Value-based methods play a fundamental role in Markov decision processes (MDPs) and reinforcement learning (RL). In this paper, we present a unified control-theoretic framework for analyzing valued-based methods such as value computation (VC), value iteration (VI), and temporal difference (TD) learning (with linear function approximation). Built upon an intrinsic connection between value-based methods and dynamic systems, we can directly use existing convex testing conditions in control theory to derive various convergence results for the aforementioned value-based methods. These testing conditions are convex programs in form of either linear programming (LP) or semidefinite programming (SDP), and can be solved to construct Lyapunov functions in a straightforward manner. Our analysis reveals some intriguing connections between feedback control systems and RL algorithms. It is our hope that such connections can inspire more work at the intersection of system/control theory and RL.
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We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying Markov random processes parameterized by the underlying optimization variable. These time-varying samples make gradient directions in our update biased and dependent, which can potentially lead to the divergence of the iterates. In our two-time-scale approach, one scale is to estimate the true gradient from these samples, which is then used to update the estimate of the optimal solution. While these two iterates are implemented simultaneously, the former is updated "faster" (using bigger step sizes) than the latter (using smaller step sizes). Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale stochastic gradient method. In particular, we provide explicit formulas for the convergence rates of this method under different structural assumptions, namely, strong convexity, convexity, the Polyak-Lojasiewicz condition, and general non-convexity. We apply our framework to two problems in control and reinforcement learning. First, we look at the standard online actor-critic algorithm over finite state and action spaces and derive a convergence rate of O(k^(-2/5)), which recovers the best known rate derived specifically for this problem. Second, we study an online actor-critic algorithm for the linear-quadratic regulator and show that a convergence rate of O(k^(-2/3)) is achieved. This is the first time such a result is known in the literature. Finally, we support our theoretical analysis with numerical simulations where the convergence rates are visualized.
In this paper we introduce a new approach to discrete-time semi-Markov decision processes based on the sojourn time process. Different characterizations of discrete-time semi-Markov processes are exploited and decision processes are constructed by their means. With this new approach, the agent is allowed to consider different actions depending also on the sojourn time of the process in the current state. A numerical method based on $Q$-learning algorithms for finite horizon reinforcement learning and stochastic recursive relations is investigated. Finally, we consider two toy examples: one in which the reward depends on the sojourn-time, according to the gambler's fallacy; the other in which the environment is semi-Markov even if the reward function does not depend on the sojourn time. These are used to carry on some numerical evaluations on the previously presented $Q$-learning algorithm and on a different naive method based on deep reinforcement learning.
We study the joint active/passive beamforming and channel blocklength (CBL) allocation in a non-ideal reconfigurable intelligent surface (RIS)-aided ultra-reliable and low-latency communication (URLLC) system. The considered scenario is a finite blocklength (FBL) regime and the problem is solved by leveraging a novel deep reinforcement learning (DRL) algorithm named twin-delayed deep deterministic policy gradient (TD3). First, assuming an industrial automation system with multiple actuators, the signal-to-interference-plus-noise ratio and achievable rate in the FBL regime are identified for each actuator in terms of the phase shift configuration matrix at the RIS. Next, the joint active/passive beamforming and CBL optimization problem is formulated where the objective is to maximize the total achievable FBL rate in all actuators, subject to non-linear amplitude response at the RIS elements, BS transmit power budget, and total available CBL. Since the amplitude response equality constraint is highly non-convex and non-linear, we resort to employing an actor-critic policy gradient DRL algorithm based on TD3. The considered method relies on interacting RIS with the industrial automation environment by taking actions which are the phase shifts at the RIS elements, CBL variables, and BS beamforming to maximize the expected observed reward, i.e., the total FBL rate. We assess the performance loss of the system when the RIS is non-ideal, i.e., with non-linear amplitude response, and compare it with ideal RIS without impairments. The numerical results show that optimizing the RIS phase shifts, BS beamforming, and CBL variables via the proposed TD3 method is highly beneficial to improving the network total FBL rate as the proposed method with deterministic policy outperforms conventional methods.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
Recommender systems have been widely applied in different real-life scenarios to help us find useful information. Recently, Reinforcement Learning (RL) based recommender systems have become an emerging research topic. It often surpasses traditional recommendation models even most deep learning-based methods, owing to its interactive nature and autonomous learning ability. Nevertheless, there are various challenges of RL when applying in recommender systems. Toward this end, we firstly provide a thorough overview, comparisons, and summarization of RL approaches for five typical recommendation scenarios, following three main categories of RL: value-function, policy search, and Actor-Critic. Then, we systematically analyze the challenges and relevant solutions on the basis of existing literature. Finally, under discussion for open issues of RL and its limitations of recommendation, we highlight some potential research directions in this field.
In light of the emergence of deep reinforcement learning (DRL) in recommender systems research and several fruitful results in recent years, this survey aims to provide a timely and comprehensive overview of the recent trends of deep reinforcement learning in recommender systems. We start with the motivation of applying DRL in recommender systems. Then, we provide a taxonomy of current DRL-based recommender systems and a summary of existing methods. We discuss emerging topics and open issues, and provide our perspective on advancing the domain. This survey serves as introductory material for readers from academia and industry into the topic and identifies notable opportunities for further research.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.
Recommender systems play a crucial role in mitigating the problem of information overload by suggesting users' personalized items or services. The vast majority of traditional recommender systems consider the recommendation procedure as a static process and make recommendations following a fixed strategy. In this paper, we propose a novel recommender system with the capability of continuously improving its strategies during the interactions with users. We model the sequential interactions between users and a recommender system as a Markov Decision Process (MDP) and leverage Reinforcement Learning (RL) to automatically learn the optimal strategies via recommending trial-and-error items and receiving reinforcements of these items from users' feedbacks. In particular, we introduce an online user-agent interacting environment simulator, which can pre-train and evaluate model parameters offline before applying the model online. Moreover, we validate the importance of list-wise recommendations during the interactions between users and agent, and develop a novel approach to incorporate them into the proposed framework LIRD for list-wide recommendations. The experimental results based on a real-world e-commerce dataset demonstrate the effectiveness of the proposed framework.
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