arXiv subjects

Insoon Yang

Publications and source records attributed to Insoon Yang.

At least 19 recordsLinked to original sources

arXiv2026

WRAP: Wasserstein-Robust Adaptive Plug-in for Robot Localization

Robotic localization under changing sensing conditions can suffer from biased errors and miscalibrated covariances. We present WRAP, an adapter-agnostic Wasserstein-robust plug-in for nonlinear extended Kalman filter (EKF) and error-state Kalman filter (ESKF) stacks. A causal module supplies time-varying effective process and measurement statistics; a mean-preserving Wasserstein local update then computes least-favorable covariances and a robust gain without changing the propagation model, residual, or retraction. This separates mean adaptation from covariance robustification and uses distinct radii for propagation and sensing. On 18 UWB--IMU sequences held out from adapter training, adapter-only and WRAP reduce mean 3-D position RMSE by $19.8\%$ and $27.4\%$ relative to the nominal ESKF; an isotropic ablation reaches $19.5\%$, linking the incremental gain to directional process-covariance redistribution. An in-sample GNSS--INS study shows that mean adaptation provides most of the accuracy gain, while DR improves consistency and mitigates over-tightened classical covariance estimates. The robust solve takes 0.05 ms for UWB and 2.92 ms for GNSS on a Jetson Orin Nano.

cs.RO↗

arXiv2026

From Prediction Uncertainty to Conformalized Distance Fields for Safe Motion Planning

Safe motion planning in dynamic environments requires reasoning about the uncertainty in predicted obstacle motion without sacrificing real-time performance. Existing conformal approaches conformalize a scalar score that aggregates per-obstacle prediction errors, losing spatial coherence and scaling poorly with scene density. We instead conformalize the entire predicted distance field at once. This functional conformal prediction (FCP) framework yields a distribution-free, field-level lower bound, from which safety follows uniformly: any trajectory satisfying the resulting constraint is certified safe, independent of how the control space is sampled. The key enabler is that the residual distance field is empirically low-rank and approximately time-invariant, which makes the bound decomposable in coefficient space. An envelope is fitted offline via functional PCA and a Gaussian-mixture inductive conformal procedure, then refined online by a lightweight adaptive functional conformal (AFCP) update on a low-dimensional vector. This keeps the per-step cost largely insensitive to obstacle count and retains long-run field coverage under distribution shift. We embed the envelope as a tightened safety constraint in a sampling-based model predictive controller, FCP-MPC. On the ETH--UCY pedestrian benchmarks and a dense 3D quadrotor task with up to 280 dynamic obstacles, FCP-MPC attains a favorable balance of safety, feasibility, and efficiency, reaching goals where pointwise and egocentric conformal baselines become too conservative or too expensive, while keeping per-step computation far below online uncertainty-reasoning baselines.

cs.RO↗

arXiv2026

Residual-Aware Distributionally Robust EKF: Absorbing Linearization Mismatch via Wasserstein Ambiguity

The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that addresses both challenges within a unified Wasserstein distributionally robust state estimation framework. The key idea is to treat linearization residuals as uncertainty and absorb them into an effective uncertainty model captured by a stage-wise ambiguity set, enabling noise-model mismatch and approximation errors to be handled within a single formulation. This approach yields a computable effective radius along with deterministic upper bounds on the prior and posterior mean-squared errors of the true nonlinear estimation error. The resulting filter admits a tractable semidefinite programming reformulation while preserving the recursive structure of the classical EKF. Simulations on coordinated-turn target tracking and uncertainty-aware robot navigation demonstrate improved estimation accuracy and safety compared to standard EKF baselines under model mismatch and nonlinear effects.

