Learning Bellman Complete Representations for Offline Policy Evaluation

We study representation learning for Offline Reinforcement Learning (RL), focusing on the important task of Offline Policy Evaluation (OPE). Recent work shows that, in contrast to supervised learning, realizability of the Q-function is not enough for learning it. Two sufficient conditions for sample-efficient OPE are Bellman completeness and coverage. Prior work often assumes that representations satisfying these conditions are given, with results being mostly theoretical in nature. In this work, we propose BCRL, which directly learns from data an approximately linear Bellman complete representation with good coverage. With this learned representation, we perform OPE using Least Square Policy Evaluation (LSPE) with linear functions in our learned representation. We present an end-to-end theoretical analysis, showing that our two-stage algorithm enjoys polynomial sample complexity provided some representation in the rich class considered is linear Bellman complete. Empirically, we extensively evaluate our algorithm on challenging, image-based continuous control tasks from the Deepmind Control Suite. We show our representation enables better OPE compared to previous representation learning methods developed for off-policy RL (e.g., CURL, SPR). BCRL achieve competitive OPE error with the state-of-the-art method Fitted Q-Evaluation (FQE), and beats FQE when evaluating beyond the initial state distribution. Our ablations show that both linear Bellman complete and coverage components of our method are crucial.

Computationally Efficient PAC RL in POMDPs with Latent Determinism and Conditional Embeddings

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action $Q$-function is linear in the state feature, and the optimal $Q$-function has a gap in actions, we provide a \emph{computationally and statistically efficient} algorithm for finding the \emph{exact optimal} policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems

We study Reinforcement Learning for partially observable dynamical systems using function approximation. We propose a new \textit{Partially Observable Bilinear Actor-Critic framework}, that is general enough to include models such as observable tabular Partially Observable Markov Decision Processes (POMDPs), observable Linear-Quadratic-Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs and observable POMDPs with latent low-rank transition. Under this framework, we propose an actor-critic style algorithm that is capable of performing agnostic policy learning. Given a policy class that consists of memory based policies (that look at a fixed-length window of recent observations), and a value function class that consists of functions taking both memory and future observations as inputs, our algorithm learns to compete against the best memory-based policy in the given policy class. For certain examples such as undercomplete observable tabular POMDPs, observable LQGs and observable POMDPs with latent low-rank transition, by implicitly leveraging their special properties, our algorithm is even capable of competing against the globally optimal policy without paying an exponential dependence on the horizon in its sample complexity.

Robust and Agnostic Learning of Conditional Distributional Treatment Effects

The conditional average treatment effect (CATE) is the best point prediction of individual causal effects given individual baseline covariates and can help personalize treatments. However, as CATE only reflects the (conditional) average, it can wash out potential risks and tail events, which are crucially relevant to treatment choice. In aggregate analyses, this is usually addressed by measuring distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit covariate-conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a wide class of problems that includes conditional quantile treatment effects, conditional super-quantile treatment effects, and conditional treatment effects on coherent risk measures given by $f$-divergences. Our method is based on constructing a special pseudo-outcome and regressing it on baseline covariates using any given regression learner. Our method is model-agnostic in the sense that it can provide the best projection of CDTE onto the regression model class. Our method is robust in the sense that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the performance of our proposal in simulation studies, and we demonstrate its use in a case study of 401(k) eligibility effects on wealth.

What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment

The fundamental problem of causal inference -- that we never observe counterfactuals -- prevents us from identifying how many might be negatively affected by a proposed intervention. If, in an A/B test, half of users click (or buy, or watch, or renew, etc.), whether exposed to the standard experience A or a new one B, hypothetically it could be because the change affects no one, because the change positively affects half the user population to go from no-click to click while negatively affecting the other half, or something in between. While unknowable, this impact is clearly of material importance to the decision to implement a change or not, whether due to fairness, long-term, systemic, or operational considerations. We therefore derive the tightest-possible (i.e., sharp) bounds on the fraction negatively affected (and other related estimands) given data with only factual observations, whether experimental or observational. Naturally, the more we can stratify individuals by observable covariates, the tighter the sharp bounds. Since these bounds involve unknown functions that must be learned from data, we develop a robust inference algorithm that is efficient almost regardless of how and how fast these functions are learned, remains consistent when some are mislearned, and still gives valid conservative bounds when most are mislearned. Our methodology altogether therefore strongly supports credible conclusions: it avoids spuriously point-identifying this unknowable impact, focusing on the best bounds instead, and it permits exceedingly robust inference on these. We demonstrate our method in simulation studies and in a case study of career counseling for the unemployed.

