We settle the sample complexity of policy learning for the maximization of the long run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of $\widetilde O(|S||A|t_{\text{mix}}^2 \epsilon^{-2})$ and a lower bound of $\Omega(|S||A|t_{\text{mix}} \epsilon^{-2})$. In these expressions, $|S|$ and $|A|$ denote the cardinalities of the state and action spaces respectively, $t_{\text{mix}}$ serves as a uniform upper limit for the total variation mixing times, and $\epsilon$ signifies the error tolerance. Therefore, a notable gap of $t_{\text{mix}}$ still remains to be bridged. Our primary contribution is to establish an estimator for the optimal policy of average reward MDPs with a sample complexity of $\widetilde O(|S||A|t_{\text{mix}}\epsilon^{-2})$, effectively reaching the lower bound in the literature. This is achieved by combining algorithmic ideas in Jin and Sidford (2021) with those of Li et al. (2020).

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods.

Classification models for electroencephalogram (EEG) data show a large decrease in performance when evaluated on unseen test sub jects. We reduce this performance decrease using new regularization techniques during model training. We propose several graphical models to describe an EEG classification task. From each model, we identify statistical relationships that should hold true in an idealized training scenario (with infinite data and a globally-optimal model) but that may not hold in practice. We design regularization penalties to enforce these relationships in two stages. First, we identify suitable proxy quantities (divergences such as Mutual Information and Wasserstein-1) that can be used to measure statistical independence and dependence relationships. Second, we provide algorithms to efficiently estimate these quantities during training using secondary neural network models. We conduct extensive computational experiments using a large benchmark EEG dataset, comparing our proposed techniques with a baseline method that uses an adversarial classifier. We find our proposed methods significantly increase balanced accuracy on test subjects and decrease overfitting. The proposed methods exhibit a larger benefit over a greater range of hyperparameters than the baseline method, with only a small computational cost at training time. These benefits are largest when used for a fixed training period, though there is still a significant benefit for a subset of hyperparameters when our techniques are used in conjunction with early stopping regularization.

The distribution of the weights of modern deep neural networks (DNNs) - crucial for uncertainty quantification and robustness - is an eminently complex object due to its extremely high dimensionality. This paper proposes one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we will shortly release the first large-scale checkpoint dataset, including thousands of real-world models and our codes.

Markov Chain Monte Carlo methods for sampling from complex distributions and estimating normalization constants often simulate samples from a sequence of intermediate distributions along an annealing path, which bridges between a tractable initial distribution and a target density of interest. Prior work has constructed annealing paths using quasi-arithmetic means, and interpreted the resulting intermediate densities as minimizing an expected divergence to the endpoints. We provide a comprehensive analysis of this 'centroid' property using Bregman divergences under a monotonic embedding of the density function, thereby associating common divergences such as Amari's and Renyi's ${\alpha}$-divergences, ${(\alpha,\beta)}$-divergences, and the Jensen-Shannon divergence with intermediate densities along an annealing path. Our analysis highlights the interplay between parametric families, quasi-arithmetic means, and divergence functions using the rho-tau Bregman divergence framework of Zhang 2004,2013.

This paper presents a method to efficiently classify the gastroenterologic section of images derived from Video Capsule Endoscopy (VCE) studies by exploring the combination of a Convolutional Neural Network (CNN) for classification with the time-series analysis properties of a Hidden Markov Model (HMM). It is demonstrated that successive time-series analysis identifies and corrects errors in the CNN output. Our approach achieves an accuracy of $98.04\%$ on the Rhode Island (RI) Gastroenterology dataset. This allows for precise localization within the gastrointestinal (GI) tract while requiring only approximately 1M parameters and thus, provides a method suitable for low power devices

The rapid increase in the number of cyber-attacks in recent years raises the need for principled methods for defending networks against malicious actors. Deep reinforcement learning (DRL) has emerged as a promising approach for mitigating these attacks. However, while DRL has shown much potential for cyber-defence, numerous challenges must be overcome before DRL can be applied to autonomous cyber-operations (ACO) at scale. Principled methods are required for environments that confront learners with very high-dimensional state spaces, large multi-discrete action spaces, and adversarial learning. Recent works have reported success in solving these problems individually. There have also been impressive engineering efforts towards solving all three for real-time strategy games. However, applying DRL to the full ACO problem remains an open challenge. Here, we survey the relevant DRL literature and conceptualize an idealised ACO-DRL agent. We provide: i.) A summary of the domain properties that define the ACO problem; ii.) A comprehensive evaluation of the extent to which domains used for benchmarking DRL approaches are comparable to ACO; iii.) An overview of state-of-the-art approaches for scaling DRL to domains that confront learners with the curse of dimensionality, and; iv.) A survey and critique of current methods for limiting the exploitability of agents within adversarial settings from the perspective of ACO. We conclude with open research questions that we hope will motivate future directions for researchers and practitioners working on ACO.

In many interactive decision-making settings, there is latent and unobserved information that remains fixed. Consider, for example, a dialogue system, where complete information about a user, such as the user's preferences, is not given. In such an environment, the latent information remains fixed throughout each episode, since the identity of the user does not change during an interaction. This type of environment can be modeled as a Latent Markov Decision Process (LMDP), a special instance of Partially Observed Markov Decision Processes (POMDPs). Previous work established exponential lower bounds in the number of latent contexts for the LMDP class. This puts forward a question: under which natural assumptions a near-optimal policy of an LMDP can be efficiently learned? In this work, we study the class of LMDPs with {\em prospective side information}, when an agent receives additional, weakly revealing, information on the latent context at the beginning of each episode. We show that, surprisingly, this problem is not captured by contemporary settings and algorithms designed for partially observed environments. We then establish that any sample efficient algorithm must suffer at least $\Omega(K^{2/3})$-regret, as opposed to standard $\Omega(\sqrt{K})$ lower bounds, and design an algorithm with a matching upper bound.

Partially observable Markov decision processes (POMDPs) have been widely applied to capture many real-world applications. However, existing theoretical results have shown that learning in general POMDPs could be intractable, where the main challenge lies in the lack of latent state information. A key fundamental question here is how much online state information (OSI) is sufficient to achieve tractability. In this paper, we establish a lower bound that reveals a surprising hardness result: unless we have full OSI, we need an exponentially scaling sample complexity to obtain an $\epsilon$-optimal policy solution for POMDPs. Nonetheless, inspired by the key insights in our lower bound design, we find that there exist important tractable classes of POMDPs even with only partial OSI. In particular, for two novel classes of POMDPs with partial OSI, we provide new algorithms that are proved to be near-optimal by establishing new regret upper and lower bounds.

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data distribution and hierarchical representations. However, such a prior model usually focuses on modeling inter-layer relations between latent variables by assuming non-informative (conditional) Gaussian distributions, which can be limited in model expressivity. To tackle this issue and learn more expressive prior models, we propose an energy-based model (EBM) on the joint latent space over all layers of latent variables with the multi-layer generator as its backbone. Such joint latent space EBM prior model captures the intra-layer contextual relations at each layer through layer-wise energy terms, and latent variables across different layers are jointly corrected. We develop a joint training scheme via maximum likelihood estimation (MLE), which involves Markov Chain Monte Carlo (MCMC) sampling for both prior and posterior distributions of the latent variables from different layers. To ensure efficient inference and learning, we further propose a variational training scheme where an inference model is used to amortize the costly posterior MCMC sampling. Our experiments demonstrate that the learned model can be expressive in generating high-quality images and capturing hierarchical features for better outlier detection.