arXiv subjects

James Anderson

Publications and source records attributed to James Anderson.

At least 19 recordsLinked to original sources

arXiv2026

TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

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arXiv2026

On the Unification of Optimal Current Reference Theory for Wound Rotor Synchronous Machines

Controllers for motor drives typically require a current reference which will satisfy the requested torque subject to system constraints. This work generalizes existing current reference theory to the case of the Wound Rotor Synchronous Machine (WRSM). By incorporating the additional rotor-current degree-of-freedom, along with magnetic saturation, cross-coupling, and speed-dependent core losses, the problem of finding an optimal current reference is formulated within affine flux regions as a quadratically constrained quadratic program using a piecewise-affine approximation derived from finite-element data. The solution is characterized according to the active constraint regime, yielding closed-form or low-dimensional polynomial solutions in several cases, and a small semidefinite program in the voltage constrained regime. The proposed framework extends unified optimal current reference theory beyond the permanent-magnet setting to three degree-of-freedom WRSMs while remaining computationally tractable. Results on a physical WRSM prototype illustrate the effectiveness of the approach across the torque-speed operating envelope.

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arXiv2026

Multitask LQG Control: Performance and Generalization Bounds

We study multitask learning for stochastic and partially observed control systems, focusing on the linear quadratic Gaussian (LQG) problem. Our goal is to learn a common stabilizing controller that generalizes across a distribution of systems and objectives. To this end, we leverage a history-dependent lifting that recasts the multitask LQG problem into an equivalent high-dimensional multitask LQR problem, allowing for the analysis of policy gradient methods. We show that learning a common lifted controller induces a heterogeneity bias which we characterize via a "bisimulation function". We establish performance and generalization guarantees that explicitly depend on such bisimulation-based heterogeneity measures. For model-free, we demonstrate that multitask learning reduces policy gradient estimation variance proportionally to the number of tasks in the training set.

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arXiv2026

Learning Invariant Visual Representations for Planning with Joint-Embedding Predictive World Models

World models learned from high-dimensional visual observations allow agents to make decisions and plan directly in latent space, avoiding pixel-level reconstruction. However, recent latent predictive architectures (JEPAs), including the DINO world model (DINO-WM), display a degradation in test time robustness due to their sensitivity to "slow features". These include visual variations such as background changes and distractors that are irrelevant to the task being solved. We address this limitation by augmenting the predictive objective with a bisimulation encoder that enforces control-relevant state equivalence, mapping states with similar transition dynamics to nearby latent states while limiting contributions from slow features. We evaluate our model on a simple navigation task under different test-time background changes and visual distractors. Across all benchmarks, our model consistently improves robustness to slow features while operating in a reduced latent space, up to 10x smaller than that of DINO-WM. Moreover, our model is agnostic to the choice of pretrained visual encoder and maintains robustness when paired with DINOv2, SimDINOv2, and iBOT features.

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arXiv2025

Adversarially Robust Multitask Adaptive Control

We study adversarially robust multitask adaptive linear quadratic control; a setting where multiple systems collaboratively learn control policies under model uncertainty and adversarial corruption. We propose a clustered multitask approach that integrates clustering and system identification with resilient aggregation to mitigate corrupted model updates. Our analysis characterizes how clustering accuracy, intra-cluster heterogeneity, and adversarial behavior affect the expected regret of certainty-equivalent (CE) control across LQR tasks. We establish non-asymptotic bounds demonstrating that the regret decreases inversely with the number of honest systems per cluster and that this reduction is preserved under a bounded fraction of adversarial systems within each cluster.

