Namhoon Cho

Youngjae Min, Namhoon Cho, Navid Azizan · mit

While large machine learning models have shown remarkable performance in various domains, their training typically requires iterating for many passes over the training data. However, due to computational and memory constraints and potential privacy concerns, storing and accessing all the data is impractical in many real-world scenarios where the data arrives in a stream. In this paper, we investigate the problem of one-pass learning, in which a model is trained on sequentially arriving data without retraining on previous datapoints. Motivated by the demonstrated effectiveness of overparameterized models and the phenomenon of benign overfitting, we propose Orthogonal Recursive Fitting (ORFit), an algorithm for one-pass learning which seeks to perfectly fit each new datapoint while minimally altering the predictions on previous datapoints. ORFit updates the parameters in a direction orthogonal to past gradients, similar to orthogonal gradient descent (OGD) in continual learning. We show that, interestingly, ORFit's update leads to an operation similar to the recursive least-squares (RLS) algorithm in adaptive filtering but with significantly improved memory and computational efficiency, i.e., linear, instead of quadratic, in the number of parameters. To further reduce memory usage, we leverage the structure of the streaming data via an incremental principal component analysis (IPCA). We show that using the principal components is minimax optimal, i.e., it minimizes the worst-case forgetting of previous predictions for unknown future updates. Further, we prove that, for overparameterized linear models, the parameter vector obtained by ORFit matches what the standard multi-pass stochastic gradient descent (SGD) would converge to. Finally, we extend our results to the nonlinear setting for highly overparameterized models, relevant for deep learning.

Saki Omi, Hyo-Sang Shin, Namhoon Cho et al.

Recent studies have greatly improved reinforcement learning, and an increased interest in real-world implementation has emerged. In many cases, the implementation is challenged by time-varying disturbances as it introduces hidden states, which makes the problem best described with Partially Observable Markov Decision Processes. An effective approach to address this problem is to introduce a Recurrent Neural Network (RNN) in place of a state estimator. However, only a few studies have investigated the types of information to be supplied to the RNN and the network architecture to handle them. This study discusses the effectiveness of the inclusion of action along with observation and the impact of network architecture to handle them by providing interpretations of how the trajectories are summarized at LSTM networks. Specifically, three novel approaches with different architectures are introduced. All algorithms demonstrated the effectiveness of the inclusion of the action trajectories in simulation environments. In particular, one of the developed algorithms, H-TD3, differs from the typical actor and critic network as the critic network is trained by utilizing the hidden states generated by the actor network as the summarized trajectory information. This novel approach exhibited the potential improvement of the computational time while maintaining the performance.

Namhoon Cho, Hyo-Sang Shin, Antonios Tsourdos et al.

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints placed on the performance output variables. The proposed approach is to linearise the dynamics around the baseline values of its arguments, and then to solve for the corrective input required to transfer the perturbed trajectory to precisely known or desired values at specific time points, i.e., the interim points. Depending on the type of decision variables to adjust, parameter correction and control function correction methods are developed. These incremental correction methods can be utilised as a means to compensate for the prediction errors of pre-trained neural networks in real-time applications where high accuracy of the prediction of dynamical systems at prescribed time points is imperative. In this regard, the online update approach can be useful for enhancing overall targeting accuracy of finite-horizon control subject to point constraints using a neural policy. Numerical example demonstrates the effectiveness of the proposed approach in an application to a powered descent problem at Mars.

Namhoon Cho, Seokwon Lee, Hyo-Sang Shin et al.

This study presents a Bayesian learning perspective towards model predictive control algorithms. High-level frameworks have been developed separately in the earlier studies on Bayesian learning and sampling-based model predictive control. On one hand, the Bayesian learning rule provides a general framework capable of generating various machine learning algorithms as special instances. On the other hand, the dynamic mirror descent model predictive control framework is capable of diversifying sample-rollout-based control algorithms. However, connections between the two frameworks have still not been fully appreciated in the context of stochastic optimal control. This study combines the Bayesian learning rule point of view into the model predictive control setting by taking inspirations from the view of understanding model predictive controller as an online learner. The selection of posterior class and natural gradient approximation for the variational formulation governs diversification of model predictive control algorithms in the Bayesian learning approach to model predictive control. This alternative viewpoint complements the dynamic mirror descent framework through streamlining the explanation of design choices.

Namhoon Cho, Hyo-Sang Shin

This study presents a constructive methodology for designing accelerated convex optimisation algorithms in continuous-time domain. The two key enablers are the classical concept of passivity in control theory and the time-dependent change of variables that maps the output of the internal dynamic system to the optimisation variables. The Lyapunov function associated with the optimisation dynamics is obtained as a natural consequence of specifying the internal dynamics that drives the state evolution as a passive linear time-invariant system. The passivity-based methodology provides a general framework that has the flexibility to generate convex optimisation algorithms with the guarantee of different convergence rate bounds on the objective function value. The same principle applies to the design of online parameter update algorithms for adaptive control by re-defining the output of internal dynamics to allow for the feedback interconnection with tracking error dynamics.

