We propose **H**e**u**ristic **Bl**ending (HUBL), a simple performance-improving technique for a broad class of offline RL algorithms based on value bootstrapping. HUBL modifies the Bellman operators used in these algorithms, partially replacing the bootstrapped values with heuristic ones that are estimated with Monte-Carlo returns. For trajectories with higher returns, HUBL relies more on the heuristic values and less on bootstrapping; otherwise, it leans more heavily on bootstrapping. HUBL is very easy to combine with many existing offline RL implementations by relabeling the offline datasets with adjusted rewards and discount factors. We derive a theory that explains HUBL's effect on offline RL as reducing offline RL's complexity and thus increasing its finite-sample performance. Furthermore, we empirically demonstrate that HUBL consistently improves the policy quality of four state-of-the-art bootstrapping-based offline RL algorithms (ATAC, CQL, TD3+BC, and IQL), by 9% on average over 27 datasets of the D4RL and Meta-World benchmarks.

In dynamic discrete choice models, a commonly studied problem is estimating parameters of agent reward functions (also known as ’structural’ parameters) using agent behavioral data. This task is also known as inverse reinforcement learning. Maximum likelihood estimation for such models requires dynamic programming, which is limited by the curse of dimensionality [Bellman, 1957]. In this work, we present a novel algorithm that provides a data-driven method for selecting and aggregating states, which lowers the computational and sample complexity of estimation. Our method works in two stages. First, we estimate agent Qfunctions, and leverage them alongside a clustering algorithm to select a subset of states that are most pivotal for driving changes in Q-functions. Second, with these selected "aggregated" states, we conduct maximum likelihood estimation using a popular nested fixed-point algorithm [Rust, 1987]. The proposed two-stage approach mitigates the curse of dimensionality by reducing the problem dimension. Theoretically, we derive finite-sample bounds on the associated estimation error, which also characterize the trade-off of computational complexity, estimation error, and sample complexity. We demonstrate the empirical performance of the algorithm in two classic dynamic discrete choice estimation applications.

We propose a reward function estimation framework for inverse reinforcement learning with deep energy-based policies. We name our method PQR, as it sequentially estimates the Policy, the Q-function, and the Reward function by deep learning. PQR does not assume that the reward solely depends on the state, instead it allows for a dependency on the choice of action. Moreover, PQR allows for stochastic state transitions. To accomplish this, we assume the existence of one anchor action whose reward is known, typically the action of doing nothing, yielding no reward. We present both estimators and algorithms for the PQR method. When the environment transition is known, we prove that the PQR reward estimator uniquely recovers the true reward. With unknown transitions, we bound the estimation error of PQR. Finally, the performance of PQR is demonstrated by synthetic and real-world datasets.

We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove a $\sqrt{n}$-sparsistency. Importantly, our approach avoids parametric constraints on the effects of confounders on the estimated graphical model structure. Empirically, the PLA-GGM is applied to both synthetic and real-world datasets, demonstrating superior performance compared to competing methods.

We propose temporal Poisson square root graphical models (TPSQRs), a generalization of Poisson square root graphical models (PSQRs) specifically designed for modeling longitudinal event data. By estimating the temporal relationships for all possible pairs of event types, TPSQRs can offer a holistic perspective about whether the occurrences of any given event type could excite or inhibit any other type. A TPSQR is learned by estimating a collection of interrelated PSQRs that share the same template parameterization. These PSQRs are estimated jointly in a pseudo-likelihood fashion, where Poisson pseudo-likelihood is used to approximate the original more computationally intensive pseudo-likelihood problem stemming from PSQRs. Theoretically, we demonstrate that under mild assumptions, the Poisson pseudolikelihood approximation is sparsistent for recovering the underlying PSQR. Empirically, we learn TPSQRs from a real-world large-scale electronic health record (EHR) with millions of drug prescription and condition diagnosis events, for adverse drug reaction (ADR) detection. Experimental results demonstrate that the learned TPSQRs can recover ADR signals from the EHR effectively and efficiently.

We discover a screening rule for l1-regularized Ising model estimation. The simple closed-form screening rule is a necessary and sufficient condition for exactly recovering the blockwise structure of a solution under any given regularization parameters. With enough sparsity, the screening rule can be combined with various optimization procedures to deliver solutions efficiently in practice. The screening rule is especially suitable for large-scale exploratory data analysis, where the number of variables in the dataset can be thousands while we are only interested in the relationship among a handful of variables within moderate-size clusters for interpretability. Experimental results on various datasets demonstrate the efficiency and insights gained from the introduction of the screening rule.