Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study value-based policy learning in stochastic optimal control: a greedy policy induced by an estimate of the optimal action-value function $Q^*$ is deployed, and its performance is measured by regret. The empirical success of this approach calls for statistical insight into the structures that enable fast regret convergence. We show that, in continuous action spaces, fast policy learning is induced by three geometric structures: a growth exponent $p$, which quantifies how quickly $Q^*$ separates suboptimal actions from its maximizers; a margin-mass exponent $m$, which controls how much deployment mass lies on states with weak growth; and an action-wise regularity exponent $q$, which measures the smoothness of the $Q^*$-estimation error across actions. Given a $n^{-1/2}$-accurate estimator of $Q^*$, we show that the minimax-optimal policy regret convergence rate is \[ \widetildeΘ\left( n^{-\min\left\{\frac{p}{2(p-q)},\frac{m+1}{2m}\right\}} \right), \] up to a logarithmic factor at the boundary between the two regimes. The exponent $q$ is crucial: $q>0$ yields faster-than-$n^{-1/2}$ regret. This regime is natural in operations applications. In particular, we verify $q>0$ under mild regularity conditions in dynamic inventory control and service allocation examples, while the mechanism underlying this fast rate regime extends beyond these settings.

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we present a scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models. Contrary to Bayesian modeling for IV, our approach does not require additional assumptions on the data generating process, and leads to a scalable approximate inference algorithm with time cost comparable to the corresponding point estimation methods. Our algorithm can be further extended to work with neural network models. We analyze the theoretical properties of the proposed quasi-posterior, and demonstrate through empirical evaluation the competitive performance of our method.

Contrastive learning has recently emerged as a promising approach for learning data representations that discover and disentangle the explanatory factors of the data.