Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of jointly inferring multiple graphs from the observation of signals at their nodes (graph signals), which are assumed to be stationary in the sought graphs. From a mathematical point of view, graph stationarity implies that the mapping between the covariance of the signals and the sparse matrix representing the underlying graph is given by a matrix polynomial. A prominent example is that of Markov random fields, where the inverse of the covariance yields the sparse matrix of interest. From a modeling perspective, stationary graph signals can be used to model linear network processes evolving on a set of (not necessarily known) networks. Leveraging that matrix polynomials commute, a convex optimization method along with sufficient conditions that guarantee the recovery of the true graphs are provided when perfect covariance information is available. Particularly important from an empirical viewpoint, we provide high-probability bounds on the recovery error as a function of the number of signals observed and other key problem parameters. Numerical experiments using synthetic and real-world data demonstrate the effectiveness of the proposed method with perfect covariance information as well as its robustness in the noisy regime.

We consider reinforcement learning (RL) in episodic Markov decision processes (MDPs) with linear function approximation under drifting environment. Specifically, both the reward and state transition functions can evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain \textit{variation budgets}. We first develop the $\texttt{LSVI-UCB-Restart}$ algorithm, an optimistic modification of least-squares value iteration combined with periodic restart, and establish its dynamic regret bound when variation budgets are known. We then propose a parameter-free algorithm, $\texttt{Ada-LSVI-UCB-Restart}$, that works without knowing the variation budgets, but with a slightly worse dynamic regret bound. We also derive the first minimax dynamic regret lower bound for nonstationary MDPs to show that our proposed algorithms are near-optimal. As a byproduct, we establish a minimax regret lower bound for linear MDPs, which is unsolved by \cite{jin2020provably}. In addition, we provide numerical experiments to demonstrate the effectiveness of our proposed algorithms. As far as we know, this is the first dynamic regret analysis in nonstationary reinforcement learning with function approximation.

In Cooperative Multi-Agent Reinforcement Learning (MARL) and under the setting of Centralized Training with Decentralized Execution (CTDE), agents observe and interact with their environment locally and independently. With local observation and random sampling, the randomness in rewards and observations leads to randomness in long-term returns. Existing methods such as Value Decomposition Network (VDN) and QMIX estimate the value of long-term returns as a scalar that does not contain the information of randomness. Our proposed model QR-MIX introduces quantile regression, modeling joint state-action values as a distribution, combining QMIX with Implicit Quantile Network (IQN). However, the monotonicity in QMIX limits the expression of joint state-action value distribution and may lead to incorrect estimation results in non-monotonic cases. Therefore, we proposed a flexible loss function to approximate the monotonicity found in QMIX. Our model is not only more tolerant of the randomness of returns, but also more tolerant of the randomness of monotonic constraints. The experimental results demonstrate that QR-MIX outperforms the previous state-of-the-art method QMIX in the StarCraft Multi-Agent Challenge (SMAC) environment.

In this work we solve for partially observable reinforcement learning (RL) environments by adding recurrency. We focus on partially observable robotic assembly tasks in the continuous action domain, with force/torque sensing being the only observation. We have developed a new distributed RL agent, named Recurrent Distributed DDPG (RD2), which adds a recurrent neural network layer to Ape-X DDPG and makes two important improvements on prioritized experience replay to stabilize training. We demonstrate the effectiveness of RD2 on a variety of joint assembly tasks and a partially observable version of the pendulum task from OpenAI Gym. Our results show that RD2 is able to achieve better performance than Ape-X DDPG and PPO with LSTM on partially observable tasks with varying complexity. We also show that the trained models adapt well to different initial states and different types of noise injected in the simulated environment. The video presenting our experiments is available at https://sites.google.com/view/rd2-rl

Recent wildfires in the United States have resulted in loss of life and billions of dollars, destroying countless structures and forests. Fighting wildfires is extremely complex. It is difficult to observe the true state of fires due to smoke and risk associated with ground surveillance. There are limited resources to be deployed over a massive area and the spread of the fire is challenging to predict. This paper proposes a decision-theoretic approach to combat wildfires. We model the resource allocation problem as a partially-observable Markov decision process. We also present a data-driven model that lets us simulate how fires spread as a function of relevant covariates. A major problem in using data-driven models to combat wildfires is the lack of comprehensive data sources that relate fires with relevant covariates. We present an algorithmic approach based on large-scale raster and vector analysis that can be used to create such a dataset. Our data with over 2 million data points is the first open-source dataset that combines existing fire databases with covariates extracted from satellite imagery. Through experiments using real-world wildfire data, we demonstrate that our forecasting model can accurately model the spread of wildfires. Finally, we use simulations to demonstrate that our response strategy can significantly reduce response times compared to baseline methods.

