We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level \zeta . At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes. Here d is the dimension of the feature space and H is the horizon.

This paper introduces a novel prior called Diversified Block Sparse Prior to characterize the widespread block sparsity phenomenon in real-world data. By allowing diversification on intra-block variance and inter-block correlation matrices, we effectively address the sensitivity issue of existing block sparse learning methods to pre-defined block information, which enables adaptive block estimation while mitigating the risk of overfitting. Based on this, a diversified block sparse Bayesian learning method (DivSBL) is proposed, utilizing EM algorithm and dual ascent method for hyperparameter estimation. Moreover, we establish the global and local optimality theory of our model.

Reinforcement learning from human feedback (RLHF) provides a principled framework for aligning AI systems with human preference data. For various reasons, e.g., personal bias, context ambiguity, lack of training, etc, human annotators may give incorrect or inconsistent preference labels. To tackle this challenge, we propose a robust RLHF approach -- R 3M, which models the potentially corrupted preference label as sparse outliers. Accordingly, we formulate the robust reward learning as an \ell_1 -regularized maximum likelihood estimation problem. Computationally, we develop an efficient alternating optimization algorithm, which only incurs negligible computational overhead compared with the standard RLHF approach.

In tasks aiming for long-term returns, planning becomes essential. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of step-wise rewards as one key technical challenge. We introduce the Latent Plan Transformer (LPT), a novel model that leverages a latent variable to connect a Transformer- based trajectory generator and the final return. LPT can be learned with maximum likelihood estimation on trajectory-return pairs.

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations.

Differentiable structure learning is a novel line of causal discovery research that transforms the combinatorial optimization of structural models into a continuous optimization problem. However, the field has lacked feasible methods to integrate partial order constraints, a critical prior information typically used in real-world scenarios, into the differentiable structure learning framework. The main difficulty lies in adapting these constraints, typically suited for the space of total orderings, to the continuous optimization context of structure learning in the graph space. To bridge this gap, this paper formalizes a set of equivalent constraints that map partial orders onto graph spaces and introduces a plug-and-play module for their efficient application. This module preserves the equivalent effect of partial order constraints in the graph space, backed by theoretical validations of correctness and completeness.

Despite the success of Large Language Models (LLMs) on various tasks following human instructions, controlling model generation to follow strict constraints at inference time poses a persistent challenge. In this paper, we introduce Ctrl-G, a neuro-symbolic framework that enables tractable and adaptable control of LLM generation to follow logical constraints reliably. Ctrl-G combines any production-ready LLM with a Hidden Markov Model (HMM), guiding LLM outputs to adhere to logical constraints represented as deterministic finite automata. We show that Ctrl-G, when a TULU2-7B model is coupled with a 2B-parameter HMM, outperforms GPT4 in text editing: on the task of generating text insertions/continuations following logical constraints, our approach achieves over 30% higher satisfaction rate in human evaluation. When applied to medium-size language models (e.g., GPT2-large), Ctrl-G also beats its counterparts on standard benchmarks by large margins.

We study the evaluation of a policy under best- and worst-case perturbations to a Markov decision process (MDP), using transition observations from the original MDP, whether they are generated under the same or a different policy. This is an important problem when there is the possibility of a shift between historical and future environments, \emph{e.g.} due to unmeasured confounding, distributional shift, or an adversarial environment. We propose a perturbation model that allows changes in the transition kernel densities up to a given multiplicative factor or its reciprocal, extending the classic marginal sensitivity model (MSM) for single time-step decision-making to infinite-horizon RL. We characterize the sharp bounds on policy value under this model -- \emph{i.e.}, the tightest possible bounds based on transition observations from the original MDP -- and we study the estimation of these bounds from such transition observations. We develop an estimator with several important guarantees: it is semiparametrically efficient, and remains so even when certain necessary nuisance functions, such as worst-case Q-functions, are estimated at slow, nonparametric rates.

Diffusion-based models have achieved notable empirical successes in reinforcement learning (RL) due to their expressiveness in modeling complex distributions. Despite existing methods being promising, the key challenge of extending existing methods for broader real-world applications lies in the computational cost at inference time, i.e., sampling from a diffusion model is considerably slow as it often requires tens to hundreds of iterations to generate even one sample. To circumvent this issue, we propose to leverage the flexibility of diffusion models for RL from a representation learning perspective. In particular, by exploiting the connection between diffusion models and energy-based models, we develop Diffusion Spectral Representation (Diff-SR), a coherent algorithm framework that enables extracting sufficient representations for value functions in Markov decision processes (MDP) and partially observable Markov decision processes (POMDP). We further demonstrate how Diff-SR facilitates efficient policy optimization and practical algorithms while explicitly bypassing the difficulty and inference cost of sampling from the diffusion model.