We study distributionally robust offline reinforcement learning (RL), which seeks to find an optimal robust policy purely from an offline dataset that can perform well in perturbed environments. We propose a generic algorithm framework Doubly Pessimistic Model-based Policy Optimization (P2MPO) for robust offline RL, which features a novel combination of a flexible model estimation subroutine and a doubly pessimistic policy optimization step. Here the double pessimism principle is crucial to overcome the distribution shift incurred by i) the mismatch between behavior policy and the family of target policies; and ii) the perturbation of the nominal model. Under certain accuracy assumptions on the model estimation subroutine, we show that P2MPOis provably sample-efficient with robust partial coverage data, which means that the offline dataset has good coverage of the distributions induced by the optimal robust policy and perturbed models around the nominal model. By tailoring specific model estimation subroutines for concrete examples including tabular Robust Markov Decision Process (RMDP), factored RMDP, and RMDP with kernel and neural function approximations, we show that P2MPO enjoys a eO(n 1/2) convergence rate, where nis the number of trajectories in the offline dataset. Notably, these models, except for the tabular case, are first identified and proven tractable by this paper. To the best of our knowledge, we first propose a general learning principle -- double pessimism -- for robust offline RL and show that it is provably efficient in the context of general function approximations.

Incorporating causality into reinforcement learning methods increases the interpretability of artificial636 intelligence, which helps humans understand the underlying mechanism of algorithms and check637 the source of failures. However, the learned causal transition model may contain human-readable638 private information about the environment, which could raise privacy issues. To mitigate this potential639 negative societal impact, the causal transition model needs to be encrypted and only accessible to640 algorithms and trustworthy users.641 In this section, besides the most related formulation, robust RL introduced in Sec 3.3, we also643 introduce some other related RL problem formulations partially shown in Figure 3. Then, we limit644 our discussion to mainly two lines of work that are related to ours: (1) promoting robustness in RL;645 (2) concerning the spurious correlation issues in RL.646 B.1 Related RL formulations647 Robustness to noisy state: POMDPs and SA-MDPs.

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 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 causal structure, 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 avoiding learning 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. Please refer to the website for more details.

Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs--namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides rigorous guarantees that methods similar to those used in practice converge on realistic inference problems.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

Deep learning practice is increasingly driven by powerful foundation models (FM), pre-trained at scale and then fine-tuned for specific tasks of interest. A key property of this workflow is the efficacy of performing sparse or parameter-efficient finetuning, meaning that by updating only a tiny fraction of the whole FM parameters on a downstream task can lead to surprisingly good performance, often even superior to a full model update. However, it is not clear what is the optimal and principled way to select which parameters to update. Although a growing number of sparse fine-tuning ideas have been proposed, they are mostly not satisfactory, relying on hand-crafted heuristics or heavy approximation. In this paper we propose a novel Bayesian sparse fine-tuning algorithm: we place a (sparse) Laplace prior for each parameter of the FM, with the mean equal to the initial value and the scale parameter having a hyper-prior that encourages small scale.

Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be interpreted as a temperature-like parameter within the statistical mechanics of learning, plays a crucial role in neural network training. Indeed, many widely adopted training strategies basically just define the decay of the learning rate over time. This process can be interpreted as decreasing a temperature, using either a global learning rate (for the entire model) or a learning rate that varies for each parameter. This paper proposes TempBalance, a straightforward yet effective layer-wise learning rate method. TempBalanceis based on Heavy-Tailed Self-Regularization (HT-SR) Theory, an approach which characterizes the implicit self-regularization of different layers in trained models. We demonstrate the efficacy of using HT-SR-motivated metrics to guide the scheduling and balancing of temperature across all network layers during model training, resulting in improved performance during testing.

We perform a non-asymptotic analysis of the contrastive divergence (CD) algorithm, a training method for unnormalized models. While prior work has established that (for exponential family distributions) the CD iterates asymptotically converge at an O(n 1/3) rate to the true parameter of the data distribution, we show, under some regularity assumptions, that CD can achieve the parametric rate O(n 1/2). Our analysis provides results for various data batching schemes, including the fully online and minibatch ones. We additionally show that CD can be near-optimal, in the sense that its asymptotic variance is close to the Cramér-Rao lower bound.