Many real-world applications, such as those in medical domains, recommendation systems, etc, can be formulated as large state space reinforcement learning problems with only a small budget of the number of policy changes, i.e., low switching cost. This paper focuses on the linear Markov Decision Process (MDP) recently studied in [Yang et al 2019, Jin et al 2020] where the linear function approximation is used for generalization on the large state space. We present the first algorithm for linear MDP with a low switching cost. Our algorithm achieves an $\widetilde{O}\left(\sqrt{d^3H^4K}\right)$ regret bound with a near-optimal $O\left(d H\log K\right)$ global switching cost where $d$ is the feature dimension, $H$ is the planning horizon and $K$ is the number of episodes the agent plays. Our regret bound matches the best existing polynomial algorithm by [Jin et al 2020] and our switching cost is exponentially smaller than theirs. When specialized to tabular MDP, our switching cost bound improves those in [Bai et al 2019, Zhang et al 20020]. We complement our positive result with an $\Omega\left(dH/\log d\right)$ global switching cost lower bound for any no-regret algorithm.

There is a growing interest in the learning-to-learn paradigm, also known as meta-learning, where models infer on new tasks using a few training examples. Recently, meta-learning based methods have been widely used in few-shot classification, regression, reinforcement learning, and domain adaptation. The model-agnostic meta-learning (MAML) algorithm is a well-known algorithm that obtains model parameter initialization at meta-training phase. In the meta-test phase, this initialization is rapidly adapted to new tasks by using gradient descent. However, meta-learning models are prone to overfitting since there are insufficient training tasks resulting in over-parameterized models with poor generalization performance for unseen tasks. In this paper, we propose a Bayesian neural network based MAML algorithm, which we refer to as the B-SMALL algorithm. The proposed framework incorporates a sparse variational loss term alongside the loss function of MAML, which uses a sparsifying approximated KL divergence as a regularizer. We demonstrate the performance of B-MAML using classification and regression tasks, and highlight that training a sparsifying BNN using MAML indeed improves the parameter footprint of the model while performing at par or even outperforming the MAML approach. We also illustrate applicability of our approach in distributed sensor networks, where sparsity and meta-learning can be beneficial.

The rise in popularity and ubiquity of Twitter has made sentiment analysis of tweets an important and well-covered area of research. However, the 140 character limit imposed on tweets makes it hard to use standard linguistic methods for sentiment classification. On the other hand, what tweets lack in structure they make up with sheer volume and rich metadata. This metadata includes geolocation, temporal and author information. We hypothesize that sentiment is dependent on all these contextual factors. Different locations, times and authors have different emotional valences. In this paper, we explored this hypothesis by utilizing distant supervision to collect millions of labelled tweets from different locations, times and authors. We used this data to analyse the variation of tweet sentiments across different authors, times and locations. Once we explored and understood the relationship between these variables and sentiment, we used a Bayesian approach to combine these variables with more standard linguistic features such as n-grams to create a Twitter sentiment classifier. This combined classifier outperforms the purely linguistic classifier, showing that integrating the rich contextual information available on Twitter into sentiment classification is a promising direction of research.

Agents trained by reinforcement learning (RL) often fail to generalize beyond the environment they were trained in, even when presented with new scenarios that seem very similar to the training environment. We study the query complexity required to train RL agents that can generalize to multiple environments. Intuitively, tractable generalization is only possible when the environments are similar or close in some sense. To capture this, we introduce Strong Proximity, a structural condition which precisely characterizes the relative closeness of different environments. We provide an algorithm which exploits Strong Proximity to provably and efficiently generalize. We also show that under a natural weakening of this condition, which we call Weak Proximity, RL can require query complexity that is exponential in the horizon to generalize. A key consequence of our theory is that even when the environments share optimal trajectories, and have highly similar reward and transition functions (as measured by classical metrics), tractable generalization is impossible.

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By Bayes rule, the external information (prior distribution) and the internal information (training data likelihood) are combined coherently, and the posterior distribution and the posterior predictive (marginal) distribution obtained by Bayes rule summarize the total information needed in the inference and prediction, respectively. In this paper, we study the Bayesian framework of the Tensor Network from two perspective. First, we introduce the prior distribution to the weights in the Tensor Network and predict the labels of the new observations by the posterior predictive (marginal) distribution. Since the intractability of the parameter integral in the normalization constant computation, we approximate the posterior predictive distribution by Laplace approximation and obtain the out-product approximation of the hessian matrix of the posterior distribution of the Tensor Network model. Second, to estimate the parameters of the stationary mode, we propose a stable initialization trick to accelerate the inference process by which the Tensor Network can converge to the stationary path more efficiently and stably with gradient descent method. We verify our work on the MNIST, Phishing Website and Breast Cancer data set. We study the Bayesian properties of the Bayesian Tensor Network by visualizing the parameters of the model and the decision boundaries in the two dimensional synthetic data set. For a application purpose, our work can reduce the overfitting and improve the performance of normal Tensor Network model.

