We study a class of reinforcement learning (RL) tasks where the objective of the agent is to accomplish temporally extended goals. In this setting, a common approach is to represent the tasks as deterministic finite automata (DFA) and integrate them into the state-space for RL algorithms. However, while these machines model the reward function, they often overlook the causal knowledge about the environment. To address this limitation, we propose the Temporal-Logic-based Causal Diagram (TL-CD) in RL, which captures the temporal causal relationships between different properties of the environment. We exploit the TL-CD to devise an RL algorithm in which an agent requires significantly less exploration of the environment. To this end, based on a TL-CD and a task DFA, we identify configurations where the agent can determine the expected rewards early during an exploration. Through a series of case studies, we demonstrate the benefits of using TL-CDs, particularly the faster convergence of the algorithm to an optimal policy due to reduced exploration of the environment.

Collecting and leveraging data with good coverage properties plays a crucial role in different aspects of reinforcement learning (RL), including reward-free exploration and offline learning. However, the notion of "good coverage" really depends on the application at hand, as data suitable for one context may not be so for another. In this paper, we formalize the problem of active coverage in episodic Markov decision processes (MDPs), where the goal is to interact with the environment so as to fulfill given sampling requirements. This framework is sufficiently flexible to specify any desired coverage property, making it applicable to any problem that involves online exploration. Our main contribution is an instance-dependent lower bound on the sample complexity of active coverage and a simple game-theoretic algorithm, CovGame, that nearly matches it. We then show that CovGame can be used as a building block to solve different PAC RL tasks. In particular, we obtain a simple algorithm for PAC reward-free exploration with an instance-dependent sample complexity that, in certain MDPs which are "easy to explore", is lower than the minimax one. By further coupling this exploration algorithm with a new technique to do implicit eliminations in policy space, we obtain a computationally-efficient algorithm for best-policy identification whose instance-dependent sample complexity scales with gaps between policy values.

Real-time on-device continual learning applications are used on mobile phones, consumer robots, and smart appliances. Such devices have limited processing and memory storage capabilities, whereas continual learning acquires data over a long period of time. By necessity, lifelong learning algorithms have to be able to operate under such constraints while delivering good performance. This study presents the Explainable Lifelong Learning (ExLL) model, which incorporates several important traits: 1) learning to learn, in a single pass, from streaming data with scarce examples and resources; 2) a self-organizing prototype-based architecture that expands as needed and clusters streaming data into separable groups by similarity and preserves data against catastrophic forgetting; 3) an interpretable architecture to convert the clusters into explainable IF-THEN rules as well as to justify model predictions in terms of what is similar and dissimilar to the inference; and 4) inferences at the global and local level using a pairwise decision fusion process to enhance the accuracy of the inference, hence ``Glocal Pairwise Fusion.'' We compare ExLL against contemporary online learning algorithms for image recognition, using OpenLoris, F-SIOL-310, and Places datasets to evaluate several continual learning scenarios for video streams, low-sample learning, ability to scale, and imbalanced data streams. The algorithms are evaluated for their performance in accuracy, number of parameters, and experiment runtime requirements. ExLL outperforms all algorithms for accuracy in the majority of the tested scenarios.

To fully exploit the benefits of the fog environment, efficient management of data locality is crucial. Blind or reactive data replication falls short in harnessing the potential of fog computing, necessitating more advanced techniques for predicting where and when clients will connect. While spatial prediction has received considerable attention, temporal prediction remains understudied. Our paper addresses this gap by examining the advantages of incorporating temporal prediction into existing spatial prediction models. We also provide a comprehensive analysis of spatio-temporal prediction models, such as Deep Neural Networks and Markov models, in the context of predictive replication. We propose a novel model using Holt-Winter's Exponential Smoothing for temporal prediction, leveraging sequential and periodical user movement patterns. In a fog network simulation with real user trajectories our model achieves a 15% reduction in excess data with a marginal 1% decrease in data availability.

