Many social services including online dating, social media, recruitment and online learning, largely rely on \matching people with the right people". The success of these services and the user experience with them often depends on their ability to match users. Reciprocal Recommender Systems (RRS) arose to facilitate this process by identifying users who are a potential match for each other, based on information provided by them. These systems are inherently more complex than user-item recommendation approaches and unidirectional user recommendation services, since they need to take into account both users' preferences towards each other in the recommendation process. This entails not only predicting accurate preference estimates as classical recommenders do, but also defining adequate fusion processes for aggregating user-to-user preferential information. The latter is a crucial and distinctive, yet barely investigated aspect in RRS research. This paper presents a snapshot analysis of the extant literature to summarize the state-of-the-art RRS research to date, focusing on the fundamental features that differentiate RRSs from other classes of recommender systems. Following this, we discuss the challenges and opportunities for future research on RRSs, with special focus on (i) fusion strategies to account for reciprocity and (ii) emerging application domains related to social recommendation.

We consider the problem of batch multi-task reinforcement learning with observed context descriptors, motivated by its application to personalized medical treatment. In particular, we study two general classes of learning algorithms: direct policy learning (DPL), an imitation-learning based approach which learns from expert trajectories, and model-based learning. First, we derive sample complexity bounds for DPL, and then show that model-based learning from expert actions can, even with a finite model class, be impossible. After relaxing the conditions under which the model-based approach is expected to learn by allowing for greater coverage of state-action space, we provide sample complexity bounds for model-based learning with finite model classes, showing that there exist model classes with sample complexity exponential in their statistical complexity. We then derive a sample complexity upper bound for model-based learning based on a measure of concentration of the data distribution. Our results give formal justification for imitation learning over model-based learning in this setting.

The synthesis problem for partially observable Markov decision processes (POMDPs) is to compute a policy that satisfies a given specification. Such policies have to take the full execution history of a POMDP into account, rendering the problem undecidable in general. A common approach is to use a limited amount of memory and randomize over potential choices. Yet, this problem is still NP-hard and often computationally intractable in practice. A restricted problem is to use neither history nor randomization, yielding policies that are called stationary and deterministic. Previous approaches to compute such policies employ mixed-integer linear programming (MILP). We provide a novel MILP encoding that supports sophisticated specifications in the form of temporal logic constraints. It is able to handle an arbitrary number of such specifications. Yet, randomization and memory are often mandatory to achieve satisfactory policies. First, we extend our encoding to deliver a restricted class of randomized policies. Second, based on the results of the original MILP, we employ a preprocessing of the POMDP to encompass memory-based decisions. The advantages of our approach over state-of-the-art POMDP solvers lie (1) in the flexibility to strengthen simple deterministic policies without losing computational tractability and (2) in the ability to enforce the provable satisfaction of arbitrarily many specifications. The latter point allows taking trade-offs between performance and safety aspects of typical POMDP examples into account. We show the effectiveness of our method on a broad range of benchmarks.

As a typical vehicle-cyber-physical-system (V-CPS), connected automated vehicles attracted more and more attention in recent years. This paper focuses on discussing the decision-making (DM) strategy for autonomous vehicles in a connected environment. First, the highway DM problem is formulated, wherein the vehicles can exchange information via wireless networking. Then, two classical reinforcement learning (RL) algorithms, Q-learning and Dyna, are leveraged to derive the DM strategies in a predefined driving scenario. Finally, the control performance of the derived DM policies in safety and efficiency is analyzed. Furthermore, the inherent differences of the RL algorithms are embodied and discussed in DM strategies.

Markov logic networks (MLNs, Richardson and Domingos, 2006) are a statistical relational learning [Getoor and Taskar, 2007] framework for probabilistic modelling of complex relational structures such as social and biological networks, molecules etc. In general, inference in MLNs is intractable. Lifted inference refers to a set of methods developed in the literature which exploit symmetries for making probabilistic inference more tractable, e.g.

