arXiv subjects

Sumin Kang

Publications and source records attributed to Sumin Kang.

3 recordsLinked to original sources

arXiv2025

Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs

We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated $L$-shaped ($L^2$) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage programs, we present a regularization-augmented variant of this method. Our computational results for a stochastic network interdiction problem show that the $L^2$ method outperforms a benchmark method, solving all instances in 23 seconds on average, while the benchmark method failed to solve any instance within 3600 seconds. The $L^2$ method also achieves optimal solutions, on average, 18.4 times faster for a stochastic facility location problem. Furthermore, we show that the $L^2$ method can effectively address distributionally robust optimization problems with decision-dependent ambiguity sets that may be empty for some first-stage decisions, achieving optimal solutions, on average, 5.3 times faster than existing methods.

math.OC↗

arXiv2024

Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations of DRR- and DRO-MSIPs by presenting multistage stochastic disjunctive programs and algorithms for solving them. These frameworks are useful for optimization problems under uncertainty where the focus is on analyzing outcomes based on multiple decision-makers' differing perspectives, such as interdiction problems that are attacker-defender games having non-cooperative players. To assess the performance of the algorithms for DRR- and DRO-MSIPs, we consider instances of distributionally ambiguous multistage maximum flow and facility location interdiction problems that are important in their own right. Based on our computational results, we observe that the cutting plane-based approaches are 2800% and 2410% (on average) faster than the reformulation-based approaches for the foregoing instances with distributional risk-aversion and risk-receptiveness, respectively. Additionally, we conducted out-of-sample tests to showcase the significance of the DRR framework in revealing network vulnerabilities and also in mitigating the impact of data corruption.

math.OC↗

arXiv2024

Transformable Gaussian Reward Function for Socially-Aware Navigation with Deep Reinforcement Learning

Robot navigation has transitioned from prioritizing obstacle avoidance to adopting socially aware navigation strategies that accommodate human presence. As a result, the recognition of socially aware navigation within dynamic human-centric environments has gained prominence in the field of robotics. Although reinforcement learning technique has fostered the advancement of socially aware navigation, defining appropriate reward functions, especially in congested environments, has posed a significant challenge. These rewards, crucial in guiding robot actions, demand intricate human-crafted design due to their complex nature and inability to be automatically set. The multitude of manually designed rewards poses issues with hyperparameter redundancy, imbalance, and inadequate representation of unique object characteristics. To address these challenges, we introduce a transformable gaussian reward function (TGRF). The TGRF significantly reduces the burden of hyperparameter tuning, displays adaptability across various reward functions, and demonstrates accelerated learning rates, particularly excelling in crowded environments utilizing deep reinforcement learning (DRL). We introduce and validate TGRF through sections highlighting its conceptual background, characteristics, experiments, and real-world application, paving the way for a more effective and adaptable approach in robotics.The complete source code is available on https://github.com/JinnnK/TGRF

cs.RO↗