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arXiv2025

Distributionally Robust Kalman Filter

We study state estimation for discrete-time linear stochastic systems under distributional ambiguity in the initial state, process noise, and measurement noise. We propose a noise-centric distributionally robust Kalman filter (DRKF) based on Wasserstein ambiguity sets imposed directly on these distributions. This formulation excludes dynamically unreachable priors and yields a Kalman-type recursion driven by least-favorable covariances computed via semidefinite programs (SDP). In the time-invariant case, the steady-state DRKF is obtained from a single stationary SDP, producing a constant gain with Kalman-level online complexity. We establish the convergence of the DR Riccati covariance iteration to the stationary SDP solution, together with an explicit sufficient condition for a prescribed convergence rate. We further show that the proposed noise-centric model induces a priori spectral bounds on all feasible covariances and a Kalman filter sandwiching property for the DRKF covariances. Finally, we prove that the steady-state error dynamics are Schur stable, and the steady-state DRKF is asymptotically minimax optimal with respect to worst-case mean-square error.

eess.SY↗

arXiv2025

Sharpness-Aware Minimization Can Hallucinate Minimizers

Sharpness-Aware Minimization (SAM) is widely used to seek flatter minima -- often linked to better generalization. In its standard implementation, SAM updates the current iterate using the loss gradient evaluated at a point perturbed by distance $\rho$ along the normalized gradient direction. We show that, for some choices of $\rho$, SAM can stall at points where this shifted (perturbed-point) gradient vanishes despite a nonzero original gradient, and therefore, they are not stationary points of the original loss. We call these points hallucinated minimizers, prove their existence under simple nonconvex landscape conditions (e.g., the presence of a local minimizer and a local maximizer), and establish sufficient conditions for local convergence of the SAM iterates to them. We corroborate this failure mode in neural network training and observe that it aligns with SAM's performance degradation often seen at large $\rho$. Finally, as a practical safeguard, we find that a short initial SGD warm-start before enabling SAM mitigates this failure mode and reduces sensitivity to the choice of $\rho$.

cs.LG↗

arXiv2025

KoopCast: Trajectory Forecasting via Koopman Operators

We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting trajectories into a higher-dimensional space. The framework follows a two-stage design: first, a probabilistic neural goal estimator predicts plausible long-term targets, specifying where to go; second, a Koopman operator-based refinement module incorporates intention and history into a nonlinear feature space, enabling linear prediction that dictates how to go. This dual structure not only ensures strong predictive accuracy but also inherits the favorable properties of linear operators while faithfully capturing nonlinear dynamics. As a result, our model offers three key advantages: (i) competitive accuracy, (ii) interpretability grounded in Koopman spectral theory, and (iii) low-latency deployment. We validate these benefits on ETH/UCY, the Waymo Open Motion Dataset, and nuScenes, which feature rich multi-agent interactions and map-constrained nonlinear motion. Across benchmarks, KoopCast consistently delivers high predictive accuracy together with mode-level interpretability and practical efficiency.

cs.LG↗

arXiv2025

Robust Continuous-Time Generation Scheduling under Power Demand Uncertainty: An Affine Decision Rule Approach

Most existing generation scheduling models for power systems under demand uncertainty rely on energy-based formulations with a finite number of time periods, which may fail to ensure that power supply and demand are balanced continuously over time. To address this issue, we propose a robust generation scheduling model in a continuous-time framework, employing a decision rule approach. First, for a given set of demand trajectories, we formulate a general robust generation scheduling problem to determine a decision rule that maps these demand trajectories and time points to the power outputs of generators. Subsequently, we derive a surrogate of it as our model by carefully designing a class of decision rules that are affine in the current demand, with coefficients invariant over time and constant terms that are continuous piecewise affine functions of time. As a result, our model can be recast as a finite-dimensional linear program to determine the coefficients and the function values of the constant terms at each breakpoint, solvable via the cutting-plane method. Our model is non-anticipative unlike most existing continuous-time models, which use Bernstein polynomials, making it more practical. We also provide illustrative numerical examples.

math.OC↗

arXiv2025

Egocentric Conformal Prediction for Safe and Efficient Navigation in Dynamic Cluttered Environments

