Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to introduce additional controls in downstream fine-tuning processes, treating these powerful models as pre-trained diffusion models. This work presents a novel method based on reinforcement learning (RL) to add such controls using an offline dataset comprising inputs and labels. We formulate this task as an RL problem, with the classifier learned from the offline dataset and the KL divergence against pre-trained models serving as the reward functions. Our method, **CTRL** (**C**onditioning pre-**T**rained diffusion models with **R**einforcement **L**earning), produces soft-optimal policies that maximize the abovementioned reward functions. We formally demonstrate that our method enables sampling from the conditional distribution with additional controls during inference. Our RL-based approach offers several advantages over existing methods. Compared to classifier-free guidance, it improves sample efficiency and can greatly simplify dataset construction by leveraging conditional independence between the inputs and additional controls. Additionally, unlike classifier guidance, it eliminates the need to train classifiers from intermediate states to additional controls. The code is available at https://github.com/zhaoyl18/CTRL.

Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences (i.e., discrete diffusion models) across domains such as natural language and biological sequence generation. For example, in the protein inverse folding task, where the goal is to generate a protein sequence from a given backbone structure, conditional diffusion models have achieved impressive results in generating "natural" sequences that fold back into the original structure. However, practical design tasks often require not only modeling a conditional distribution but also optimizing specific task objectives. For instance, in the inverse folding task, we may prefer proteins with high stability. To address this, we consider the scenario where we have pre-trained discrete diffusion models that can generate "natural" sequences, as well as reward models that map sequences to task objectives. We then formulate the reward maximization problem within discrete diffusion models, analogous to reinforcement learning (RL), while minimizing the KL divergence against pre-trained diffusion models to preserve naturalness. To solve this RL problem, we propose a novel algorithm that enables direct backpropagation of rewards through entire trajectories generated by diffusion models, by making the originally non-differentiable trajectories differentiable using the Gumbel-Softmax trick. Our theoretical analysis indicates that our approach can generate sequences that are both "natural" (i.e., have a high probability under a pre-trained model) and yield high rewards. While similar tasks have been recently explored in diffusion models for continuous domains, our work addresses unique algorithmic and theoretical challenges specific to discrete diffusion models, which arise from their foundation in continuous-time Markov chains rather than Brownian motion. Finally, we demonstrate the effectiveness of our algorithm in generating DNA and protein sequences that optimize enhancer activity and protein stability, respectively, important tasks for gene therapies and protein-based therapeutics. The code is available at https://github.com/ChenyuWang-Monica/DRAKES.

To fully leverage the capabilities of diffusion models, we are often interested in optimizing downstream reward functions during inference. While numerous algorithms for reward-guided generation have been recently proposed due to their significance, current approaches predominantly focus on single-shot generation, transitioning from fully noised to denoised states. We propose a novel framework for inference-time reward optimization with diffusion models. Our approach employs an iterative refinement process consisting of two steps in each iteration: noising and reward-guided denoising. This sequential refinement allows for the gradual correction of errors introduced during reward optimization. Finally, we provide a theoretical guarantee for our framework. Finally, we demonstrate its superior empirical performance in protein and DNA design.

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require differentiable proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation.

While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want to optimize for a new protein with the highest possible fluorescence. This kind of data-driven optimization (DDO) presents a range of challenges beyond those in standard prediction problems, since we need models that successfully predict the performance of new designs that are better than the best designs seen in the training set. It is not clear theoretically when existing approaches can even perform better than the na ïve approach that simply selects the best design in the dataset. In this paper, we study how structure can enable sample-efficient data-driven optimization. To formalize the notion of structure, we introduce functional graphical models (FGMs) and show theoretically how they can provide for principled data-driven optimization by decomposing the original high-dimensional optimization problem into smaller sub-problems. This allows us to derive much more practical regret bounds for DDO, and the result implies that DDO with FGMs can achieve nearly optimal designs in situations where naïve approaches fail due to insufficient coverage of the offline data. We further present a data-driven optimization algorithm that inferes the FGM structure itself, either over the original input variables or a latent variable representation of the inputs.

Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals. While PbRL has demonstrated practical success in fine-tuning language models, existing theoretical work focuses on regret minimization and fails to capture most of the practical frameworks. In this study, we fill in such a gap between theoretical PbRL and practical algorithms by proposing a theoretical reward-agnostic PbRL framework where exploratory trajectories that enable accurate learning of hidden reward functions are acquired before collecting any human feedback. Theoretical analysis demonstrates that our algorithm requires less human feedback for learning the optimal policy under preference-based models with linear parameterization and unknown transitions, compared to the existing theoretical literature. Specifically, our framework can incorporate linear and low-rank MDPs with efficient sample complexity. Additionally, we investigate reward-agnostic RL with action-based comparison feedback and introduce an efficient querying algorithm tailored to this scenario.

