arXiv subjects

Dong Ho Lee

Publications and source records attributed to Dong Ho Lee.

8 recordsLinked to original sources

arXiv2026

Efficiently Solving Mixed-Hierarchy Games with Quasi-Policy Approximations

Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to handle mixed information structures that combine simultaneous (Nash) and hierarchical (Stackelberg) decision-making. We study N-robot forest-structured mixed-hierarchy games, in which each robot acts as a Stackelberg leader over its subtree while robots in different branches interact via Nash equilibria. We derive the Karush-Kuhn-Tucker (KKT) first-order optimality conditions for this class of games and show that they involve increasingly high-order derivatives of robots' best-response policies as the hierarchy depth grows, rendering a direct solution intractable. To overcome this challenge, we introduce a quasi-policy approximation that removes higher-order policy derivatives and develop an inexact Newton method for efficiently solving the resulting approximated KKT systems. We prove local exponential convergence of the proposed algorithm for games with non-quadratic objectives and nonlinear constraints. The approach is implemented in a highly optimized Julia library (MixedHierarchyGames.jl) and evaluated in hardware and simulated multi-agent experiments, demonstrating real-time convergence for complex mixed-hierarchy information structures.

cs.GT↗

arXiv2026

Breaking Exponential Complexity in Games of Ordered Preference: A Tractable Reformulation

Games of ordered preference (GOOPs) model multi-player equilibrium problems in which each player maintains a distinct hierarchy of strictly prioritized objectives. Existing approaches solve GOOPs by deriving and enforcing the necessary optimality conditions that characterize lexicographically constrained Nash equilibria through a single-level reformulation. However, the number of primal and dual variables in the resulting KKT system grows exponentially with the number of preference levels, leading to severe scalability challenges. We derive a compact reformulation of these necessary conditions that preserves the essential primal stationarity structure across hierarchy levels, yielding a "reduced" KKT system whose size grows polynomially with both the number of players and the number of preference levels. The reduced system constitutes a relaxation of the complete KKT system, yet it remains a valid necessary condition for local GOOP equilibria. For GOOPs with quadratic objectives and linear constraints, we prove that the primal solution sets of the reduced and complete KKT systems coincide. More generally, for GOOPs with arbitrary (but smooth) nonlinear objectives and constraints, the reduced KKT conditions recover all local GOOP equilibria but may admit spurious non-equilibrium solutions. We introduce a second-order sufficient condition to certify when a candidate point corresponds to a local GOOP equilibrium. We also develop a primal-dual interior-point method for computing a local GOOP equilibrium with local quadratic convergence. The resulting framework enables scalable and efficient computation of GOOP equilibria beyond the tractable range of existing exponentially complex formulations.

cs.GT↗

arXiv2025

Amplified Photocurrent in Heterojunctions comprising Nano-rippled Zinc Oxide and Perovskite-inspired Cs3Cu2I5

Molecular zero-dimensional (0D) halide perovskite-inspired cesium copper iodide (Cs3Cu2I5) is a highly promising candidate for optoelectronic applications due to their low toxicity, high stability, and intense blue emission. However, their intrinsically poor electrical conductivity, stemming from isolated conductive copper iodide tetrahedra by cesium atoms, severely limits charge transport which poses a critical challenge for optoelectronic applications. In this study, we propose a novel strategy to overcome this limitation by utilizing precisely optimized zinc oxide nanoripple structures within a lateral Cs3Cu2I5 photodetector (PD) architecture featuring interdigitated electrodes (IDEs). The ZnO nanoripple was systematically tuned to improve the percolation paths, providing efficient routes for photogenerated carriers to migrate to the IDEs. Consequently, the optimized heterojunctions comprising Cs3Cu2I5 and ZnO exhibited superior photocurrent compared to the pristine Cs3Cu2I5 counterparts. This nanostructure-mediated charge transport engineering strategy for lateral structured PDs offers a new pathway for utilizing low-conductivity 0D materials for conventional optoelectronics, next-generation Internet of Things sensor networks, and plausibly biosensing applications.

