arXiv subjects

Minchan Jung

Publications and source records attributed to Minchan Jung.

5 recordsLinked to original sources

arXiv2026

Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent

The rate-optimal convergence rate of gradient descent (GD) with a fixed step-size is well known to be $\Theta(N^{-1})$ for $L$-Lipschitz smooth convex objectives in the prior art in convex optimization. Surprisingly, several recent works show that we can accelerate vanilla GD by applying a nonconstant, nonadaptive, deterministic step-size schedule. The best-known upper bounds so far in the non-anytime & anytime setups are $O(N^{-1.271})$ [Altschuler and Parrilo, 2025, Grimmer et al., 2023] and $O(N^{-1.119})$ [Zhang et al., 2025], respectively. On the other hand, the best reported lower bounds (or barriers) up to date in the non-anytime & anytime setups are $\Omega(N^{-1.635})$ and $\Omega(N^{-1.241})$ [Ye and Liu, 2026], respectively. We narrow these gaps by establishing stronger lower bounds for GD's convergence rate in both settings: $\Omega(N^{-1.450})$ for the non-anytime rate bound and $\Omega(N^{-1.184})$ for the anytime rate barrier.

math.OC↗

arXiv2026

Deep-Unfolded Coordination

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.

cs.RO↗

arXiv2026

Beyond Pure Sampling: Hybrid Optimization Mechanisms for Non-Convex Model Predictive Control

This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. We demonstrate a dual-step optimization mechanism designed to overcome these traps. (1) an initial phase of using DDP to exploit the gradient of the cost landscape, followed by (2) disruption of the optimization via sampling from policies characterized by the inverse Hessian of the action-value function. We provide a rigorous analysis of this sampling mechanism of three ME-DDP variants: Unimodal Gaussian ME-DDP, Multimodal Gaussian ME-DDP, and Stein Variational DDP. Furthermore, with navigation tasks of four robotic systems under cluttered environments, we conduct extensive benchmarking of three variants of the ME-DDP, against deterministic DDP, and one of the most successful sampling-based schemes, Model Predictive Path Integral (MPPI) control with three policy parameterizations and update laws that correspond to those of ME-DDPs. The results show that in low-dimensional systems where the cost landscapes are relatively simple and local information is sufficiently representative, our framework consistently outperforms MPPIs. In high-dimensional systems, MPPI can occasionally discover aggressive maneuvers that enable it to steer the systems faster than DDP-based methods, whereas our method maintains a higher, more stable success rate. Finally, we validate the practical efficacy of the framework through hardware experiments with a quadrotor navigating a dense, non-convex obstacle field, confirming the robustness of the proposed framework for real-world deployment.

cs.RO↗

arXiv2024

MPPI-IPDDP: Hybrid Method of Collision-Free Smooth Trajectory Generation for Autonomous Robots

This paper presents a hybrid trajectory optimization method designed to generate collision-free, smooth trajectories for autonomous mobile robots. By combining sampling-based Model Predictive Path Integral (MPPI) control with gradient-based Interior-Point Differential Dynamic Programming (IPDDP), we leverage their respective strengths in exploration and smoothing. The proposed method, MPPI-IPDDP, involves three steps: First, MPPI control is used to generate a coarse trajectory. Second, a collision-free convex corridor is constructed. Third, IPDDP is applied to smooth the coarse trajectory, utilizing the collision-free corridor from the second step. To demonstrate the effectiveness of our approach, we apply the proposed algorithm to trajectory optimization for differential-drive wheeled mobile robots and point-mass quadrotors. In comparisons with other MPPI variants and continuous optimization-based solvers, our method shows superior performance in terms of computational robustness and trajectory smoothness. Code: https://github.com/i-ASL/mppi-ipddp Video: https://youtu.be/-oUAt5sd9Bk

cs.RO↗

arXiv2024

BiC-MPPI: Goal-Pursuing, Sampling-Based Bidirectional Rollout Clustering Path Integral for Trajectory Optimization

This paper introduces the Bidirectional Clustered MPPI (BiC-MPPI) algorithm, a novel trajectory optimization method aimed at enhancing goal-directed guidance within the Model Predictive Path Integral (MPPI) framework. BiC-MPPI incorporates bidirectional dynamics approximations and a new guide cost mechanism, improving both trajectory planning and goal-reaching performance. By leveraging forward and backward rollouts, the bidirectional approach ensures effective trajectory connections between initial and terminal states, while the guide cost helps discover dynamically feasible paths. Experimental results demonstrate that BiC-MPPI outperforms existing MPPI variants in both 2D and 3D environments, achieving higher success rates and competitive computation times across 900 simulations on a modified BARN dataset for autonomous navigation. GitHub: https://github.com/i-ASL/BiC-MPPI

cs.RO↗