In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model. Consequently, the resulting objective function can only partially capture the specifications and optimizing that may lead to poor performance with respect to the true specifications. Motivated by this challenge, we formulate a problem, called diverse stochastic planning, that aims to generate a set of representative -- small and diverse -- behaviors that are near-optimal with respect to the known objective. In particular, the problem aims to compute a set of diverse and near-optimal policies for systems modeled by a Markov decision process. We cast the problem as a constrained nonlinear optimization for which we propose a solution relying on the Frank-Wolfe method. We then prove that the proposed solution converges to a stationary point and demonstrate its efficacy in several planning problems.

Recent technological progress in the development of Unmanned Aerial Vehicles (UAVs) together with decreasing acquisition costs make the application of drone fleets attractive for a wide variety of tasks. In agriculture, disaster management, search and rescue operations, commercial and military applications, the advantage of applying a fleet of drones originates from their ability to cooperate autonomously. Multi-Agent Reinforcement Learning approaches that aim to optimize a neural network based control policy, such as the best performing actor-critic policy gradient algorithms, struggle to effectively back-propagate errors of distinct rewards signal sources and tend to favor lucrative signals while neglecting coordination and exploitation of previously learned similarities. We propose a Multi-Critic Policy Optimization architecture with multiple value estimating networks and a novel advantage function that optimizes a stochastic actor policy network to achieve optimal coordination of agents. Consequently, we apply the algorithm to several tasks that require the collaboration of multiple drones in a physics-based reinforcement learning environment. Our approach achieves a stable policy network update and similarity in reward signal development for an increasing number of agents. The resulting policy achieves optimal coordination and compliance with constraints such as collision avoidance.

Deep ReLU networks trained with the square loss have been observed to perform well in classification tasks. We provide here a theoretical justification based on analysis of the associated gradient flow. We show that convergence to a solution with the absolute minimum norm is expected when normalization techniques such as Batch Normalization (BN) or Weight Normalization (WN) are used together with Weight Decay (WD). The main property of the minimizers that bounds their expected error is the norm: we prove that among all the close-to-interpolating solutions, the ones associated with smaller Frobenius norms of the unnormalized weight matrices have better margin and better bounds on the expected classification error. With BN but in the absence of WD, the dynamical system is singular. Implicit dynamical regularization -- that is zero-initial conditions biasing the dynamics towards high margin solutions -- is also possible in the no-BN and no-WD case. The theory yields several predictions, including the role of BN and weight decay, aspects of Papyan, Han and Donoho's Neural Collapse and the constraints induced by BN on the network weights.

Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness is a recently established area of machine learning that studies how to ensure that biases in the data and model inaccuracies do not lead to models that treat individuals unfavorably on the basis of characteristics such as e.g. race, gender, disabilities, and sexual or political orientation. In this manuscript, we discuss some of the limitations present in the current reasoning about fairness and in methods that deal with it, and describe some work done by the authors to address them. More specifically, we show how causal Bayesian networks can play an important role to reason about and deal with fairness, especially in complex unfairness scenarios. We describe how optimal transport theory can be used to develop methods that impose constraints on the full shapes of distributions corresponding to different sensitive attributes, overcoming the limitation of most approaches that approximate fairness desiderata by imposing constraints on the lower order moments or other functions of those distributions. We present a unified framework that encompasses methods that can deal with different settings and fairness criteria, and that enjoys strong theoretical guarantees. We introduce an approach to learn fair representations that can generalize to unseen tasks. Finally, we describe a technique that accounts for legal restrictions about the use of sensitive attributes.

Conditional inference provides a rigorous approach to counter bias when data from automated model selections is reused for inference. We develop in this paper a statistically consistent Bayesian framework to assess uncertainties within linear models that are informed by grouped sparsities in covariates. Finding wide applications when genes, proteins, genetic variants, neuroimaging measurements are grouped respectively by their biological pathways, molecular functions, regulatory regions, cognitive roles, these models are selected through a useful class of group-sparse learning algorithms. An adjustment factor to account precisely for the selection of promising groups, deployed with a generalized version of Laplace-type approximations is the centerpiece of our new methods. Accommodating well known group-sparse models such as those selected by the Group LASSO, the overlapping Group LASSO, the sparse Group LASSO etc., we illustrate the efficacy of our methodology in extensive experiments and on data from a human neuroimaging application.