Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive applications such as clinical decision making and autonomous driving. However, the structure of an expert's preferences implicit in observed actions is closely linked to the expert's model of the environment dynamics (i.e. the world''). Thus, inaccurate models of the world obtained from finite data with limited coverage could compound inaccuracy in estimated rewards. To address this issue, we propose a bi-level optimization formulation of the estimation task wherein the upper level is likelihood maximization based upon a conservative model of the expert's policy (lower level). The policy model is conservative in that it maximizes reward subject to a penalty that is increasing in the uncertainty of the estimated model of the world.

Offline Reinforcement Learning (RL) has demonstrated promising results in various applications by learning policies from previously collected datasets, reducing the need for online exploration and interactions. However, real-world scenarios usually involve partial observability, which brings crucial challenges of the deployment of offline RL methods: i) the policy trained on data with full observability is not robust against the masked observations during execution, and ii) the information of which parts of observations are masked is usually unknown during training. In order to address these challenges, we present Offline RL with DiscrEte pRoxy representations (ORDER), a probabilistic framework which leverages novel state representations to improve the robustness against diverse masked observabilities. Specifically, we propose a discrete representation of the states and use a proxy representation to recover the states from masked partial observable trajectories. The training of ORDER can be compactly described as the following three steps. We conduct extensive experiments to evaluate ORDER, showcasing its effectiveness in offline RL for diverse partially observable scenarios and highlighting the significance of discrete proxy representations in generalization performance.ORDER is a flexible framework to employ any offline RL algorithms and we hope that ORDER can pave the way for the deployment of RL policy against various partial observabilities in the real world.

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors.

We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. Building on distributionally robust optimization and a regression approach, we propose to optimize the most adverse risk over a family of distributions within bounded Wasserstein distance or KL divergence to the empirical distribution. The proposed approach applies for general categorical random variables without assuming faithfulness, an ordinal relationship or a specific form of conditional distribution. We present efficient algorithms and show the proposed methods are closely related to the standard regularized regression approach. Under mild assumptions, we derive non-asymptotic guarantees for successful structure learning with logarithmic sample complexities for bounded-degree graphs.

Policy gradient methods have become a standard for training reinforcement learning agents in a scalable and efficient manner. However, they do not account for transition uncertainty, whereas learning robust policies can be computationally expensive. In this paper, we introduce robust policy gradient (RPG), a policy-based method that efficiently solves rectangular robust Markov decision processes (MDPs). We provide a closed-form expression for the worst occupation measure. Incidentally, we find that the worst kernel is a rank-one perturbation of the nominal.

In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to the learner at the end of each episode. We propose a policy optimization-based algorithm POLO, and we prove that it attains the \widetilde{O}(K {\frac{5}{6}}A {\frac{1}{2}}d\ln(1 M)/(1-\gamma) 2) regret guarantee, where d is rank of the transition kernel (and hence the dimension of the unknown representations), A is the cardinality of the action space, M is the cardinality of the model class that contains all the plausible representations, and \gamma is the discounted factor. Notably, our algorithm is oracle-efficient and has a regret guarantee with no dependence on the size of potentially arbitrarily large state space. Furthermore, we also prove an \Omega(\frac{\gamma 2}{1-\gamma} \sqrt{d A K}) regret lower bound for this problem, showing that low-rank MDPs are statistically more difficult to learn than linear MDPs in the regret minimization setting.

An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation, but are parameter intensive when modeling long dependencies, and hence are prone to overfitting. In contrast, SLDSs can capture long-range dependencies in a parameter efficient way through Markovian latent dynamics, but present an intractable likelihood and a challenging parameter estimation task.

Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of continuous joint distributions in a compact but flexible manner with minimal parametric assumptions on the dependencies between variables. Bayesian structure learning of GPNs requires computing the posterior over graphs of the network and is computationally infeasible even in low dimensions. This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample from the posterior distribution of network structures. As such, the approach follows the Bayesian paradigm, comparing models via their marginal likelihood and computing the posterior probability of the GPN features.

What are the functionals of the reward that can be computed and optimized exactly in Markov Decision Processes?In the finite-horizon, undiscounted setting, Dynamic Programming (DP) can only handle these operations efficiently for certain classes of statistics. We summarize the characterization of these classes for policy evaluation, and give a new answer for the planning problem. Interestingly, we prove that only generalized means can be optimized exactly, even in the more general framework of Distributional Reinforcement Learning (DistRL).DistRL permits, however, to evaluate other functionals approximately. We provide error bounds on the resulting estimators, and discuss the potential of this approach as well as its limitations.These results contribute to advancing the theory of Markov Decision Processes by examining overall characteristics of the return, and particularly risk-conscious strategies.

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of interest in recent years, a limitation of the PAC-Bayesian framework is that most bounds involve a Kullback-Leibler (KL) divergence term (or its variations), which might exhibit erratic behavior and fail to capture the underlying geometric structure of the learning problem -- hence restricting its use in practical applications.As a remedy, recent studies have attempted to replace the KL divergence in the PAC-Bayesian bounds with the Wasserstein distance. Even though these bounds alleviated the aforementioned issues to a certain extent, they either hold in expectation, are for bounded losses, or are nontrivial to minimize in an SRM framework. In this work, we contribute to this line of research and prove novel Wasserstein distance-based PAC-Bayesian generalisation bounds for both batch learning with independent and identically distributed (i.i.d.) data, and online learning with potentially non-i.i.d. Contrary to previous art, our bounds are stronger in the sense that (i) they hold with high probability, (ii) they apply to unbounded (potentially heavy-tailed) losses, and (iii) they lead to optimizable training objectives that can be used in SRM.