In this paper, we investigate the problem of offline Preference-based Reinforcement Learning (PbRL) with human feedback where feedback is available in the form of preference between trajectory pairs rather than explicit rewards. Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE. We consider the general reward setting where the reward can be defined over the whole trajectory and provide a novel guarantee that allows us to learn any target policy with a polynomial number of samples, as long as the target policy is covered by the offline data. This guarantee is the first of its kind with general function approximation. To measure the coverage of the target policy, we introduce a new single-policy concentrability coefficient, which can be upper bounded by the per-trajectory concentrability coefficient. We also establish lower bounds that highlight the necessity of such concentrability and the difference from standard RL, where state-action-wise rewards are directly observed. We further extend and analyze our algorithm when the feedback is given over action pairs.

Diffusion models excel at modeling complex data distributions, including those of images, proteins, and small molecules. However, in many cases, our goal is to model parts of the distribution that maximize certain properties: for example, we may want to generate images with high aesthetic quality, or molecules with high bioactivity. It is natural to frame this as a reinforcement learning (RL) problem, in which the objective is to finetune a diffusion model to maximize a reward function that corresponds to some property. Even with access to online queries of the ground-truth reward function, efficiently discovering high-reward samples can be challenging: they might have a low probability in the initial distribution, and there might be many infeasible samples that do not even have a well-defined reward (e.g., unnatural images or physically impossible molecules). In this work, we propose a novel reinforcement learning procedure that efficiently explores on the manifold of feasible samples. We present a theoretical analysis providing a regret guarantee, as well as empirical validation across three domains: images, biological sequences, and molecules.

AI-driven design problems, such as DNA/protein sequence design, are commonly tackled from two angles: generative modeling, which efficiently captures the feasible design space (e.g., natural images or biological sequences), and model-based optimization, which utilizes reward models for extrapolation. To combine the strengths of both approaches, we adopt a hybrid method that fine-tunes cutting-edge diffusion models by optimizing reward models through RL. Although prior work has explored similar avenues, they primarily focus on scenarios where accurate reward models are accessible. In contrast, we concentrate on an offline setting where a reward model is unknown, and we must learn from static offline datasets, a common scenario in scientific domains. In offline scenarios, existing approaches tend to suffer from overoptimization, as they may be misled by the reward model in out-of-distribution regions. To address this, we introduce a conservative fine-tuning approach, BRAID, by optimizing a conservative reward model, which includes additional penalization outside of offline data distributions. Through empirical and theoretical analysis, we demonstrate the capability of our approach to outperform the best designs in offline data, leveraging the extrapolation capabilities of reward models while avoiding the generation of invalid designs through pre-trained diffusion models.

We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisance functions that depend on the target parameter as an input. A central example is the efficient estimating equation for the (local) quantile treatment effect ((L)QTE) in causal inference, which involves the covariate-conditional cumulative distribution function evaluated at the quantile to be estimated. Existing approaches based on flexibly estimating the nuisances and plugging in the estimates, such as debiased machine learning (DML), require we learn the nuisance at all possible inputs. For (L)QTE, DML requires we learn the whole covariate-conditional cumulative distribution function. We instead propose localized debiased machine learning (LDML), which avoids this burdensome step and needs only estimate nuisances at a single initial rough guess for the target parameter. For (L)QTE, LDML involves learning just two regression functions, a standard task for machine learning methods. We prove that under lax rate conditions our estimator has the same favorable asymptotic behavior as the infeasible estimator that uses the unknown true nuisances. Thus, LDML notably enables practically-feasible and theoretically-grounded efficient estimation of important quantities in causal inference such as (L)QTEs when we must control for many covariates and/or flexible relationships, as we demonstrate in empirical studies.