We study a variation of vanilla stochastic gradient descent where the optimizer only has access to a Markovian sampling scheme. These schemes encompass applications that range from decentralized optimization with a random walker (token algorithms), to RL and online system identification problems. We focus on obtaining rates of convergence under the least restrictive assumptions possible on the underlying Markov chain and on the functions optimized. We first unveil the theoretical lower bound for methods that sample stochastic gradients along the path of a Markov chain, making appear a dependency in the hitting time of the underlying Markov chain. We then study Markov chain SGD (MC-SGD) under much milder regularity assumptions than prior works (e.g., no bounded gradients or domain, and infinite state spaces). We finally introduce MC-SAG, an alternative to MC-SGD with variance reduction, that only depends on the hitting time of the Markov chain, therefore obtaining a communication-efficient token algorithm.

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their excessive computational cost and by the difficulty in adapting them for analyzing sequences (e.g. amino acid and nucleotide sequences) and graphs (e.g. ones representing small molecules). In this study, we develop efficient and scalable approaches for fitting GP models as well as fast convolution kernels which scale linearly with graph or sequence size. We implement these improvements by building an open-source Python library called xGPR. We compare the performance of xGPR with the reported performance of various deep learning models on 20 benchmarks, including small molecule, protein sequence and tabular data. We show that xGRP achieves highly competitive performance with much shorter training time. Furthermore, we also develop new kernels for sequence and graph data and show that xGPR generally outperforms convolutional neural networks on predicting key properties of proteins and small molecules. Importantly, xGPR provides uncertainty information not available from typical deep learning models. Additionally, xGPR provides a representation of the input data that can be used for clustering and data visualization. These results demonstrate that xGPR provides a powerful and generic tool that can be broadly useful in protein engineering and drug discovery.

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is challenging and requires restrictive approximations. Monte Carlo Dropout has been widely used as a relatively cheap way for approximate Inference and to estimate uncertainty with deep neural networks. Traditionally, the dropout mask is sampled independently from a fixed distribution. Recent works show that the dropout mask can be viewed as a latent variable, which can be inferred with variational inference. These methods face two important challenges: (a) the posterior distribution over masks can be highly multi-modal which can be difficult to approximate with standard variational inference and (b) it is not trivial to fully utilize sample-dependent information and correlation among dropout masks to improve posterior estimation. In this work, we propose GFlowOut to address these issues. GFlowOut leverages the recently proposed probabilistic framework of Generative Flow Networks (GFlowNets) to learn the posterior distribution over dropout masks. We empirically demonstrate that GFlowOut results in predictive distributions that generalize better to out-of-distribution data, and provide uncertainty estimates which lead to better performance in downstream tasks.

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that ensuring \emph{marginal fairness} for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In this paper, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high-probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.

In this paper, we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train. Instead, we formulate and solve a sequence of small linear systems for the individual tensor train cores. This approach can avoid the curse of dimensionality that threatens both the algorithmic and sample complexities of the recovery problem. Specifically, for Markov models under natural conditions, we prove that the tensor cores can be recovered with a sample complexity that scales logarithmically in the dimensionality. Finally, we illustrate the performance of the method with several numerical experiments.

To date, various neural methods have been proposed for causal effect estimation based on observational data, where a default assumption is the same distribution and availability of variables at both training and inference (i.e., runtime) stages. However, distribution shift (i.e., domain shift) could happen during runtime, and bigger challenges arise from the impaired accessibility of variables. This is commonly caused by increasing privacy and ethical concerns, which can make arbitrary variables unavailable in the entire runtime data and imputation impractical. We term the co-occurrence of domain shift and inaccessible variables runtime domain corruption, which seriously impairs the generalizability of a trained counterfactual predictor. To counter runtime domain corruption, we subsume counterfactual prediction under the notion of domain adaptation. Specifically, we upper-bound the error w.r.t. the target domain (i.e., runtime covariates) by the sum of source domain error and inter-domain distribution distance. In addition, we build an adversarially unified variational causal effect model, named VEGAN, with a novel two-stage adversarial domain adaptation scheme to reduce the latent distribution disparity between treated and control groups first, and between training and runtime variables afterwards. We demonstrate that VEGAN outperforms other state-of-the-art baselines on individual-level treatment effect estimation in the presence of runtime domain corruption on benchmark datasets.