We study the problem of online learning Markov Decision Processes (MDPs) when both the transition distributions and loss functions are chosen by an adversary. We present an algorithm that, under a mixing assumption, achieves O(\sqrt{T\log \Pi } \log \Pi) regret with respect to a comparison set of policies \Pi . The regret is independent of the size of the state and action spaces. When expectations over sample paths can be computed efficiently and the comparison set \Pi has polynomial size, this algorithm is efficient. We also consider the episodic adversarial online shortest path problem.

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial-temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance.Projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently highly sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20x compression in model size with under 3\% performance drop, and up to 20x FLOPs reduction during training compared with dense VI training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs on both accuracy and uncertainty metrics.

This paper develops flexible nowcasting and forecasting methods by combining elements from three strands of econometric literature. First, drawing from the mixed data sampling (MIDAS) framework introduced by Ghysels et al. (2007), see also Andreou et al. (2010), Ghysels (2016), or Ghysels et al. (2024) for a recent review, we leverage techniques that permit the efficient use of predictors sampled at a higher frequency than the target variable. Second, the Big Data literature, based on the idea that using a large set of predictors combined with penalized estimators or Bayesian shrinkage can improve predictive accuracy, see e.g., Babii et al. (2022) and Mogliani and Simoni (2021) in the context of mixed frequency models. Third, the machine learning literature, which postulates that proper algorithms combined with computing power can uncover complicated relationships among variables (economic and financial ones, in our case) and hence improve predictions, see e.g., Hastie et al. (2009). Our baseline framework uses Gaussian Processes (GPs) to estimate the unknown and perhaps nonlinear relationships between a target variable and a large set of mixed frequency predictors nonparametrically.

Distinguishing sources of predictive uncertainty is of crucial importance in the application of forecasting models across various domains. Despite the presence of a great variety of proposed uncertainty measures, there are no strict definitions to disentangle them. Furthermore, the relationship between different measures of uncertainty quantification remains somewhat unclear. In this work, we introduce a general framework, rooted in statistical reasoning, which not only allows the creation of new uncertainty measures but also clarifies their interrelations. Our approach leverages statistical risk to distinguish aleatoric and epistemic uncertainty components and utilizes proper scoring rules to quantify them. To make it practically tractable, we propose an idea to incorporate Bayesian reasoning into this framework and discuss the properties of the proposed approximation.

Goal recognition is a fundamental cognitive process that enables individuals to infer intentions based on available cues. Current goal recognition algorithms often take only observed actions as input, but here we use a Bayesian framework to explore the role of actions, timing, and goal solvability in goal recognition. We analyze human responses to goal-recognition problems in the Sokoban domain, and find that actions are assigned most importance, but that timing and solvability also influence goal recognition in some cases, especially when actions are uninformative. We leverage these findings to develop a goal recognition model that matches human inferences more closely than do existing algorithms. Our work provides new insight into human goal recognition and takes a step towards more human-like AI models.

When multiple agents interact in a common environment, each agent's actions impact others' future decisions, and noncooperative dynamic games naturally capture this coupling. In interactive motion planning, however, agents typically do not have access to a complete model of the game, e.g., due to unknown objectives of other players. Therefore, we consider the inverse game problem, in which some properties of the game are unknown a priori and must be inferred from observations. Existing maximum likelihood estimation (MLE) approaches to solve inverse games provide only point estimates of unknown parameters without quantifying uncertainty, and perform poorly when many parameter values explain the observed behavior. To address these limitations, we take a Bayesian perspective and construct posterior distributions of game parameters. To render inference tractable, we employ a variational autoencoder (VAE) with an embedded differentiable game solver. This structured VAE can be trained from an unlabeled dataset of observed interactions, naturally handles continuous, multi-modal distributions, and supports efficient sampling from the inferred posteriors without computing game solutions at runtime. Extensive evaluations in simulated driving scenarios demonstrate that the proposed approach successfully learns the prior and posterior objective distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.

In many collaborative settings, artificial intelligence (AI) agents must be able to adapt to new teammates that use unknown or previously unobserved strategies. While often simple for humans, this can be challenging for AI agents. For example, if an AI agent learns to drive alongside others (a training set) that only drive on one side of the road, it may struggle to adapt this experience to coordinate with drivers on the opposite side, even if their behaviours are simply flipped along the left-right symmetry. To address this we introduce symmetry-breaking augmentations (SBA), which increases diversity in the behaviour of training teammates by applying a symmetry-flipping operation. By learning a best-response to the augmented set of teammates, our agent is exposed to a wider range of behavioural conventions, improving performance when deployed with novel teammates. We demonstrate this experimentally in two settings, and show that our approach improves upon previous ad hoc teamwork results in the challenging card game Hanabi. We also propose a general metric for estimating symmetry-dependency amongst a given set of policies.

We consider the problem of sampling from a discrete and structured distribution as a sequential decision problem, where the objective is to find a stochastic policy such that objects are sampled at the end of this sequential process proportionally to some predefined reward. While we could use maximum entropy Reinforcement Learning (MaxEnt RL) to solve this problem for some distributions, it has been shown that in general, the distribution over states induced by the optimal policy may be biased in cases where there are multiple ways to generate the same object. To address this issue, Generative Flow Networks (GFlowNets) learn a stochastic policy that samples objects proportionally to their reward by approximately enforcing a conservation of flows across the whole Markov Decision Process (MDP). In this paper, we extend recent methods correcting the reward in order to guarantee that the marginal distribution induced by the optimal MaxEnt RL policy is proportional to the original reward, regardless of the structure of the underlying MDP. We also prove that some flow-matching objectives found in the GFlowNet literature are in fact equivalent to well-established MaxEnt RL algorithms with a corrected reward. Finally, we study empirically the performance of multiple MaxEnt RL and GFlowNet algorithms on multiple problems involving sampling from discrete distributions.

Detecting abrupt changes in real-time data streams from scientific simulations presents a challenging task, demanding the deployment of accurate and efficient algorithms. Identifying change points in live data stream involves continuous scrutiny of incoming observations for deviations in their statistical characteristics, particularly in high-volume data scenarios. Maintaining a balance between sudden change detection and minimizing false alarms is vital. Many existing algorithms for this purpose rely on known probability distributions, limiting their feasibility. In this study, we introduce the Kernel-based Cumulative Sum (KCUSUM) algorithm, a non-parametric extension of the traditional Cumulative Sum (CUSUM) method, which has gained prominence for its efficacy in online change point detection under less restrictive conditions. KCUSUM splits itself by comparing incoming samples directly with reference samples and computes a statistic grounded in the Maximum Mean Discrepancy (MMD) non-parametric framework. This approach extends KCUSUM's pertinence to scenarios where only reference samples are available, such as atomic trajectories of proteins in vacuum, facilitating the detection of deviations from the reference sample without prior knowledge of the data's underlying distribution. Furthermore, by harnessing MMD's inherent random-walk structure, we can theoretically analyze KCUSUM's performance across various use cases, including metrics like expected delay and mean runtime to false alarms. Finally, we discuss real-world use cases from scientific simulations such as NWChem CODAR and protein folding data, demonstrating KCUSUM's practical effectiveness in online change point detection.