In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and missing-not-at-random data with shadow variables, we are interested in inference on a continuous linear functional (e.g., average causal effects) of nuisance function (e.g., NPIV regression) defined by conditional moment restrictions. These nuisance functions are generally weakly identified, in that the conditional moment restrictions can be severely ill-posed as well as admit multiple solutions. This is sometimes resolved by imposing strong conditions that imply the function can be estimated at rates that make inference on the functional possible. In this paper, we study a novel condition for the functional to be strongly identified even when the nuisance function is not; that is, the functional is amenable to asymptotically-normal estimation at root-n-rates. The condition implies the existence of debiasing nuisance functions, and we propose penalized minimax estimators for both the primary and debiasing nuisance functions. The proposed nuisance estimators can accommodate flexible function classes, and importantly they can converge to fixed limits determined by the penalization regardless of the identifiability of the nuisances. We use the penalized nuisance estimators to form a debiased estimator for the functional of interest and prove its asymptotic normality under generic high-level conditions, which provide for asymptotically valid confidence intervals. We also illustrate our method in a novel partially linear proximal causal inference problem and a partially linear instrumental variable regression problem.

In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one of the following limitations: (1) restricting the IV regression to be uniquely identified; (2) only obtaining estimation error rates in terms weak metrics (e.g., projected norm) rather than strong metrics (e.g., L_2 norm); or (3) imposing the so-called closedness condition that requires a certain conditional expectation operator to be sufficiently smooth. In this paper, we present the first method and analysis that can avoid all three limitations, while still permitting general function approximation. Specifically, we propose a new penalized minimax estimator that can converge to a fixed IV solution even when there are multiple solutions, and we derive a strong L_2 error rate for our estimator under lax conditions. Notably, this guarantee only needs a widely-used source condition and realizability assumptions, but not the so-called closedness condition. We argue that the source condition and the closedness condition are inherently conflicting, so relaxing the latter significantly improves upon the existing literature that requires both conditions. Our estimator can achieve this improvement because it builds on a novel formulation of the IV estimation problem as a constrained optimization problem.

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 computationally and statistically efficient algorithm for finding the 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.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Ranking interfaces are everywhere in online platforms. There is thus an ever growing interest in their Off-Policy Evaluation (OPE), aiming towards an accurate performance evaluation of ranking policies using logged data. A de-facto approach for OPE is Inverse Propensity Scoring (IPS), which provides an unbiased and consistent value estimate. However, it becomes extremely inaccurate in the ranking setup due to its high variance under large action spaces. To deal with this problem, previous studies assume either independent or cascade user behavior, resulting in some ranking versions of IPS. While these estimators are somewhat effective in reducing the variance, all existing estimators apply a single universal assumption to every user, causing excessive bias and variance. Therefore, this work explores a far more general formulation where user behavior is diverse and can vary depending on the user context. We show that the resulting estimator, which we call Adaptive IPS (AIPS), can be unbiased under any complex user behavior. Moreover, AIPS achieves the minimum variance among all unbiased estimators based on IPS. We further develop a procedure to identify the appropriate user behavior model to minimize the mean squared error (MSE) of AIPS in a data-driven fashion. Extensive experiments demonstrate that the empirical accuracy improvement can be significant, enabling effective OPE of ranking systems even under diverse user behavior.

We study off-policy evaluation (OPE) for partially observable MDPs (POMDPs) with general function approximation. Existing methods such as sequential importance sampling estimators and fitted-Q evaluation suffer from the curse of horizon in POMDPs. To circumvent this problem, we develop a novel model-free OPE method by introducing future-dependent value functions that take future proxies as inputs. Future-dependent value functions play similar roles as classical value functions in fully-observable MDPs. We derive a new off-policy Bellman equation for future-dependent value functions as conditional moment equations that use history proxies as instrumental variables. We further propose a minimax learning method to learn future-dependent value functions using the new Bellman equation. We obtain the PAC result, which implies our OPE estimator is close to the true policy value as long as futures and histories contain sufficient information about latent states, and the Bellman completeness. Our code is available at https://github.com/aiueola/neurips2023-future-dependent-ope

We consider offline reinforcement learning (RL) where we only have only access to offline data. In contrast to numerous offline RL algorithms that necessitate the uniform coverage of the offline data over state and action space, we propose value-based algorithms with PAC guarantees under partial coverage, specifically, coverage of offline data against a single policy, and realizability of soft Q-function (a.k.a., entropy-regularized Q-function) and another function, which is defined as a solution to a saddle point of certain minimax optimization problem). Furthermore, we show the analogous result for Q-functions instead of soft Q-functions. To attain these guarantees, we use novel algorithms with minimax loss functions to accurately estimate soft Q-functions and Q-functions with -convergence guarantees measured on the offline data. We introduce these loss functions by casting the estimation problems into nonlinear convex optimization problems and taking the Lagrange functions.