Estimating Structural Disparities for Face Models

In machine learning, disparity metrics are often defined by measuring the difference in the performance or outcome of a model, across different sub-populations (groups) of datapoints. Thus, the inputs to disparity quantification consist of a model's predictions $\hat{y}$, the ground-truth labels for the predictions $y$, and group labels $g$ for the data points. Performance of the model for each group is calculated by comparing $\hat{y}$ and $y$ for the datapoints within a specific group, and as a result, disparity of performance across the different groups can be calculated. In many real world scenarios however, group labels ($g$) may not be available at scale during training and validation time, or collecting them might not be feasible or desirable as they could often be sensitive information. As a result, evaluating disparity metrics across categorical groups would not be feasible. On the other hand, in many scenarios noisy groupings may be obtainable using some form of a proxy, which would allow measuring disparity metrics across sub-populations. Here we explore performing such analysis on computer vision models trained on human faces, and on tasks such as face attribute prediction and affect estimation. Our experiments indicate that embeddings resulting from an off-the-shelf face recognition model, could meaningfully serve as a proxy for such estimation.

Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning

Off-policy evaluation and learning (OPE/L) use offline observational data to make better decisions, which is crucial in applications where experimentation is necessarily limited. OPE/L is nonetheless sensitive to discrepancies between the data-generating environment and that where policies are deployed. Recent work proposed distributionally robust OPE/L (DROPE/L) to remedy this, but the proposal relies on inverse-propensity weighting, whose regret rates may deteriorate if propensities are estimated and whose variance is suboptimal even if not. For vanilla OPE/L, this is solved by doubly robust (DR) methods, but they do not naturally extend to the more complex DROPE/L, which involves a worst-case expectation. In this paper, we propose the first DR algorithms for DROPE/L with KL-divergence uncertainty sets. For evaluation, we propose Localized Doubly Robust DROPE (LDR$^2$OPE) and prove its semiparametric efficiency under weak product rates conditions. Notably, thanks to a localization technique, LDR$^2$OPE only requires fitting a small number of regressions, just like DR methods for vanilla OPE. For learning, we propose Continuum Doubly Robust DROPL (CDR$^2$OPL) and show that, under a product rate condition involving a continuum of regressions, it enjoys a fast regret rate of $\mathcal{O}(N^{-1/2})$ even when unknown propensities are nonparametrically estimated. We further extend our results to general $f$-divergence uncertainty sets. We illustrate the advantage of our algorithms in simulations.

Long-term Causal Inference Under Persistent Confounding via Data Combination

We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.

Treatment Effect Risk: Bounds and Inference

Since the average treatment effect (ATE) measures the change in social welfare, even if positive, there is a risk of negative effect on, say, some 10% of the population. Assessing such risk is difficult, however, because any one individual treatment effect (ITE) is never observed so the 10% worst-affected cannot be identified, while distributional treatment effects only compare the first deciles within each treatment group, which does not correspond to any 10%-subpopulation. In this paper we consider how to nonetheless assess this important risk measure, formalized as the conditional value at risk (CVaR) of the ITE distribution. We leverage the availability of pre-treatment covariates and characterize the tightest-possible upper and lower bounds on ITE-CVaR given by the covariate-conditional average treatment effect (CATE) function. Some bounds can also be interpreted as summarizing a complex CATE function into a single metric and are of interest independently of being a bound. We then proceed to study how to estimate these bounds efficiently from data and construct confidence intervals. This is challenging even in randomized experiments as it requires understanding the distribution of the unknown CATE function, which can be very complex if we use rich covariates so as to best control for heterogeneity. We develop a debiasing method that overcomes this and prove it enjoys favorable statistical properties even when CATE and other nuisances are estimated by black-box machine learning or even inconsistently. Studying a hypothetical change to French job-search counseling services, our bounds and inference demonstrate a small social benefit entails a negative impact on a substantial subpopulation.

Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding

We study the problem of constructing bounds on the average treatment effect in the presence of unobserved confounding under the marginal sensitivity model of Tan (2006). Combining an existing characterization involving adversarial propensity scores with a new distributionally robust characterization of the problem, we propose novel estimators of these bounds that we call "doubly-valid/doubly-sharp" (DVDS) estimators. Double sharpness corresponds to the fact that DVDS estimators consistently estimate the tightest possible (i.e., sharp) bounds implied by the sensitivity model even when one of two nuisance parameters is misspecified and achieve semiparametric efficiency when all nuisance parameters are suitably consistent. Double validity is an entirely new property for partial identification: DVDS estimators still provide valid, though not sharp, bounds even when most nuisance parameters are misspecified. In fact, even in cases when DVDS point estimates fail to be asymptotically normal, standard Wald confidence intervals may remain valid. In the case of binary outcomes, the DVDS estimators are particularly convenient and possesses a closed-form expression in terms of the outcome regression and propensity score. We demonstrate the DVDS estimators in a simulation study as well as a case study of right heart catheterization.