We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value of a criterion function (e.g., utility). We focus on an episodic setting with the function approximation where the reward and criterion functions and the Markov transition kernels all have a linear structure but do not impose any additional assumptions on the sampling model. Designing SRL algorithms with provable computational and statistical efficiency is particularly challenging under this setting because of the need to incorporate both the safety constraint and the function approximation into the fundamental exploitation/exploration tradeoff. To this end, we present an {O}ptimistic {P}rimal-{D}ual Proximal Policy {OP}timization (OPDOP) algorithm where the value function is estimated by combining the least-squares policy evaluation and an additional bonus term for safe exploration. We prove that the proposed algorithm achieves an O(d^{1.5}H^{3.5}\sqrt{T}) regret and an O(d^{1.5}H^{3.5}\sqrt{T}) constraint violation, where d is the dimension of the feature mapping, H is the horizon of each episode, and T is the total number of steps. We establish these bounds under the following two settings: (i) Both the reward and criterion functions can change adversarially but are revealed entirely after each episode. (ii) The reward/criterion functions are fixed but the feedback after each episode is bandit. Our bounds depend on the capacity of the state space only through the dimension of the feature mapping and thus our results hold even when the number of states goes to infinity. To the best of our knowledge, we provide the first provably efficient policy optimization algorithm for CMDPs with safe exploration.

Gradient Langevin dynamics (GLD) and stochastic GLD (SGLD) have attracted considerable attention lately, as a way to provide convergence guarantees in a non-convex setting. However, the known rates grow exponentially with the dimension of the space. In this work, we provide a convergence analysis of GLD and SGLD when the optimization space is an infinite dimensional Hilbert space. More precisely, we derive non-asymptotic, dimension-free convergence rates for GLD/SGLD when performing regularized non-convex optimization in a reproducing kernel Hilbert space. Amongst others, the convergence analysis relies on the properties of a stochastic differential equation, its discrete time Galerkin approximation and the geometric ergodicity of the associated Markov chains.

A large portion of passenger requests is reportedly unserviced, partially due to vacant for-hire drivers' cruising behavior during the passenger seeking process. This paper aims to model the multi-driver repositioning task through a mean field multi-agent reinforcement learning (MARL) approach that captures competition among multiple agents. Because the direct application of MARL to the multi-driver system under a given reward mechanism will likely yield a suboptimal equilibrium due to the selfishness of drivers, this study proposes an reward design scheme with which a more desired equilibrium can be reached. To effectively solve the bilevel optimization problem with upper level as the reward design and the lower level as a multi-agent system, a Bayesian optimization (BO) algorithm is adopted to speed up the learning process. We then apply the bilevel optimization model to two case studies, namely, e-hailing driver repositioning under service charge and multiclass taxi driver repositioning under NYC congestion pricing. In the first case study, the model is validated by the agreement between the derived optimal control from BO and that from an analytical solution. With a simple piecewise linear service charge, the objective of the e-hailing platform can be increased by 4.0%. In the second case study, an optimal toll charge of $5.1 is solved using BO, which improves the objective of city planners by 7.9%, compared to that without any toll charge. Under this optimal toll charge, the number of taxis in the NYC central business district is decreased, indicating a better traffic condition, without substantially increasing the crowdedness of the subway system.

As machine learning (ML) being applied to many mission-critical scenarios, certifying ML model robustness becomes increasingly important. Many previous works focuses on the robustness of independent ML and ensemble models, and can only certify a very small magnitude of the adversarial perturbation. In this paper, we take a different viewpoint and improve learning robustness by going beyond independent ML and ensemble models. We aim at promoting the generic Sensing-Reasoning machine learning pipeline which contains both the sensing (e.g. deep neural networks) and reasoning (e.g. Markov logic networks (MLN)) components enriched with domain knowledge. Can domain knowledge help improve learning robustness? Can we formally certify the end-to-end robustness of such an ML pipeline? We first theoretically analyze the computational complexity of checking the provable robustness in the reasoning component. We then derive the provable robustness bound for several concrete reasoning components. We show that for reasoning components such as MLN and a specific family of Bayesian networks it is possible to certify the robustness of the whole pipeline even with a large magnitude of perturbation which cannot be certified by existing work. Finally, we conduct extensive real-world experiments on large scale datasets to evaluate the certified robustness for Sensing-Reasoning ML pipelines.

