takes into account the availability of data in future time stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. In the second half of the chapter, we consider infinite-horizon BR-MDP. To solve the infinite-horizon BR-MDP with a class of convex risk measures, we propose a computationally efficient approach of approximate bilevel difference convex programming. The optimization is performed offline and produces the optimal policy that is represented as a finite state controller with desirable performance guarantees. We also demonstrate the empirical performance of the infinite-horizon BR-MDP formulation and proposed algorithms. In Chapter 5, we consider a more general RL setting, and focus on improving the sample efficiency of policy optimization algorithm. The success of RL largely depends on the amount of data it can utilize. The efficient utilization of historical trajectories obtained from previous policies is essential for expediting policy optimization. Empirical evidence has shown that policy gradient methods based on importance sampling work well. However, existing literature often neglect the interdependence between trajectories from different iterations, and the good empirical performance lacks a rigorous theoretical justification. In this paper, we study a variant of the natural policy gradient method with reusing historical trajectories via importance sampling. We show that the bias of the proposed estimator of the gradient is asymptotically negligible, the resultant algorithm is convergent, and reusing past trajectories helps improve the convergence rate. We further apply the proposed estimator to popular policy optimization algorithms such as trust region policy optimization. Our theoretical results are verified on classical benchmarks.
Efficient two-sample Bernoulli confidence intervals and submodular dispatching

(Georgia Institute of Technology, 2024-03-18) Erazo Neira, Ignacio Ismael

In this thesis, we focus on two different problems: the computation of confidence intervals of the difference between the success parameter of two Bernoulli populations, and how to optimize the trade-off between batching orders and dispatching, when waiting helps to increase economies of scale, but produces idleness. The former problem is motivated by applications in healthcare and manufacturing, among others; whereas the latter is motivated by applications in e-commerce, machine scheduling, and others. In Chapter 2, we study the two-sample Bernoulli confidence interval problem, for which we propose computationally efficient methods that: i) minimize the number of observations taken to construct the confidence interval; and ii) minimize the total cost incurred over the sampling procedure. We extensively test our algorithms and study their successful performance versus commonly used benchmarks. Furthermore, we present a case study comparing the efficacy and costs of generic vs. brand-name drugs; we establish the effectiveness of our methods for real-world applications. In Chapter 3, motivated by applications in e-commerce logistics where orders or items arrive at different times and must be dispatched or processed in batches, we propose the subadditive dispatching problem (SAD), a strongly NP-hard problem defined by a set of orders with release times and a non-decreasing subadditive dispatch time function. A single uncapacitated vehicle must dispatch orders in batches to minimize the makespan, the time at which all orders have been dispatched. We propose a mixed-integer linear formulation for SAD; based on the linear relaxation's optimal solution, we construct a two-dispatch solution with a 3/2 approximation ratio, and a solution with at most three dispatches that has a 4/3 approximation ratio under an additional assumption. The guarantees hold for fractionally subadditive functions and are respectively the best possible for solutions using at most two or three dispatches. Moreover, we analyze FIFO solutions, discuss cases when they are optimal, and provide a dynamic program to obtain them. Finally, we computationally test our methods on applications inspired by same-day delivery and routing on restricted topologies. In Chapter 4 we build upon Chapter 3 and propose the Multi-Vehicle Submodular Dispatching problem (MSMD); this problem considers a fleet with multiple vehicles, each vehicle with a submodular dispatch time function. This chapter focuses mainly on the case where the fleet is homogeneous, and we propose four different mixed-integer programming formulations to solve this problem. We analyze the complexity of solving each formulation's linear relaxation, study the quality of the corresponding bounds, and leverage column generation to create heuristics. Moreover, we analyze solutions where all batches are intervals of consecutive orders and identify two classes of functions for which such a solution is optimal. Finally, we computationally test our methods on applications in same-day delivery and machine scheduling with family setups.
Controlling Behavior with Shared Knowledge

(Georgia Institute of Technology, 2024-01-10) Peng, Xiangyu

Controlling agent behavior is a fundamental challenge across diverse domains within artificial intelligence and robotics. The central idea of this dissertation is that shared knowledge can be used as a powerful tool to control AI agents’ behavior. This dissertation explores the utilization of shared knowledge in constructing coherent narratives and enhancing the expression of shared knowledge in Reinforcement Learning agents. In this dissertation, I first investigate the utilization of shared knowledge for constructing narratives by developing a story-generation agent that emulates the cognitive processes of how human readers create detailed mental models, referred to as the “reader model”, which they use to understand and interpret stories with shared knowledge. Employing the reader model has resulted in the generation of significantly more coherent and goal-directed stories. I also explore how to input unique constraints into the story generator allowing for the modification of the shared knowledge. Subsequently, I delve into the application of shared knowledge in controlling reinforcement learning agents through the introduction of a technique called “Story Shaping.” This technique involves the agent inferring tacit knowledge from an exemplar story and rewarding itself for actions that align with the inferred reader model. Following proposing this agent, I propose the Thespian agent to leverage the knowledge learned in this technique to adapt to the new environment under a few-shot setting. Additionally, I investigate the potential of using shared knowledge to explain behavior by examining the impact of symbolic knowledge graph-based state representation and Hierarchical Graph Attention mechanism on the decision-making process of a reinforcement learning agent. The goal of this dissertation is to create AI-driven systems that are more coherent, controllable, and aligned with human expectations and preferences, thereby fostering trust and safety in human-AI interactions.
Compatibility, Predictions and Optimization in Large-scale Online Decision Making

