IFML Seminar: 10/24/25 - Learning from Many Trajectories

This talk will highlight our recent efforts towards a deeper understanding of learning from many trajectories, beyond naive i.i.d. reductions. We first start from the basic problem of linear least-squares regression with dependent covariates. Given n-dimensional examples produced by m trajectories, each of length T, we show that the worst-case excess risk of this problem is Θ(n/mT) whenever m exceeds a constant factor the dimension n. Notably, this error rate behaves as if all of the examples were independent, drawn from their time-marginals. We then consider more general models and loss functions via an approach we call the Hellinger localization framework—a general recipe for deriving instance-optimal parameter recovery rates for maximum likelihood estimation over multiple trajectories. Applying our framework yields sharp bounds across a diverse set of problems, including generalized linear models with non-monotonic activations and a simple linear-attention sequence model, under a fairly natural set of assumptions. We conclude with future directions for applying Hellinger localization to more structured forms of dependency, and to downstream objectives beyond just parameter recovery, e.g., filtering and control tasks.