Stochastic Gradient Descent (SGD) has become a cornerstone method in modern data science. However, deploying SGD in high-stakes applications necessitates rigorous quantification of its inherent uncertainty. In this work, we establishnon-asymptotic Berry–Esseen boundsfor linear functionals of online least-squares SGD, thereby providing a Gaussian Central Limit Theorem (CLT) in agrowing-dimensional regime. Existing approaches to high-dimensional inference for projection parameters, such as [1], rely on inverting empirical covariance matrices and require at leastt≳d3/2iterations to achieve finite-sample Berry–Esseen guarantees, rendering them computationally expensive and restrictive in the allowable dimensional scaling. In contrast, we show that a CLT holds for SGD iterates when the number of iterations grows ast≳d1+δfor any δ > 0, significantly extending the dimensional regime permitted by prior works while improving computational efficiency. The proposed online SGD-based procedure operates inO(td) time and requires onlyO(d) memory, in contrast to theO(td2+d3) runtime of covariance-inversion methods. To render the theory practically applicable, we further develop anonline variance estimatorfor the asymptotic variance appearing in the CLT and establishhigh-probability deviation boundsfor this estimator. Collectively, these results yield the first fully online and data-driven framework for constructing confidence intervals for SGD iterates in the near-optimal scaling regimet≳d1+δ.

Imaging systems consist of cameras to encode visual information about the world and perception models to interpret this encoding. Cameras contain (1) illumination sources, (2) optical elements, and (3) sensors, while perception models use (4) algorithms. Directly searching over all combinations of these four building blocks to design an imaging system is challenging due to the size of the search space. Moreover, cameras and perception models are often designed independently, leading to sub-optimal task performance. In this paper, we formulate these four building blocks of imaging systems as a context-free grammar (CFG), which can be automatically searched over with a learned camera designer to jointly optimize the imaging system with task-specific perception models. By transforming the CFG to a state-action space, we then show how the camera designer can be implemented with reinforcement learning to intelligently search over the combinatorial space of possible imaging system configurations. We demonstrate our approach on two tasks, depth estimation and camera rig design for autonomous vehicles, showing that our method yields rigs that outperform industry-wide standards. We believe that our proposed approach is an important step towards automating imaging system design. Our project page is https://tzofi.github.io/diser.