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs), where the evaluation policy depends only on observable variables and the behavior policy depends on unobservable latent variables. Existing works either assume no unmeasured confounders, or focus on settings where both the observation and the state spaces are tabular. In this work, we first propose novel identification methods for OPE in POMDPs with latent confounders, by introducing bridge functions that link the target policy’s value and the observed data distribution. We next propose minimax estimation methods for learning these bridge functions, and construct three estimators based on these estimated bridge functions, corresponding to a value function-based estimator, a marginalized importance sampling estimator, and a doubly-robust estimator. Our proposal permits general function approximation and is thus applicable to settings with continuous or large observation/state spaces. The nonasymptotic and asymptotic properties of the proposed estimators are investigated in detail. A Python implementation of our proposal is available at https://github.com/jiaweihhuang/ Confounded-POMDP-Exp.

We present BRIEE, an algorithm for efficient reinforcement learning in Markov Decision Processes with block-structured dynamics (i.e., Block MDPs), where rich observations are generated from a set of unknown latent states. BRIEE interleaves latent states discovery, exploration, and exploitation together, and can provably learn a near-optimal policy with sample complexity scaling polynomially in the number of latent states, actions, and the time horizon, with no dependence on the size of the potentially infinite observation space. Empirically, we show that BRIEE is more sample efficient than the state-of-art Block MDP algorithm HOMER and other empirical RL baselines on challenging rich-observation combination lock problems which require deep exploration.

We study Reinforcement Learning for partially observable systems using function approximation. We propose a new PO-bilinear framework, that is general enough to include models such as undercomplete tabular Partially Observable Markov Decision Processes (POMDPs), Linear Quadratic Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs. Under this framework, we propose an actor-critic style algorithm that is capable to performing agnostic policy learning. Given a policy class that consists of memory based policies (i.e., policy that looks 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 among the policy class. For certain examples such as undercomplete POMDPs and LQGs, by leveraging their special properties, our algorithm is even capable of competing against the globally optimal policy without paying an exponential dependence on the horizon.

We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted $Q$-iteration (FQI), suggest a $O(1/\sqrt{n})$ convergence for regret, empirical behavior exhibits much faster convergence. In this paper, we present a finer regret analysis that exactly characterized this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal quality function $Q^*$, the regret of the policy it defines converges at a rate given by the exponentiation of the $Q^*$-estimate’s pointwise convergence rate, thus speeding it up. The level of exponentiation depends on the level of noise in the decision-making problem, rather than the estimation problem. We establish such noise levels for linear and tabular MDPs as examples. Second, we provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. As specific cases, our results imply $O(1/n)$ regret rates in linear cases and $\exp(-\Omega(n))$ regret rates in tabular cases.

We study off-policy evaluation (OPE) from multiple logging policies, each generating a dataset of fixed size, i.e., stratified sampling. Previous work noted that in this setting the ordering of the variances of different importance sampling estimators is instance-dependent, which brings up a dilemma as to which importance sampling weights to use. In this paper, we resolve this dilemma by finding the OPE estimator for multiple loggers with minimum variance for any instance, i.e., the efficient one. In particular, we establish the efficiency bound under stratified sampling and propose an estimator achieving this bound when given consistent $q$-estimates. To guard against misspecification of $q$-functions, we also provide a way to choose the control variate in a hypothesis class to minimize variance. Extensive experiments demonstrate the benefits of our methods’ efficiently leveraging of the stratified sampling of off-policy data from multiple loggers.

This paper studies offline Imitation Learning (IL) where an agent learns to imitate an expert demonstrator without additional online environment interactions. Instead, the learner is presented with a static offline dataset of state-action-next state triples from a potentially less proficient behavior policy. We introduce Model-based IL from Offline data (MILO): an algorithmic framework that utilizes the static dataset to solve the offline IL problem efficiently both in theory and in practice. In theory, even if the behavior policy is highly sub-optimal compared to the expert, we show that as long as the data from the behavior policy provides sufficient coverage on the expert state-action traces (and with no necessity for a global coverage over the entire state-action space), MILO can provably combat the covariate shift issue in IL. Complementing our theory results, we also demonstrate that a practical implementation of our approach mitigates covariate shift on benchmark MuJoCo continuous control tasks. We demonstrate that with behavior policies whose performances are less than half of that of the expert, MILO still successfully imitates with an extremely low number of expert state-action pairs while traditional offline IL methods such as behavior cloning (BC) fail completely. Source code is provided at https://github.com/jdchang1/milo.

Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general nonnormalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are approximately unbiased estimators of discrepancy measures for non-normalized models. Simulation results and applications to real data demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner.

