arXiv subjects

Yunsoo Ha

Publications and source records attributed to Yunsoo Ha.

8 recordsLinked to original sources

arXiv2026

Computing Equilibria in Simulation-Based Insurance Markets with Discontinuous Demand

We study a simulation-based equilibrium problem arising in competitive insurance markets under hurricane risk. Each insurer seeks to maximize its own profit by selecting regional pricing and reinsurance decisions while satisfying insolvency constraints. The resulting problem is particularly challenging because customer purchase decisions induce discontinuous demand functions, while insolvency constraints create nonconvex feasible regions. To address these challenges, we introduce a pricing-dependent reinsurance optimization operator that reoptimizes reinsurance for each candidate pricing vector, transforming each insurer's joint response problem into a structured pricing problem in which insolvency feasibility is handled through reinsurance reoptimization. This reformulation avoids simultaneous optimization of pricing and reinsurance over the nonconvex joint feasible set. We optimize the resulting nonsmooth and nonconvex reduced objective using a trust-region framework that exploits both the smoothed and original objectives while incorporating direct-search exploration. The computed approximate responses are embedded within a damped better-response scheme to stabilize the equilibrium iterations. In a case study of the North Carolina hurricane insurance market, the framework identifies multiple equilibrium candidates with practical runtimes, while radius-based local Nash tests find no profitable sampled deviations within the tested neighborhoods.

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arXiv2026

Adaptive Regularization within Trust Region Methods for Stochastic Nonconvex Optimization

We propose a stochastic nonconvex optimization algorithm that achieves almost sure $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ iteration complexity for problems with smooth objective functions and gradients only observable with noise. The mean-zero stochastic noise is decision-dependent and has unbounded support with subexponential tail, allowing our framework to cover a broad class of problems. The improved almost sure iteration complexity is achieved with a new variant of the adaptive sampling trust-region optimization (ASTRO) augmented with an adaptively regularized local model, which we term Reg-ASTRO. Adaptive sampling ensures that the estimation precision is aligned with a measure of stationarity, so that iterates closer to stationarity trigger higher accuracy requirement for sampling. A key analytical challenge arises because the trust-region radius and regularization are coupled and not determined prior to gradient estimation at each iteration. We further establish an almost sure $\tilde{\mathcal{O}}(\epsilon^{-4.5})$ sample complexity for Reg-ASTRO, which improves to $\tilde{\mathcal{O}}(\epsilon^{-3.5})$ under stronger regularity conditions and use of common random numbers, substantially outperforming first-order methods in theory and numerical experiments.

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arXiv2025

Multi-Fidelity Stochastic Trust Region Method with Adaptive Sampling

Simulation optimization is often hindered by the high cost of running simulations. Multi-fidelity methods offer a promising solution by incorporating cheaper, lower-fidelity simulations to reduce computational time. However, the bias in low-fidelity models can mislead the search, potentially steering solutions away from the high-fidelity optimum. To overcome this, we propose ASTRO-MFDF, an adaptive sampling trust-region method for multi-fidelity simulation optimization. ASTRO-MFDF features two key strategies: (i) it adaptively determines the sample size and selects appropriate sampling strategies to reduce computational cost; and (ii) it selectively uses low-fidelity information only when a high correlation with the high-fidelity is anticipated, reducing the risk of bias. We validate the performance and computational efficiency of ASTRO-MFDF through numerical experiments using the SimOpt library.

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arXiv2024

Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Derivative-Free Stochastic Optimization

Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them, and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to the first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic problems and simulation optimization problems involving discrete event systems.

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arXiv2024

Complexity of Zeroth- and First-order Stochastic Trust-Region Algorithms

Model update (MU) and candidate evaluation (CE) are classical steps incorporated inside many stochastic trust-region (TR) algorithms. The sampling effort exerted within these steps, often decided with the aim of controlling model error, largely determines a stochastic TR algorithm's sample complexity. Given that MU and CE are amenable to variance reduction, we investigate the effect of incorporating common random numbers (CRN) within MU and CE on complexity. Using ASTRO and ASTRO-DF as prototype first-order and zeroth-order families of algorithms, we demonstrate that CRN's effectiveness leads to a range of complexities depending on sample-path regularity and the oracle order. For instance, we find that in first-order oracle settings with smooth sample paths, CRN's effect is pronounced -- ASTRO with CRN achieves $\tilde{O}(\epsilon^{-2})$ a.s. sample complexity compared to $\tilde{O}(\epsilon^{-6})$ a.s. in the generic no-CRN setting. By contrast, CRN's effect is muted when the sample paths are not Lipschitz, with the sample complexity improving from $\tilde{O}(\epsilon^{-6})$ a.s. to $\tilde{O}(\epsilon^{-5})$ and $\tilde{O}(\epsilon^{-4})$ a.s. in the zeroth- and first-order settings, respectively. Since our results imply that improvements in complexity are largely inherited from generic aspects of variance reduction, e.g., finite-differencing for zeroth-order settings and sample-path smoothness for first-order settings within MU, we anticipate similar trends in other contexts.

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arXiv2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The Quantum Approximate Optimization Algorithm (QAOA) has enjoyed increasing attention in noisy intermediate-scale quantum computing due to its application to combinatorial optimization problems. Because combinatorial optimization problems are NP-hard, QAOA could serve as a potential demonstration of quantum advantage in the future. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem, in which the simulation outcomes are attainable only through the quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method, derived from a derivative-free adaptive sampling trust-region optimization (ASTRO-DF) method, intended to efficiently solve the classical optimization problem in QAOA, by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function, and a model of the variance of the objective function. Exploiting the variance model allows us to both restrict the number of communications with the quantum computer, and also helps navigate the nonconvex objective landscapes typical in the QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit, when we consider a metric of computational burden that explicitly accounts for communication costs.

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arXiv2023

Iteration Complexity and Finite-Time Efficiency of Adaptive Sampling Trust-Region Methods for Stochastic Derivative-Free Optimization

Adaptive sampling with interpolation-based trust regions or ASTRO-DF is a successful algorithm for stochastic derivative-free optimization with an easy-to-understand-and-implement concept that guarantees almost sure convergence to a first-order critical point. To reduce its dependence on the problem dimension, we present local models with diagonal Hessians constructed on interpolation points based on a coordinate basis. We also leverage the interpolation points in a direct search manner whenever possible to boost ASTRO-DF's performance in a finite time. We prove that the algorithm has a canonical iteration complexity of $\mathcal{O}(\epsilon^{-2})$ almost surely, which is the first guarantee of its kind without placing assumptions on the quality of function estimates or model quality or independence between them. Numerical experimentation reveals the computational advantage of ASTRO-DF with coordinate direct search due to saving and better steps in the early iterations of the search.

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arXiv2022

Latency considerations for stochastic optimizers in variational quantum algorithms

Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.

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