Offline Reinforcement Learning with On-Policy Q-Function Regularization

The core challenge of offline reinforcement learning (RL) is dealing with the (potentially catastrophic) extrapolation error induced by the distribution shift between the history dataset and the desired policy. A large portion of prior work tackles this challenge by implicitly/explicitly regularizing the learning policy towards the behavior policy, which is hard to estimate reliably in practice. In this work, we propose to regularize towards the Q-function of the behavior policy instead of the behavior policy itself, under the premise that the Q-function can be estimated more reliably and easily by a SARSA-style estimate and handles the extrapolation error more straightforwardly. We propose two algorithms taking advantage of the estimated Q-function through regularizations, and demonstrate they exhibit strong performance on the D4RL benchmarks.

Seeing is not Believing: Robust Reinforcement Learning against Spurious Correlation

Robustness has been extensively studied in reinforcement learning (RL) to handle various forms of uncertainty such as random perturbations, rare events, and malicious attacks. In this work, we consider one critical type of robustness against spurious correlation, where different portions of the state do not have causality but have correlations induced by unobserved confounders. These spurious correlations are ubiquitous in real-world tasks, for instance, a self-driving car usually observes heavy traffic in the daytime and light traffic at night due to unobservable human activity. A model that learns such useless or even harmful correlation could catastrophically fail when the confounder in the test case deviates from the training one. Although motivated, enabling robustness against spurious correlation poses significant challenges since the uncertainty set, shaped by the unobserved confounder and sequential structure of RL, is difficult to characterize and identify. Existing robust algorithms that assume simple and unstructured uncertainty sets are therefore inadequate to address this challenge. To solve this issue, we propose Robust State-Confounded Markov Decision Processes (RSC-MDPs) and theoretically demonstrate its superiority in breaking spurious correlations compared with other robust RL counterparts. We also design an empirical algorithm to learn the robust optimal policy for RSC-MDPs, which outperforms all baselines in eight realistic self-driving and manipulation tasks.

Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to reliable estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model (DDPM)), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Our theory imposes only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), and is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs. Further, we design two accelerated variants, improving the convergence to $1/T^2$ for the ODE-based sampler and $1/T$ for the DDPM-type sampler, which might be of independent theoretical and empirical interest.

Identification of Nonlinear Latent Hierarchical Models

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

Understanding Masked Autoencoders via Hierarchical Latent Variable Models

Masked autoencoder (MAE), a simple and effective self-supervised learning framework based on the reconstruction of masked image regions, has recently achieved prominent success in a variety of vision tasks. Despite the emergence of intriguing empirical observations on MAE, a theoretically principled understanding is still lacking. In this work, we formally characterize and justify existing empirical insights and provide theoretical guarantees of MAE. We formulate the underlying data-generating process as a hierarchical latent variable model and show that under reasonable assumptions, MAE provably identifies a set of latent variables in the hierarchical model, explaining why MAE can extract high-level information from pixels. Further, we show how key hyperparameters in MAE (the masking ratio and the patch size) determine which true latent variables to be recovered, therefore influencing the level of semantic information in the representation. Specifically, extremely large or small masking ratios inevitably lead to low-level representations. Our theory offers coherent explanations of existing empirical observations and provides insights for potential empirical improvements and fundamental limitations of the masking-reconstruction paradigm. We conduct extensive experiments to validate our theoretical insights.

Sharp high-probability sample complexities for policy evaluation with linear function approximation

This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.

The Curious Price of Distributional Robustness in Reinforcement Learning with a Generative Model

This paper investigates model robustness in reinforcement learning (RL) to reduce the sim-to-real gap in practice. We adopt the framework of distributionally robust Markov decision processes (RMDPs), aimed at learning a policy that optimizes the worst-case performance when the deployed environment falls within a prescribed uncertainty set around the nominal MDP. Despite recent efforts, the sample complexity of RMDPs remained mostly unsettled regardless of the uncertainty set in use. It was unclear if distributional robustness bears any statistical consequences when benchmarked against standard RL. Assuming access to a generative model that draws samples based on the nominal MDP, we characterize the sample complexity of RMDPs when the uncertainty set is specified via either the total variation (TV) distance or $\chi^2$ divergence. The algorithm studied here is a model-based method called {\em distributionally robust value iteration}, which is shown to be near-optimal for the full range of uncertainty levels. Somewhat surprisingly, our results uncover that RMDPs are not necessarily easier or harder to learn than standard MDPs. The statistical consequence incurred by the robustness requirement depends heavily on the size and shape of the uncertainty set: in the case w.r.t.~the TV distance, the minimax sample complexity of RMDPs is always smaller than that of standard MDPs; in the case w.r.t.~the $\chi^2$ divergence, the sample complexity of RMDPs can often far exceed the standard MDP counterpart.

The Blessing of Heterogeneity in Federated Q-learning: Linear Speedup and Beyond

When the data used for reinforcement learning (RL) are collected by multiple agents in a distributed manner, federated versions of RL algorithms allow collaborative learning without the need of sharing local data. In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and sharper dependencies on other salient problem parameters. Moreover, existing approaches to federated Q-learning adopt an equally-weighted averaging of local Q-estimates, which can be highly sub-optimal in the asynchronous setting since the local trajectories can be highly heterogeneous due to different local behavior policies. Existing sample complexity scales inverse proportionally to the minimum entry of the stationary state-action occupancy distributions over all agents, requiring that every agent covers the entire state-action space. Instead, we propose a novel importance averaging algorithm, giving larger weights to more frequently visited state-action pairs. The improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents collectively cover the entire state-action space, unveiling the blessing of heterogeneity.

Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression

Achieving communication efficiency in decentralized machine learning has been attracting significant attention, with communication compression recognized as an effective technique in algorithm design. This paper takes a first step to understand the role of gradient clipping, a popular strategy in practice, in decentralized nonconvex optimization with communication compression. We propose PORTER, which considers two variants of gradient clipping added before or after taking a mini-batch of stochastic gradients, where the former variant PORTER-DP allows local differential privacy analysis with additional Gaussian perturbation, and the latter variant PORTER-GC helps to stabilize training. We develop a novel analysis framework that establishes their convergence guarantees without assuming the stringent bounded gradient assumption. To the best of our knowledge, our work provides the first convergence analysis for decentralized nonconvex optimization with gradient clipping and communication compression, highlighting the trade-offs between convergence rate, compression ratio, network connectivity, and privacy.

Reward-agnostic Fine-tuning: Provable Statistical Benefits of Hybrid Reinforcement Learning

This paper studies tabular reinforcement learning (RL) in the hybrid setting, which assumes access to both an offline dataset and online interactions with the unknown environment. A central question boils down to how to efficiently utilize online data collection to strengthen and complement the offline dataset and enable effective policy fine-tuning. Leveraging recent advances in reward-agnostic exploration and model-based offline RL, we design a three-stage hybrid RL algorithm that beats the best of both worlds -- pure offline RL and pure online RL -- in terms of sample complexities. The proposed algorithm does not require any reward information during data collection. Our theory is developed based on a new notion called single-policy partial concentrability, which captures the trade-off between distribution mismatch and miscoverage and guides the interplay between offline and online data.