cond-mat.mtrl-sci↗

arXiv2025

Approximate solutions to games of ordered preference

Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as the time horizon, number of players, or number of preference levels increase. While receding horizon frameworks mitigate long-horizon intractability by solving sequential shorter games, often warm-started, they do not resolve the complexity growth inherent in existing methods for solving games of ordered preference. This paper introduces a solution strategy that avoids excessive complexity growth by approximating solutions using lexicographic iterated best response (IBR) in receding horizon, termed "lexicographic IBR over time." Lexicographic IBR over time uses past information to accelerate convergence. We demonstrate through simulated traffic scenarios that lexicographic IBR over time efficiently computes approximate-optimal solutions for receding horizon games of ordered preference, converging towards generalized Nash equilibria.

eess.SY↗

arXiv2025

You Can't Always Get What You Want: Games of Ordered Preference

We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy intersection must balance the desire to make forward progress with the risk of collision. Mathematically, these problems possess a nested structure, and to behave properly players must prioritize their most important preference, and only consider less important preferences to the extent that they do not compromise performance on more important ones. We consider multi-agent, noncooperative variants of these problems, and seek generalized Nash equilibria in which each player's decision reflects both its hierarchy of preferences and other players' actions. We make two key contributions. First, we develop a recursive approach for deriving the first-order optimality conditions of each player's nested problem. Second, we propose a sequence of increasingly tight relaxations, each of which can be transcribed as a mixed complementarity problem and solved via existing methods. Experimental results demonstrate that our approach reliably converges to equilibrium solutions that strictly reflect players' individual ordered preferences.

cs.GT↗

arXiv2025

A Convex Formulation of Game-theoretic Hierarchical Routing

Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios.

cs.MA↗

arXiv2024

Smooth Information Gathering in Two-Player Noncooperative Games

We present a mathematical framework for modeling two-player noncooperative games in which one player is uncertain of the other player's costs but can preemptively allocate information-gathering resources to reduce this uncertainty. We refer to the players as the uncertain player (UP) and the certain player (CP), respectively. We obtain UP's decisions by solving a two-stage problem where, in Stage 1, UP allocates information-gathering resources that smoothly transform the information structure in the second stage. Then, in Stage 2, a signal (that is, a function of the Stage 1 allocation) informs UP about CP's costs, and both players execute strategies which depend upon the signal's value. This framework allows for a smooth resource allocation, in contrast to existing literature on the topic. We also identify conditions under which the gradient of UP's overall cost with respect to the information-gathering resources is well-defined. Then we provide a gradient-based algorithm to solve the two-stage game. Finally, we apply our framework to a tower-defense game which can be interpreted as a variant of a Colonel Blotto game with smooth payoff functions and uncertainty over battlefield valuations. We include an analysis of how optimal decisions shift with changes in information-gathering allocations and perturbations in the cost functions.

cs.GT↗

arXiv2023

Multi-Start Team Orienteering Problem for UAS Mission Re-Planning with Data-Efficient Deep Reinforcement Learning

In this paper, we study the Multi-Start Team Orienteering Problem (MSTOP), a mission re-planning problem where vehicles are initially located away from the depot and have different amounts of fuel. We consider/assume the goal of multiple vehicles is to travel to maximize the sum of collected profits under resource (e.g., time, fuel) consumption constraints. Such re-planning problems occur in a wide range of intelligent UAS applications where changes in the mission environment force the operation of multiple vehicles to change from the original plan. To solve this problem with deep reinforcement learning (RL), we develop a policy network with self-attention on each partial tour and encoder-decoder attention between the partial tour and the remaining nodes. We propose a modified REINFORCE algorithm where the greedy rollout baseline is replaced by a local mini-batch baseline based on multiple, possibly non-duplicate sample rollouts. By drawing multiple samples per training instance, we can learn faster and obtain a stable policy gradient estimator with significantly fewer instances. The proposed training algorithm outperforms the conventional greedy rollout baseline, even when combined with the maximum entropy objective.

cs.LG↗