In this paper, we provide the first practical algorithms with provable guarantees for the problem of inferring the topics assigned to each document in an LDA topic model. This is the primary inference problem for many applications of topic models in social science, data exploration, and causal inference settings. We obtain this result by showing a novel non-gradient-based, combinatorial approach to estimating topic models. This yields algorithms that converge to near-optimal posterior probability in logarithmic parallel computation time (adaptivity) -- exponentially faster than any known LDA algorithm. We also show that our approach can provide interpretability guarantees such that each learned topic is formally associated with a known keyword. Finally, we show that unlike alternatives, our approach can maintain the independence assumptions necessary to use the learned topic model for downstream causal inference methods that allow researchers to study topics as treatments. In terms of practical performance, our approach consistently returns solutions of higher semantic quality than solutions from state-of-the-art LDA algorithms, neural topic models, and LLM-based topic models across a diverse range of text datasets and evaluation parameters.

We consider stochastic planning problems that involve multiple objectives such as minimizing task completion time and energy consumption. These problems can be modeled as multi-objective Markov decision processes (MOMDPs), an extension of the widely-used MDP model to handle problems involving multiple value functions. We focus on a subclass of MOMDPs in which the objectives have a {\em relaxed lexicographic structure}, allowing an agent to seek improvement in a lower-priority objective when the impact on a higher-priority objective is within some small given tolerance. We examine the relationship between this class of problems and {\em constrained MDPs}, showing that the latter offer an alternative solution method with strong guarantees. We show empirically that a recently introduced algorithm for MOMDPs may not offer the same strong guarantees, but it does perform well in practice.