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arXiv2025

Online Energy Storage Arbitrage under Imperfect Predictions: A Conformal Risk-Aware Approach

This work proposes a conformal approach for energy storage arbitrage to control the downside risk arising from imperfect price forecasts. Energy storage arbitrage relies solely on predictions of future market prices, while inaccurate price predictions may lead to significant profit losses. Based on conformal decision theory, we describe a controller that dynamically adjusts decision conservativeness through prediction sets without distributional assumptions. To enable online calibration when online profit loss feedback is unobservable, we establish that a temporal difference error serves as a measurable proxy. Building on this insight, we develop two online calibration strategies: prediction error-based adaptation targeting forecast accuracy, and value error-based calibration focusing on decision quality. Analysis of the conformal controller proves bounded long-term risk with convergence guarantees in temporal difference error, which further effectively manages risk exposure in potential profit losses. Case studies demonstrate superior performance in balancing risk and opportunity compared to benchmarks under varying forecast conditions.

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arXiv2025

Physics-informed learning under mixing: How physical knowledge speeds up learning

A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.

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arXiv2025

Policy Gradient Bounds in Multitask LQR

We analyze the performance of policy gradient in multitask linear quadratic regulation (LQR), where the system and cost parameters differ across tasks. The main goal of multitask LQR is to find a controller with satisfactory performance on every task. Prior analyses on relevant contexts fail to capture closed-loop task similarities, resulting in conservative performance guarantees. To account for such similarities, we propose bisimulation-based measures of task heterogeneity. Our measures employ new bisimulation functions to bound the cost gradient distance between a pair of tasks in closed loop with a common stabilizing controller. Employing these measures, we derive suboptimality bounds for both the multitask optimal controller and the asymptotic policy gradient controller with respect to each of the tasks. We further provide conditions under which the policy gradient iterates remain stabilizing for every system. For multiple random sets of certain tasks, we observe that our bisimulation-based measures improve upon baseline measures of task heterogeneity dramatically.

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arXiv2025

On the Gradient Domination of the LQG Problem

We consider solutions to the linear quadratic Gaussian (LQG) regulator problem via policy gradient (PG) methods. Although PG methods have demonstrated strong theoretical guarantees in solving the linear quadratic regulator (LQR) problem, despite its nonconvex landscape, their theoretical understanding in the LQG setting remains limited. Notably, the LQG problem lacks gradient dominance in the classical parameterization, i.e., with a dynamic controller, which hinders global convergence guarantees. In this work, we study PG for the LQG problem by adopting an alternative parameterization of the set of stabilizing controllers and employing a lifting argument. We refer to this parameterization as a history representation of the control input as it is parameterized by past input and output data from the previous p time-steps. This representation enables us to establish gradient dominance and approximate smoothness for the LQG cost. We prove global convergence and per-iteration stability guarantees for policy gradient LQG in model-based and model-free settings. Numerical experiments on an open-loop unstable system are provided to support the global convergence guarantees and to illustrate convergence under different history lengths of the history representation.

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arXiv2025

Learning Stabilizing Policies via an Unstable Subspace Representation

We study the problem of learning to stabilize (LTS) a linear time-invariant (LTI) system. Policy gradient (PG) methods for control assume access to an initial stabilizing policy. However, designing such a policy for an unknown system is one of the most fundamental problems in control, and it may be as hard as learning the optimal policy itself. Existing work on the LTS problem requires large data as it scales quadratically with the ambient dimension. We propose a two-phase approach that first learns the left unstable subspace of the system and then solves a series of discounted linear quadratic regulator (LQR) problems on the learned unstable subspace, targeting to stabilize only the system's unstable dynamics and reduce the effective dimension of the control space. We provide non-asymptotic guarantees for both phases and demonstrate that operating on the unstable subspace reduces sample complexity. In particular, when the number of unstable modes is much smaller than the state dimension, our analysis reveals that LTS on the unstable subspace substantially speeds up the stabilization process. Numerical experiments are provided to support this sample complexity reduction achieved by our approach.

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arXiv2025

A Decision-Focused Predict-then-Bid Framework for Strategic Energy Storage

This paper introduces a novel decision-focused framework for energy storage arbitrage bidding. Inspired by the bidding process for energy storage in electricity markets, we propose a predict-then-bid end-to-end method incorporating the storage arbitrage optimization and market clearing models. This is achieved through a tri-layer framework that combines a price prediction layer with a two-stage optimization problem: an energy storage optimization layer and a market-clearing optimization layer. We leverage the implicit function theorem for gradient computation in the first optimization layer and incorporate a perturbation-based approach into the decision-focused loss function to ensure differentiability in the market-clearing layer. Numerical experiments using electricity market data from New York demonstrate that our bidding design substantially outperforms existing methods, achieving the highest profits and showcasing the effectiveness of the proposed approach.