Lekan Molu, Venkatraman Renganathan, Namhoon Cho

Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However, classical grid-based HJ solvers require $O(M^n)$ memory footprint for $M$ grid points per $n$ state dimension. This renders them impractical for high-dimensional systems. We address this bottleneck with a local PDE linearization that enables a frozen-coefficient sampling scheme for the viscous HJ PDE: a generalized Cole-Hopf-type transformation reduces the nonlinear HJ equation to a sequence of linear heat equations whose solutions admit Gaussian heat-kernel representations. The value function and its spatial gradient are then recovered via roll-outs of Monte Carlo expectations on Gaussian densities, yielding a storage and grid-free algorithm that scales as $N\cdot n$ for $N$ samples. This decoupling of memory from dimensionality enables reachability analysis on problems where grid-based methods are simply impossible. We prove a finite-sample concentration bound $O(N^{-1/2})$ error and conditional linear convergence for the introduced Monte-Carlo Picard iterative scheme. Numerical validation on pursuit-evasion games demonstrates relative $L^2_{\text{rel}}$ errors of $0.03 - 0.20$, with $14-26$ second wall-clock times per 2D slice on a CPU. Crucially, the method scales with validation on up to (but not limited to) $n=45$-dimensional multi-agent games.

Seyeon Kim, Joonhun Lee, Namhoon Cho et al.

Conventional uncertainty-aware temporal difference (TD) learning often assumes a zero-mean Gaussian distribution for TD errors, leading to inaccurate error representations and compromised uncertainty estimation. We introduce a novel framework for generalized Gaussian error modeling in deep reinforcement learning to enhance the flexibility of error distribution modeling by incorporating additional higher-order moment, particularly kurtosis, thereby improving the estimation and mitigation of data-dependent aleatoric uncertainty. We examine the influence of the shape parameter of the generalized Gaussian distribution (GGD) on aleatoric uncertainty and provide a closed-form expression that demonstrates an inverse relationship between uncertainty and the shape parameter. Additionally, we propose a theoretically grounded weighting scheme to address epistemic uncertainty by fully leveraging the GGD. We refine batch inverse variance weighting with bias reduction and kurtosis considerations, enhancing robustness. Experiments with policy gradient algorithms demonstrate significant performance gains.

Jeongeun Park, Jihwan Yoon, Byungwoo Jeon et al.

Prior Vision-Language-Action (VLA) models are typically trained on teleoperated successful demonstrations, while discarding numerous failed attempts that occur naturally during data collection. However, these failures encode where and how policies can be fragile, information that can be exploited to improve robustness. We address this problem by leveraging mixed-quality datasets to learn failure-aware reasoning at planning time. We introduce VINE, a hierarchical vision-language-action model that separates high-level reasoning (System 2) from low-level control (System 1) under a hierarchical reinforcement learning formalism, making failures usable as a structured learning signal rather than noisy supervision. System 2 performs feasibility-guided tree search over a 2D scene-graph abstraction: it proposes subgoal transitions, predicts success probabilities from both successes and failures, and prunes brittle branches before execution, effectively casting plan evaluation as feasibility scoring. The selected subgoal sequence is then passed to System 1, which executes low-level actions without modifying the agent's core skills. Trained entirely from offline teleoperation data, VINE integrates negative experience directly into the decision loop. Across challenging manipulation tasks, this approach consistently improves success rates and robustness, demonstrating that failure data is an essential resource for converting the broad competence of VLAs into robust execution.

Namhoon Cho, Hyo-Sang Shin

We propose automatic optimisation methods considering the geometry of matrix manifold for the normalised parameters of neural networks. Layerwise weight normalisation with respect to Frobenius norm is utilised to bound the Lipschitz constant and to enhance gradient reliability so that the trained networks are suitable for control applications. Our approach first initialises the network and normalises the data with respect to the $\ell^{2}$-$\ell^{2}$ gain of the initialised network. Then, the proposed algorithms take the update structure based on the exponential map on high-dimensional spheres. Given an update direction such as that of the negative Riemannian gradient, we propose two different ways to determine the stepsize for descent. The first algorithm utilises automatic differentiation of the objective function along the update curve defined on the combined manifold of spheres. The directional second-order derivative information can be utilised without requiring explicit construction of the Hessian. The second algorithm utilises the majorisation-minimisation framework via architecture-aware majorisation for neural networks. With these new developments, the proposed methods avoid manual tuning and scheduling of the learning rate, thus providing an automated pipeline for optimizing normalised neural networks.

Namhoon Cho, Hyo-Sang Shin

This study presents a policy optimisation framework for structured nonlinear control of continuous-time (deterministic) dynamic systems. The proposed approach prescribes a structure for the controller based on relevant scientific knowledge (such as Lyapunov stability theory or domain experiences) while considering the tunable elements inside the given structure as the point of parametrisation with neural networks. To optimise a cost represented as a function of the neural network weights, the proposed approach utilises the continuous-time policy gradient method based on adjoint sensitivity analysis as a means for correct and performant computation of cost gradient. This enables combining the stability, robustness, and physical interpretability of an analytically-derived structure for the feedback controller with the representational flexibility and optimised resulting performance provided by machine learning techniques. Such a hybrid paradigm for fixed-structure control synthesis is particularly useful for optimising adaptive nonlinear controllers to achieve improved performance in online operation, an area where the existing theory prevails the design of structure while lacking clear analytical understandings about tuning of the gains and the uncertainty model basis functions that govern the performance characteristics. Numerical experiments on aerospace applications illustrate the utility of the structured nonlinear controller optimisation framework.