Recent technological advancements in data acquisition tools allowed life scientists to acquire multimodal data from different biological application domains. Broadly categorized in three types (i.e., sequences, images, and signals), these data are huge in amount and complex in nature. Mining such an enormous amount of data for pattern recognition is a big challenge and requires sophisticated data-intensive machine learning techniques. Artificial neural network-based learning systems are well known for their pattern recognition capabilities and lately their deep architectures - known as deep learning (DL) - have been successfully applied to solve many complex pattern recognition problems. Highlighting the role of DL in recognizing patterns in biological data, this article provides - applications of DL to biological sequences, images, and signals data; overview of open access sources of these data; description of open source DL tools applicable on these data; and comparison of these tools from qualitative and quantitative perspectives. At the end, it outlines some open research challenges in mining biological data and puts forward a number of possible future perspectives.

A key assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of various organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a common task is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover latent tree graphical models. In contrast to distance based methods, SNJ is based on a spectral measure of similarity between all pairs of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that SNJ requires fewer samples to accurately recover trees in regimes where the tree contains a large number of leaves or long edges. We provide theoretical support for this observation by analyzing the model of a perfect binary tree.

We consider reinforcement learning (RL) in Markov Decision Processes (MDPs) in which at each time step the agent, in addition to earning a reward, also incurs an $M$ dimensional vector of costs. The objective is to design a learning rule that maximizes the cumulative reward earned over a finite time horizon of $T$ steps, while simultaneously ensuring that the cumulative cost expenditures are bounded appropriately. The considerations on the cumulative cost expenditures is in departure from the existing RL literature, in that the agent now additionally needs to balance the cost expenses in an \emph{online manner}, while simultaneously performing optimally the exploration-exploitation trade-off typically encountered in RL tasks. This is challenging since either of the duo objectives of exploration and exploitation necessarily require the agent to expend resources. When the constraints are placed on the average costs, we present a version of UCB algorithm and prove that its reward as well as cost regrets are upper-bounded as $O\left(T_{M}S\sqrt{AT\log(T)}\right)$, where $T_{M}$ is the mixing time of the MDP, $S$ is the number of states, $A$ is the number of actions, and $T$ is the time horizon. We further show how to modify the algorithm in order to reduce regrets of a desired subset of the $M$ costs, at the expense of increasing the regrets of rewards and the remaining costs. We then consider RL under the constraint that the vector comprising of the cumulative cost expenditures until each time $t\le T$ must be less than $\mathbf{c}^{ub}t$. We propose a "finite ($B$)-state" algorithm and show that its average reward is within $O\left(e^{-B}\right)$ of $r^{\star}$, the latter being the optimal average reward under average cost constraints.

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in which proposals are obtained using Normalizing Flows. The marginal distribution produced by such MCMC algorithms is a mixture of flow-based distributions, thus drastically increasing the expressivity of the variational family. Unlike previous methods following this direction, our approach is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels. Extensive numerical experiments show clear computational and performance improvements over state-of-the-art methods.

Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which ignores low probability catastrophic events withhighly negative impact on the system. On the other hand,risk-averse policies require the probability of undesirableevents to be below a given threshold, but they do not accountfor optimization of the expected payoff. We consider MDPswith discounted-sum payoff with failure states which repre-sent catastrophic outcomes. The objective of risk-constrainedplanning is to maximize the expected discounted-sum payoffamong risk-averse policies that ensure the probability to en-counter a failure state is below a desired threshold. Our maincontribution is an efficient risk-constrained planning algo-rithm that combines UCT-like search with a predictor learnedthrough interaction with the MDP (in the style of AlphaZero)and with a risk-constrained action selection via linear pro-gramming. We demonstrate the effectiveness of our approachwith experiments on classical MDPs from the literature, in-cluding benchmarks with an order of 10^6 states.