This paper studies the problem of information freshness-aware task offloading in an air-ground integrated multi-access edge computing system, which is deployed by an infrastructure provider (InP). A third-party real-time application service provider provides computing services to the subscribed mobile users (MUs) with the limited communication and computation resources from the InP based on a long-term business agreement. Due to the dynamic characteristics, the interactions among the MUs are modelled by a non-cooperative stochastic game, in which the control policies are coupled and each MU aims to selfishly maximize its own expected long-term payoff. To address the Nash equilibrium solutions, we propose that each MU behaves in accordance with the local system states and conjectures, based on which the stochastic game is transformed into a single-agent Markov decision process. Moreover, we derive a novel online deep reinforcement learning (RL) scheme that adopts two separate double deep Q-networks for each MU to approximate the Q-factor and the post-decision Q-factor. Using the proposed deep RL scheme, each MU in the system is able to make decisions without a priori statistical knowledge of dynamics. Numerical experiments examine the potentials of the proposed scheme in balancing the age of information and the energy consumption.

In state of the art model-free off-policy deep reinforcement learning, a replay memory is used to store past experience and derive all network updates. Even if both state and action spaces are continuous, the replay memory only holds a finite number of transitions. We represent these transitions in a data graph and link its structure to soft divergence. By selecting a subgraph with a favorable structure, we construct a simplified Markov Decision Process for which exact Q-values can be computed efficiently as more data comes in. The subgraph and its associated Q-values can be represented as a QGraph. We show that the Q-value for each transition in the simplified MDP is a lower bound of the Q-value for the same transition in the original continuous Q-learning problem. By using these lower bounds in temporal difference learning, our method QG-DDPG is less prone to soft divergence and exhibits increased sample efficiency while being more robust to hyperparameters. QGraphs also retain information from transitions that have already been overwritten in the replay memory, which can decrease the algorithm's sensitivity to the replay memory capacity.

This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct supervision. In a tabular episodic Markov game with $S$ states, $A$ max-player actions and $B$ min-player actions, the best existing algorithm for finding an approximate Nash equilibrium requires $\tilde{\mathcal{O}}(S^2AB)$ steps of game playing, when only highlighting the dependency on $(S,A,B)$. In contrast, the best existing lower bound scales as $\Omega(S(A+B))$ and has a significant gap from the upper bound. This paper closes this gap for the first time: we propose an optimistic variant of the \emph{Nash Q-learning} algorithm with sample complexity $\tilde{\mathcal{O}}(SAB)$, and a new \emph{Nash V-learning} algorithm with sample complexity $\tilde{\mathcal{O}}(S(A+B))$. The latter result matches the information-theoretic lower bound in all problem-dependent parameters except for a polynomial factor of the length of each episode. In addition, we present a computational hardness result for learning the best responses against a fixed opponent in Markov games---a learning objective different from finding the Nash equilibrium.

A common assumption in reinforcement learning (RL) is to have access to a generative model (i.e., a simulator of the environment), which allows to generate samples from any desired state-action pair. Nonetheless, in many settings a generative model may not be available and an adaptive exploration strategy is needed to efficiently collect samples from an unknown environment by direct interaction. In this paper, we study the scenario where an algorithm based on the generative model assumption defines the (possibly time-varying) amount of samples $b(s,a)$ required at each state-action pair $(s,a)$ and an exploration strategy has to learn how to generate $b(s,a)$ samples as fast as possible. Building on recent results for regret minimization in the stochastic shortest path (SSP) setting (Cohen et al., 2020; Tarbouriech et al., 2020), we derive an algorithm that requires $\tilde{O}( B D + D^{3/2} S^2 A)$ time steps to collect the $B = \sum_{s,a} b(s,a)$ desired samples, in any unknown and communicating MDP with $S$ states, $A$ actions and diameter $D$. Leveraging the generality of our strategy, we readily apply it to a variety of existing settings (e.g., model estimation, pure exploration in MDPs) for which we obtain improved sample-complexity guarantees, and to a set of new problems such as best-state identification and sparse reward discovery.

We study the exploration-exploitation dilemma in the linear quadratic regulator (LQR) setting. Inspired by the extended value iteration algorithm used in optimistic algorithms for finite MDPs, we propose to relax the optimistic optimization of \ofulq and cast it into a constrained \textit{extended} LQR problem, where an additional control variable implicitly selects the system dynamics within a confidence interval. We then move to the corresponding Lagrangian formulation for which we prove strong duality. As a result, we show that an $\epsilon$-optimistic controller can be computed efficiently by solving at most $O\big(\log(1/\epsilon)\big)$ Riccati equations. Finally, we prove that relaxing the original \ofu problem does not impact the learning performance, thus recovering the $\tilde{O}(\sqrt{T})$ regret of \ofulq. To the best of our knowledge, this is the first computationally efficient confidence-based algorithm for LQR with worst-case optimal regret guarantees.