Conformal prediction (CP) has emerged as a powerful tool in robotics and control, thanks to its ability to calibrate complex, data-driven models with formal guarantees. However, in robot navigation tasks, existing CP-based methods often decouple prediction from control, evaluating models without considering whether prediction errors actually compromise safety. Consequently, ego-vehicles may become overly conservative or even immobilized when all potential trajectories appear infeasible. To address this issue, we propose a novel CP-based navigation framework that responds exclusively to safety-critical prediction errors. Our approach introduces egocentric score functions that quantify how much closer obstacles are to a candidate vehicle position than anticipated. These score functions are then integrated into a model predictive control scheme, wherein each candidate state is individually evaluated for safety. Combined with an adaptive CP mechanism, our framework dynamically adjusts to changes in obstacle motion without resorting to unnecessary conservatism. Theoretical analyses indicate that our method outperforms existing CP-based approaches in terms of cost-efficiency while maintaining the desired safety levels, as further validated through experiments on real-world datasets featuring densely populated pedestrian environments.

cs.RO↗

arXiv2025

On the Steady-State Distributionally Robust Kalman Filter

State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when distributional mismatches occur, potentially leading to instability or divergence. To address this limitation, we introduce a novel steady-state distributionally robust (DR) Kalman filter that leverages Wasserstein ambiguity sets to explicitly account for uncertainties in both process and measurement noise distributions. Our filter achieves computational efficiency by requiring merely the offline solution of a single convex semidefinite program, which yields a constant DR Kalman gain for robust state estimation under distributional mismatches. Additionally, we derive explicit theoretical conditions on the ambiguity set radius that ensure the asymptotic convergence of the time-varying DR Kalman filter to the proposed steady-state solution. Numerical simulations demonstrate that our approach outperforms existing baseline filters in terms of robustness and accuracy across both Gaussian and non-Gaussian uncertainty scenarios, highlighting its significant potential for real-world control and estimation applications.

eess.SY↗

arXiv2024

Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methods

Recent research has indicated a substantial rise in interest in understanding Nesterov's accelerated gradient methods via their continuous-time models. However, most existing studies focus on specific classes of Nesterov's methods, which hinders the attainment of an in-depth understanding and a unified perspective. To address this deficit, we present generalized continuous-time models that cover a broad range of Nesterov's methods, including those previously studied under existing continuous-time frameworks. Our key contributions are as follows. First, we identify the convergence rates of the generalized models, eliminating the need to determine the convergence rate for any specific continuous-time model derived from them. Second, we show that six existing continuous-time models are special cases of our generalized models, thereby positioning our framework as a unifying tool for analyzing and understanding these models. Third, we design a restart scheme for Nesterov's methods based on our generalized models and show that it ensures a monotonic decrease in objective function values. Owing to the broad applicability of our models, this scheme can be used to a broader class of Nesterov's methods compared to the original restart scheme. Fourth, we uncover a connection between our generalized models and gradient flow in continuous time, showing that the accelerated convergence rates of our generalized models can be attributed to a time reparametrization in gradient flow. Numerical experiment results are provided to support our theoretical analyses and results.

math.OC↗

arXiv2024

Wasserstein Distributionally Robust Control and State Estimation for Partially Observable Linear Systems

This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are unknown. Our method consists of the control and state estimation phases to handle distributional ambiguities of system disturbances and measurement noises, respectively. Leveraging tools from modern distributionally robust optimization, we consider an approximation of the control problem with an arbitrary nominal distribution and derive its closed-form optimal solution. We show that the separation principle holds, thereby allowing the state estimator to be designed separately. A novel distributionally robust Kalman filter is then proposed as an optimal solution to the state estimation problem with Gaussian nominal distributions. Our key contribution is the combination of distributionally robust control and state estimation into a unified algorithm. This is achieved by formulating a tractable semidefinite programming problem that iteratively determines the worst-case covariance matrices of all uncertainties, leading to a scalable and efficient algorithm. Our method is also shown to enjoy a guaranteed cost property as well as a probabilistic out-of-sample performance guarantee. The results of our numerical experiments demonstrate the performance and computational efficiency of the proposed method.

