Efficient Spectral Control of Partially Observed Linear Dynamical Systems

We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while exponentially improving runtime complexity over previous approaches in its dependence on the system's stability margin. Our key innovation is a two-level spectral approximation strategy, leveraging double convolution with a universal basis of spectral filters, enabling efficient and accurate learning of the best linear dynamical controllers.

SpectraLDS: Provable Distillation for Linear Dynamical Systems

We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that represents symmetric LDSs as convolutions learnable via fixed spectral transformations. We show how to invert this representation, thereby recovering an LDS model from its spectral transform and yielding an end-to-end convex optimization procedure. This distillation preserves predictive accuracy while enabling constant-time and constant-space inference per token, independent of sequence length. We evaluate our method, SpectraLDS, as a component in sequence prediction architectures and demonstrate that accuracy is preserved while inference efficiency is improved on tasks such as language modeling.

Discretion in the Loop: Human Expertise in Algorithm-Assisted College Advising

In higher education, many institutions use algorithmic alerts to flag at-risk students and deliver advising at scale. While much research has focused on evaluating algorithmic predictions, relatively little is known about how discretionary interventions by human experts shape outcomes in algorithm-assisted settings. We study this question using rich quantitative and qualitative data from a randomized controlled trial of an algorithm-assisted advising program at Georgia State University. Taking a mixed-methods approach, we examine whether and how advisors use context unavailable to an algorithm to guide interventions and influence student success. We develop a causal graphical framework for human expertise in the interventional setting, extending prior work on discretion in purely predictive settings. We then test a necessary condition for discretionary expertise using structured advisor logs and student outcomes data, identifying several interventions that meet the criterion for statistical significance. Accordingly, we estimate that 2 out of 3 interventions taken by advisors in the treatment arm were plausibly "expertly targeted" to students using non-algorithmic context. Systematic qualitative analysis of advisor notes corroborates these findings, showing that advisors incorporate diverse forms of contextual information--such as personal circumstances, financial issues, and student engagement--into their decisions. Finally, we explore the broader implications of human discretion for long-term outcomes and equity, using heterogeneous treatment effect estimation. Our results offer theoretical and practical insight into the real-world effectiveness of algorithm-supported college advising, and underscore the importance of accounting for human expertise in the design, evaluation, and implementation of algorithmic decision systems.

A New Approach to Controlling Linear Dynamical Systems

We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.