The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficiency remains. In this study, we propose a unified, statistically efficient estimation framework for unnormalized models and several efficient estimators, whose asymptotic variance is the same as the MLE. The computational cost of these estimators is also reasonable and they can be employed whether the sample space is discrete or continuous. The loss functions of the proposed estimators are derived by combining the following two methods: (1) density-ratio matching using Bregman divergence, and (2) plugging-in nonparametric estimators. We also analyze the properties of the proposed estimators when the unnormalized models are misspecified. The experimental results demonstrate the advantages of our method over existing approaches.

Several statistical models are given in the form of unnormalized densities and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. Further, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction demonstrate that the proposed methods enable statistical inference from missing data properly.

Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. We consider for the first time the semiparametric efficiency limits of OPE in Markov decision processes (MDPs), where actions, rewards, and states are memoryless. We show existing OPE estimators may fail to be efficient in this setting. We develop a new estimator based on cross-fold estimation of $q$-functions and marginalized density ratios, which we term double reinforcement learning (DRL). We show that DRL is efficient when both components are estimated at fourth-root rates and is also doubly robust when only one component is consistent. We investigate these properties empirically and demonstrate the performance benefits due to harnessing memorylessness.

Policy gradient methods in reinforcement learning update policy parameters by taking steps in the direction of an estimated gradient of policy value. In this paper, we consider the efficient estimation of policy gradients from off-policy data, where the estimation is particularly non-trivial. We derive the asymptotic lower bound on the feasible mean-squared error in both Markov and non-Markov decision processes and show that existing estimators fail to achieve it in general settings. We propose a meta-algorithm that achieves the lower bound without any parametric assumptions and exhibits a unique 4-way double robustness property. We discuss how to estimate nuisances that the algorithm relies on. Finally, we establish guarantees at the rate at which we approach a stationary point when we take steps in the direction of our new estimated policy gradient.

We provide theoretical investigations into off-policy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et.al, 2018), (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can be combined with MWL in a doubly robust manner, (3) Several additional results that offer further insights, including the sample complexities of MWL and MQL, their asymptotic optimality in the tabular setting, how the learned importance weights depend the choice of the discriminator class, and how our methods provide a unified view of some old and new algorithms in RL.

Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and gradient fail because the density ratio does not exist. To circumvent this issue, we propose several new doubly robust estimators based on different kernelization approaches. We analyze the asymptotic mean-squared error of each of these under mild rate conditions for nuisance estimators. Specifically, we demonstrate how to obtain a rate that is independent of the horizon length.

We consider the evaluation and training of a new policy for the evaluation data by using the historical data obtained from a different policy. The goal of off-policy evaluation (OPE) is to estimate the expected reward of a new policy over the evaluation data, and that of off-policy learning (OPL) is to find a new policy that maximizes the expected reward over the evaluation data. Although the standard OPE and OPL assume the same distribution of covariate between the historical and evaluation data, there often exists a problem of a covariate shift,i.e., the distribution of the covariate of the historical data is different from that of the evaluation data. In this paper, we derive the efficiency bound of OPE under a covariate shift. Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using an estimator of the density ratio between the distributions of the historical and evaluation data. We also discuss other possible estimators and compare their theoretical properties. Finally, we confirm the effectiveness of the proposed estimators through experiments.

Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. We consider for the first time the semiparametric efficiency limits of OPE in Markov decision processes (MDPs), where actions, rewards, and states are memoryless. We show existing OPE estimators may fail to be efficient in this setting. We develop a new estimator based on cross-fold estimation of $q$-functions and marginalized density ratios, which we term double reinforcement learning (DRL). We show that DRL is efficient when both components are estimated at fourth-root rates and is also doubly robust when only one component is consistent. We investigate these properties empirically and demonstrate the performance benefits due to harnessing memorylessness.

Off-policy evaluation (OPE) in both contextual bandits and reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. The problem's importance has attracted many proposed solutions, including importance sampling (IS), self-normalized IS (SNIS), and doubly robust (DR) estimates. DR and its variants ensure semiparametric local efficiency if Q-functions are well-specified, but if they are not they can be worse than both IS and SNIS. It also does not enjoy SNIS's inherent stability and boundedness. We propose new estimators for OPE based on empirical likelihood that are always more efficient than IS, SNIS, and DR and satisfy the same stability and boundedness properties as SNIS. On the way, we categorize various properties and classify existing estimators by them. Besides the theoretical guarantees, empirical studies suggest the new estimators provide advantages.