eess.SY↗

arXiv2024

Approximate Thompson Sampling for Learning Linear Quadratic Regulators with $O(\sqrt{T})$ Regret

We propose a novel Thompson sampling algorithm that learns linear quadratic regulators (LQR) with a Bayesian regret bound of $O(\sqrt{T})$. Our method leverages Langevin dynamics with a carefully designed preconditioner and incorporates a simple excitation mechanism. We show that the excitation signal drives the minimum eigenvalue of the preconditioner to grow over time, thereby accelerating the approximate posterior sampling process. Furthermore, we establish nontrivial concentration properties of the approximate posteriors generated by our algorithm. These properties enable us to bound the moments of the system state and attain an $O(\sqrt{T})$ regret bound without relying on the restrictive assumptions that are often used in the literature.

stat.ML↗

arXiv2023

On Task-Relevant Loss Functions in Meta-Reinforcement Learning and Online LQR

Designing a competent meta-reinforcement learning (meta-RL) algorithm in terms of data usage remains a central challenge to be tackled for its successful real-world applications. In this paper, we propose a sample-efficient meta-RL algorithm that learns a model of the system or environment at hand in a task-directed manner. As opposed to the standard model-based approaches to meta-RL, our method exploits the value information in order to rapidly capture the decision-critical part of the environment. The key component of our method is the loss function for learning the task inference module and the system model that systematically couples the model discrepancy and the value estimate, thereby facilitating the learning of the policy and the task inference module with a significantly smaller amount of data compared to the existing meta-RL algorithms. The idea is also extended to a non-meta-RL setting, namely an online linear quadratic regulator (LQR) problem, where our method can be simplified to reveal the essence of the strategy. The proposed method is evaluated in high-dimensional robotic control and online LQR problems, empirically verifying its effectiveness in extracting information indispensable for solving the tasks from observations in a sample efficient manner.

cs.LG↗

arXiv2023

Risk-Aware Wasserstein Distributionally Robust Control of Vessels in Natural Waterways

In the realm of maritime transportation, autonomous vessel navigation in natural inland waterways faces persistent challenges due to unpredictable natural factors. Existing scheduling algorithms fall short in handling these uncertainties, compromising both safety and efficiency. Moreover, these algorithms are primarily designed for non-autonomous vessels, leading to labor-intensive operations vulnerable to human error. To address these issues, this study proposes a risk-aware motion control approach for vessels that accounts for the dynamic and uncertain nature of tide islands in a distributionally robust manner. Specifically, a model predictive control method is employed to follow the reference trajectory in the time-space map while incorporating a risk constraint to prevent grounding accidents. To address uncertainties in tide islands, a novel modeling technique represents them as stochastic polytopes. Additionally, potential inaccuracies in waterway depth are addressed through a risk constraint that considers the worst-case uncertainty distribution within a Wasserstein ambiguity set around the empirical distribution. Using sensor data collected in the Guadalquivir River, we empirically demonstrate the performance of the proposed method through simulations on a vessel. As a result, the vessel successfully navigates the waterway while avoiding grounding accidents, even with a limited dataset of observations. This stands in contrast to existing non-robust controllers, highlighting the robustness and practical applicability of the proposed approach.

cs.RO↗

arXiv2023

Distributionally Robust Differential Dynamic Programming with Wasserstein Distance

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown disturbance distributions. To address this limitation, we propose a novel DDP method that approximately solves the Wasserstein distributionally robust control (WDRC) problem, where the true disturbance distribution is unknown but a disturbance sample dataset is given. Our approach aims to develop a practical and computationally efficient DDP solution. To achieve this, we use the Kantrovich duality principle to decompose the value function in a novel way and derive closed-form expressions of the distributionally robust control and worst-case distribution policies to be used in each iteration of our DDP algorithm. This characterization makes our method tractable and scalable without the need for numerically solving any minimax optimization problems. The superior out-of-sample performance and scalability of our algorithm are demonstrated through kinematic car navigation and coupled oscillator problems.

