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Nathan P. Lawrence

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eess.SY Machine Learning Systems and Control math.OC

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preprint2026arXiv

Error whitening: Why Gauss-Newton outperforms Newton

The Gauss-Newton matrix is widely viewed as a positive semidefinite approximation of the Hessian, yet mounting empirical evidence shows that Gauss-Newton descent outperforms Newton's method. We adopt a function space perspective to analyze this phenomenon. We show that the generalized Gauss-Newton (GGN) matrix projects the Newton direction in function space onto the model's tangent space, while a Jacobian-only variant obtained by applying the least squares Gauss-Newton matrix to non-least squares losses projects the function space loss gradient onto this same tangent space. Both projections eliminate distortions from the model's parameterization. Specifically, the evolution of the prediction-target mismatch depends on the model's parameterization through the matrix $JJ^\top$ where $J$ is the Jacobian of the model with respect to its parameters. The projections effectively replace $JJ^\top$ with the identity. We call this effect error whitening. Once the parameterization is removed, the prediction-target mismatch evolves according to dynamics dictated by the structure of the loss and the projection produced by the optimizer. Error whitening is a special property of Gauss-Newton descent that rigorously distinguishes it from Newton's method. We empirically demonstrate that Gauss-Newton optimizers follow the theoretically predicted function space dynamics and outperforms Newton's method, Adam, and Muon across case studies spanning supervised learning, physics-informed deep learning, and approximate dynamic programming.

preprint2023arXiv

Automated deep reinforcement learning for real-time scheduling strategy of multi-energy system integrated with post-carbon and direct-air carbon captured system

The carbon-capturing process with the aid of CO2 removal technology (CDRT) has been recognised as an alternative and a prominent approach to deep decarbonisation. However, the main hindrance is the enormous energy demand and the economic implication of CDRT if not effectively managed. Hence, a novel deep reinforcement learning agent (DRL), integrated with an automated hyperparameter selection feature, is proposed in this study for the real-time scheduling of a multi-energy system coupled with CDRT. Post-carbon capture systems (PCCS) and direct-air capture systems (DACS) are considered CDRT. Various possible configurations are evaluated using real-time multi-energy data of a district in Arizona and CDRT parameters from manufacturers' catalogues and pilot project documentation. The simulation results validate that an optimised soft-actor critic (SAC) algorithm outperformed the TD3 algorithm due to its maximum entropy feature. We then trained four (4) SAC agents, equivalent to the number of considered case studies, using optimised hyperparameter values and deployed them in real time for evaluation. The results show that the proposed DRL agent can meet the prosumers' multi-energy demand and schedule the CDRT energy demand economically without specified constraints violation. Also, the proposed DRL agent outperformed rule-based scheduling by 23.65%. However, the configuration with PCCS and solid-sorbent DACS is considered the most suitable configuration with a high CO2 captured-released ratio of 38.54, low CO2 released indicator value of 2.53, and a 36.5% reduction in CDR cost due to waste heat utilisation and high absorption capacity of the selected sorbent. However, the adoption of CDRT is not economically viable at the current carbon price. Finally, we showed that CDRT would be attractive at a carbon price of 400-450USD/ton with the provision of tax incentives by the policymakers.

preprint2021arXiv

Deep Reinforcement Learning with Shallow Controllers: An Experimental Application to PID Tuning

Deep reinforcement learning (RL) is an optimization-driven framework for producing control strategies for general dynamical systems without explicit reliance on process models. Good results have been reported in simulation. Here we demonstrate the challenges in implementing a state of the art deep RL algorithm on a real physical system. Aspects include the interplay between software and existing hardware; experiment design and sample efficiency; training subject to input constraints; and interpretability of the algorithm and control law. At the core of our approach is the use of a PID controller as the trainable RL policy. In addition to its simplicity, this approach has several appealing features: No additional hardware needs to be added to the control system, since a PID controller can easily be implemented through a standard programmable logic controller; the control law can easily be initialized in a "safe'' region of the parameter space; and the final product -- a well-tuned PID controller -- has a form that practitioners can reason about and deploy with confidence.

preprint2020arXiv

Deep Reinforcement Learning for Process Control: A Primer for Beginners

Advanced model-based controllers are well established in process industries. However, such controllers require regular maintenance to maintain acceptable performance. It is a common practice to monitor controller performance continuously and to initiate a remedial model re-identification procedure in the event of performance degradation. Such procedures are typically complicated and resource-intensive, and they often cause costly interruptions to normal operations. In this paper, we exploit recent developments in reinforcement learning and deep learning to develop a novel adaptive, model-free controller for general discrete-time processes. The DRL controller we propose is a data-based controller that learns the control policy in real time by merely interacting with the process. The effectiveness and benefits of the DRL controller are demonstrated through many simulations.