We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets. This result generalizes prior analyses restricted to either stationary (single-task) deep models or continual linear models. We show that global convergence generally fails, even for simple models linear in data but nonlinear in parameters. Nevertheless, by leveraging results from nonconvex projection theory, we identify regularity properties of homogeneous deep networks that guarantee local linear convergence under random and cyclic task sequences. Finally, we extend our analysis to continual regression, unifying the framework for homogeneous models.
Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics. In this work, we…
Singular value soft-thresholding can be computed via a reduction to the matrix polar decomposition, which allows one to exploit GPU-friendly algorithms for computing the polar decomposition. Empirically, there is a significant speed-up on GPUs compared to the standard approach us…
Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley--Terry (BT) model, but its convergence can be slow in practice. To accelerate computation, Newman introduced a family of Zermelo-type fixed-point iterations parameterized by $α…
We study the expected improvement (EI) policy for minimizing a deterministic objective function $f$ on a nonempty compact set $\mathcal X \subset\mathbb R^d$. We assume that $f$ belongs to the RKHS $\mathcal H_k$ of a continuous positive-semidefinite kernel $k$ on $\mathcal X$. F…
A data-driven inverse optimization problem (DDIOP) is the problem of estimating the objective-function parameters (weights) that explain observed optimal-solution data, and it arises in many applications, including integer linear programming (ILP). It is known that, by applying g…
Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge. Given the link between learning and compression, network compression offers a promising lens to analyze this knowledge. However, standard compression heuristics of…