eess.SY↗

arXiv2023

Unifying Nesterov's Accelerated Gradient Methods for Convex and Strongly Convex Objective Functions: From Continuous-Time Dynamics to Discrete-Time Algorithms

Although Nesterov's accelerated gradient (NAG) methods have been studied from various perspectives, it remains unclear why the most popular forms of NAG must handle convex and strongly convex objective functions separately. Motivated by this inconsistency, we propose an NAG method that unifies the existing ones for the convex and strongly convex cases. We first design a Lagrangian function that continuously extends the first Bregman Lagrangian to the strongly convex setting. As a specific case of the Euler--Lagrange equation for this Lagrangian, we derive an ordinary differential equation (ODE) model, which we call the unified NAG ODE, that bridges the gap between the ODEs that model NAG for convex and strongly convex objective functions. We then design the unified NAG, a novel momentum method whereby the continuous-time limit corresponds to the unified ODE. The coefficients and the convergence rates of the unified NAG and unified ODE are continuous in the strong convexity parameter $\mu$ on $[0, +\infty)$. Unlike the existing popular algorithm and ODE for strongly convex objective functions, the unified NAG and the unified NAG ODE always have superior convergence guarantees compared to the known algorithms and ODEs for non-strongly convex objective functions. This property is beneficial in practical perspective when considering strongly convex objective functions with small $\mu$. Furthermore, we extend our unified dynamics and algorithms to the higher-order setting. Last but not least, we propose the unified NAG-G ODE, a novel ODE model for minimizing the gradient norm of strongly convex objective functions. Our unified Lagrangian framework is crucial in the process of constructing this ODE. Fascinatingly, using our novel tool, called the differential kernel, we observe that the unified NAG ODE and the unified NAG-G ODE have an anti-transpose relationship.

math.OC↗

arXiv2022

Using affine policies to reformulate two-stage Wasserstein distributionally robust linear programs to be independent of sample size

Intensively studied in theory as a promising data-driven tool for decision-making under ambiguity, two-stage distributionally robust optimization (DRO) problems over Wasserstein balls are not necessarily easy to solve in practice. This is partly due to large sample size. In this article, we study a generic two-stage distributionally robust linear program (2-DRLP) over a 1-Wasserstein ball using an affine policy. The 2-DRLP has right-hand-side uncertainty with a rectangular support. Our main contribution is to show that the 2-DRLP problem has a tractable reformulation with a scale independent of sample size. The reformulated problem can be solved within a pre-defined optimality tolerance using robust optimization techniques. To reduce the inevitable conservativeness of the affine policy while preserving independence of sample size, we further develop a method for constructing an uncertainty set with a probabilistic guarantee over which the Wasserstein ball is re-defined. As an application, we present a novel unit commitment model for power systems under uncertainty of renewable energy generation to examine the effectiveness of the proposed 2-DRLP technique. Extensive numerical experiments demonstrate that our model leads to better out-of-sample performance on average than other state-of-the-art distributionally robust unit commitment models while staying computationally competent.

math.OC↗

arXiv2022

Wasserstein Distributionally Robust Control of Partially Observable Linear Stochastic Systems

Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially observable DRC problem for discrete-time linear systems using the Wasserstein metric. For a tractable solution, we propose a novel approximation method exploiting the Gelbrich bound of Wasserstein distance. Using techniques from modern distributionally robust optimization, we derive a closed-form expression for the optimal control policy and a tractable semidefinite programming problem for the worst-case distribution policy in both finite-horizon and infinite-horizon average-cost settings. The proposed method features several salient theoretical properties, such as a guaranteed cost property and a probabilistic out-of-sample performance guarantee, demonstrating the distributional robustness of our controller. Furthermore, the resulting controller is shown to ensure the closed-loop stability of the mean-state system. The empirical performance of our method is tested through numerical experiments on a power system frequency control problem.

eess.SY↗