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arXiv2025

Collaborative Bayesian Optimization via Wasserstein Barycenters

Motivated by the growing need for black-box optimization and data privacy, we introduce a collaborative Bayesian optimization (BO) framework that addresses both of these challenges. In this framework agents work collaboratively to optimize a function they only have oracle access to. In order to mitigate against communication and privacy constraints, agents are not allowed to share their data but can share their Gaussian process (GP) surrogate models. To enable collaboration under these constraints, we construct a central model to approximate the objective function by leveraging the concept of Wasserstein barycenters of GPs. This central model integrates the shared models without accessing the underlying data. A key aspect of our approach is a collaborative acquisition function that balances exploration and exploitation, allowing for the optimization of decision variables collaboratively in each iteration. We prove that our proposed algorithm is asymptotically consistent and that its implementation via Monte Carlo methods is numerically accurate. Through numerical experiments, we demonstrate that our approach outperforms other baseline collaborative frameworks and is competitive with centralized approaches that do not consider data privacy.

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arXiv2025

Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning

We study task selection to enhance sample efficiency in model-agnostic meta-reinforcement learning (MAML-RL). Traditional meta-RL typically assumes that all available tasks are equally important, which can lead to task redundancy when they share significant similarities. To address this, we propose a coreset-based task selection approach that selects a weighted subset of tasks based on how diverse they are in gradient space, prioritizing the most informative and diverse tasks. Such task selection reduces the number of samples needed to find an $\epsilon$-close stationary solution by a factor of O(1/$\epsilon$). Consequently, it guarantees a faster adaptation to unseen tasks while focusing training on the most relevant tasks. As a case study, we incorporate task selection to MAML-LQR (Toso et al., 2024b), and prove a sample complexity reduction proportional to O(log(1/$\epsilon$)) when the task specific cost also satisfy gradient dominance. Our theoretical guarantees underscore task selection as a key component for scalable and sample-efficient meta-RL. We numerically validate this trend across multiple RL benchmark problems, illustrating the benefits of task selection beyond the LQR baseline.

math.OC↗

arXiv2025

Energy Storage Arbitrage Under Price Uncertainty: Market Risks and Opportunities

We investigate the profitability and risk of energy storage arbitrage in electricity markets under price uncertainty, exploring both robust and chance-constrained optimization approaches. We analyze various uncertainty representations, including polyhedral, ellipsoidal uncertainty sets and probabilistic approximations, to model price fluctuations and construct efficient frontiers that highlight the tradeoff between risk and profit. Using historical electricity price data, we quantify the impact of uncertainty on arbitrage strategies and compare their performance under distinct market conditions. The results reveal that arbitrage strategies under uncertainties can effectively secure expected profits, and robust strategies perform better in risk management across varying levels of conservativeness, especially under highly volatile market conditions. This work provides insights into storage arbitrage strategy selection for market participants with differing risk preferences, emphasizing the adaptability of efficient frontiers to the electricity market.

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arXiv2024

Defective correspondence coloring of planar graphs

Defective coloring (also known as relaxed or improper coloring) is a generalization of proper coloring defined as follows: for $d \in \mathbb{N}$, a coloring of a graph is $d$-defective if every vertex is colored the same as at most $d$ of its neighbors. We investigate defective coloring of planar graphs in the context of correspondence coloring, a generalization of list coloring introduced by Dvo\v{r}\'ak and Postle. First we show there exists a planar graph that is not $3$-defective $3$-correspondable, strengthening a recent result of Cho, Choi, Kim, Park, Shan, and Zhu. Then we construct a planar graph that is $1$-defective $3$-correspondable but not $4$-correspondable, thereby extending a recent result of Ma, Xu, and Zhu from list coloring to correspondence coloring. Finally we show all outerplanar graphs are $3$-defective $2$-correspondence colorable, with 3 defects being best possible.