This paper presents a model-free reinforcement learning (RL) algorithm to synthesize a control policy that maximizes the satisfaction probability of linear temporal logic (LTL) specifications. Due to the consideration of environment and motion uncertainties, we model the robot motion as a probabilistic labeled Markov decision process with unknown transition probabilities and unknown probabilistic label functions. The LTL task specification is converted to a limit deterministic generalized B\"uchi automaton (LDGBA) with several accepting sets to maintain dense rewards during learning. The novelty of applying LDGBA is to construct an embedded LDGBA (E-LDGBA) by designing a synchronous tracking-frontier function, which enables the record of non-visited accepting sets without increasing dimensional and computational complexity. With appropriate dependent reward and discount functions, rigorous analysis shows that any method that optimizes the expected discount return of the RL-based approach is guaranteed to find the optimal policy that maximizes the satisfaction probability of the LTL specifications. A model-free RL-based motion planning strategy is developed to generate the optimal policy in this paper. The effectiveness of the RL-based control synthesis is demonstrated via simulation and experimental results.

Humans learn from past experiences, Machines follow the instructions given by humans but, what if humans can train the machines to learn from the past experiences (data) and can do act much faster, here comes the concept of Machine Learning. Machine learning is the field of study that gives computers the capability to learn without being explicitly programmed. Machine learning algorithms build a mathematical model based on the data, known as training data, in order to make predictions or decisions. Machine learning is not only about learning, but also about understanding and reasoning. Machine Learning is not programmed, it is taught with data.

Healthcare programs such as Medicaid provide crucial services to vulnerable populations, but due to limited resources, many of the individuals who need these services the most languish on waiting lists. Survival models, e.g. the Cox proportional hazards model, can potentially improve this situation by predicting individuals' levels of need, which can then be used to prioritize the waiting lists. Providing care to those in need can prevent institutionalization for those individuals, which both improves quality of life and reduces overall costs. While the benefits of such an approach are clear, care must be taken to ensure that the prioritization process is fair or independent of demographic information-based harmful stereotypes. In this work, we develop multiple fairness definitions for survival models and corresponding fair Cox proportional hazards models to ensure equitable allocation of healthcare resources. We demonstrate the utility of our methods in terms of fairness and predictive accuracy on two publicly available survival datasets.

Modern deep learning models have achieved great success in predictive accuracy for many data modalities. However, their application to many real-world tasks is restricted by poor uncertainty estimates, such as overconfidence on out-of-distribution (OOD) data and ungraceful failing under distributional shift. Previous benchmarks have found that ensembles of neural networks (NNs) are typically the best calibrated models on OOD data. Inspired by this, we leverage recent theoretical advances that characterize the function-space prior of an ensemble of infinitely-wide NNs as a Gaussian process, termed the neural network Gaussian process (NNGP). We use the NNGP with a softmax link function to build a probabilistic model for multi-class classification and marginalize over the latent Gaussian outputs to sample from the posterior. This gives us a better understanding of the implicit prior NNs place on function space and allows a direct comparison of the calibration of the NNGP and its finite-width analogue. We also examine the calibration of previous approaches to classification with the NNGP, which treat classification problems as regression to the one-hot labels. In this case the Bayesian posterior is exact, and we compare several heuristics to generate a categorical distribution over classes. We find these methods are well calibrated under distributional shift. Finally, we consider an infinite-width final layer in conjunction with a pre-trained embedding. This replicates the important practical use case of transfer learning and allows scaling to significantly larger datasets. As well as achieving competitive predictive accuracy, this approach is better calibrated than its finite width analogue.

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models can be adapted to more realistic settings where train and test distributions differ. Unfortunately, there is severely limited theoretical support for these algorithms and little is known about the difficulty of these problems. In this work, we provide novel information-theoretic lower-bounds on minimax rates of convergence for algorithms that are trained on data from multiple sources and tested on novel data. Our bounds depend intuitively on the information shared between sources of data, and characterize the difficulty of learning in this setting for arbitrary algorithms. We demonstrate these bounds on a hierarchical Bayesian model of meta-learning, computing both upper and lower bounds on parameter estimation via maximum-a-posteriori inference.