(Georgia Institute of Technology, 2024-01-10) Rutten, Daan

The last few years have seen a shift in server architecture towards large-scale, dedicated data centers. The massive scale of these datacenters has highlighted important, unsolved problems in the optimization of such large-scale service systems. Many of the mathematical problems abstracted from these challenges form fundamental problems in the field of online decision making and require a combination of tools from probability, stochastic processes and online algorithms together with new insights to be solvable. This thesis broadly addresses three of these problems, as detailed below. In Chapter 2, we consider a large-scale, parallel-server system, where tasks of a particular type can only be routed to a small subset of servers. The task-server constraints are represented by a bipartite graph where vertices represent task types and servers, respectively. The analysis of these systems has historically relied heavily on mean-field analysis. However, due to the lack of exchangeability in the constrained system, mean-field techniques fundamentally break down. In this chapter, we develop a novel coupling-based approach to establish the mean-field approximation for a large class of sparse graphs, including spatial graphs. The method extends the scope of mean-field analysis far beyond the classical full-flexibility setup. In Chapter 3, we consider a large-scale, parallel-server system with an unknown arrival rate, where each server is able to adjust its processing speed. The objective is to minimize the system cost, which consists of a power cost to maintain the servers' processing speed and a quality of service cost depending on the tasks' sojourn times. We draw on ideas from stochastic approximation to design a novel speed scaling algorithm and prove that the server's processing speeds converge to the globally asymptotically optimum value. Curiously, the algorithm is fully distributed and does not require any communication between servers. A key contribution of our approach lies in demonstrating how concepts from the stochastic approximation literature can be leveraged to effectively tackle learning problems in large-scale, distributed systems. In Chapter 4, we consider learning-augmented algorithms, where the decision maker has access to a machine learning model which provides untrusted and potentially inaccurate predictions of future inputs. The goal of the decision maker is to exploit the predictions if they are accurate, while guaranteeing performance that is not much worse than the hindsight optimal sequence of decisions, even when predictions are inaccurate. We consider two applications: capacity scaling and smoothed online optimization. For both applications, we design a novel algorithm and prove a competitive ratio guarantee as a function of the predictions' accuracy. Interestingly, we identify a fundamental trade-off between the competitive ratio in the worst- and best-case, which we prove is necessary for any algorithm.
On Parameter Efficiency of Neural Language Models

(Georgia Institute of Technology, 2024-01-04) Liang, Chen

In recent years, pre-trained neural language models have achieved remarkable capabilities across various natural language understanding and generation tasks. However, the trend of scaling these models to encompass billions of parameters, while enhancing adaptability and emergent capabilities, has brought forth significant deployment challenges due to their massive size. These challenges include constraints in model storage and inference latency for real-world deployment, intensive time and computational costs for task adaptation, and the presence of substantial redundant parameters that affect task adaptability. Motivated by these challenges, this thesis aims to improve the parameter efficiency of these models, seeking to minimize storage requirements, accelerate inference and adaptation, and enhance generalizability. \noindent {\it -- Improving Parameter Utilization in Neural Language Models} \\ While recent studies have identified significant redundancy in pre-trained neural language models, the impact of parameter redundancy on model generalizability remains largely underexplored. We first examine the relationship between parameter redundancy and model generalizability. Observing that removing redundant parameters improves generalizability, we propose an adaptive optimization algorithm for fine-tuning to improve the utilization of the redundant parameters. Experimental results validate increased generalization across various downstream tasks. \noindent {\it -- Model Compression in Neural Language Models} \\ We explore model compression methods, including weight pruning and knowledge distillation, to reduce model storage and accelerate inference. We first develop a reliable iterative pruning method that accounts for uncertainties in training dynamics. Then, we dive into the realm of knowledge distillation, addressing the large teacher-student ``knowledge gap" that often hampers the student's performance. To tackle this, we offer two solutions for producing students for specific tasks by selectively distilling task-relevant knowledge. In scenarios demanding student adaptability across diverse tasks, we propose to reduce the knowledge gap by combining iterative pruning with distillation. Our approaches significantly surpass conventional distillation methods at similar compression ratios. \noindent {\it -- Efficient Task Adaptation in Neural Language Models} \\ While fine-tuning is an essential adaptation method for attaining satisfactory performance on downstream tasks, it is both computation-intensive and time-consuming. To speed up task adaptation, we study the hypernetwork approach, which employs an auxiliary hypernetwork to swiftly generate task-specific weights based on few-shot demonstration examples. We improve the weight generation scheme by exploiting the intrinsic weight structure as an inductive bias, enhancing sample efficiency for hypernetwork training. The method shows superior generalization performance on unseen tasks compared to existing hypernetwork methods.