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arXiv2024

Approximate Projections onto the Positive Semidefinite Cone Using Randomization

This paper presents two algorithms that compute approximate Positive Semidefinite (PSD) projections of real symmetric matrices using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection of an $n\times n$ matrix relies on a deterministic eigen-decomposition with computation that scales as $\mathcal{O}(n^3)$. Our approach leverages RNLA to construct low-rank matrix approximations before projection, significantly reducing the required numerical resources to $\mathcal{O}(k n^2)$, for some user defined fixed parameter $k$. The first algorithm utilizes random sampling to generate a low-rank approximation, followed by a standard eigen-decomposition on this smaller matrix. The second algorithm enhances this process by introducing a scaling approach that aligns the leading-order singular values with the positive eigenvalues, biasing the low-rank approximation to focus on capturing the essential information about the positive eigenvalues for PSD projection. Both methods offer a trade-off between accuracy and computational speed, supported by probabilistic error bounds. Numerical experiments on large-scale matrices ( $n\approx 20K$) demonstrate that the proposed randomized algorithms effectively approximate PSD projections.

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arXiv2024

Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Control

Representation learning is a powerful tool that enables learning over large multitudes of agents or domains by enforcing that all agents operate on a shared set of learned features. However, many robotics or controls applications that would benefit from collaboration operate in settings with changing environments and goals, whereas most guarantees for representation learning are stated for static settings. Toward rigorously establishing the benefit of representation learning in dynamic settings, we analyze the regret of multi-task representation learning for linear-quadratic control. This setting introduces unique challenges. Firstly, we must account for and balance the $\textit{misspecification}$ introduced by an approximate representation. Secondly, we cannot rely on the parameter update schemes of single-task online LQR, for which least-squares often suffices, and must devise a novel scheme to ensure sufficient improvement. We demonstrate that for settings where exploration is "benign", the regret of any agent after $T$ timesteps scales as $\tilde O(\sqrt{T/H})$, where $H$ is the number of agents. In settings with "difficult" exploration, the regret scales as $\tilde O(\sqrt{d_u d_\theta} \sqrt{T} + T^{3/4}/H^{1/5})$, where $d_x$ is the state-space dimension, $d_u$ is the input dimension, and $d_\theta$ is the task-specific parameter count. In both cases, by comparing to the minimax single-task regret $O(\sqrt{d_x d_u^2}\sqrt{T})$, we see a benefit of a large number of agents. Notably, in the difficult exploration case, by sharing a representation across tasks, the effective task-specific parameter count can often be small $d_\theta < d_x d_u$. Lastly, we provide numerical validation of the trends we predict.

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arXiv2024

Momentum for the Win: Collaborative Federated Reinforcement Learning across Heterogeneous Environments

We explore a Federated Reinforcement Learning (FRL) problem where $N$ agents collaboratively learn a common policy without sharing their trajectory data. To date, existing FRL work has primarily focused on agents operating in the same or ``similar" environments. In contrast, our problem setup allows for arbitrarily large levels of environment heterogeneity. To obtain the optimal policy which maximizes the average performance across all potentially completely different environments, we propose two algorithms: FedSVRPG-M and FedHAPG-M. In contrast to existing results, we demonstrate that both FedSVRPG-M and FedHAPG-M, both of which leverage momentum mechanisms, can exactly converge to a stationary point of the average performance function, regardless of the magnitude of environment heterogeneity. Furthermore, by incorporating the benefits of variance-reduction techniques or Hessian approximation, both algorithms achieve state-of-the-art convergence results, characterized by a sample complexity of $\mathcal{O}\left(\epsilon^{-\frac{3}{2}}/N\right)$. Notably, our algorithms enjoy linear convergence speedups with respect to the number of agents, highlighting the benefit of collaboration among agents in finding a common policy.

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