Reinforcement learning (RL) has recently achieved tremendous successes in many artificial intelligence applications. Many of the forefront applications of RL involve multiple agents, e.g., playing chess and Go games, autonomous driving, and robotics. Unfortunately, the framework upon which classical RL builds is inappropriate for multi-agent learning, as it assumes an agent's environment is stationary and does not take into account the adaptivity of other agents. In this review paper, we present the model of stochastic games for multi-agent learning in dynamic environments. We focus on the development of simple and independent learning dynamics for stochastic games: each agent is myopic and chooses best-response type actions to other agents' strategy without any coordination with her opponent. There has been limited progress on developing convergent best-response type independent learning dynamics for stochastic games. We present our recently proposed simple and independent learning dynamics that guarantee convergence in zero-sum stochastic games, together with a review of other contemporaneous algorithms for dynamic multi-agent learning in this setting. Along the way, we also reexamine some classical results from both the game theory and RL literature, to situate both the conceptual contributions of our independent learning dynamics, and the mathematical novelties of our analysis. We hope this review paper serves as an impetus for the resurgence of studying independent and natural learning dynamics in game theory, for the more challenging settings with a dynamic environment.
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In reinforcement learning, it is common to let an agent interact for a fixed amount of time with its environment before resetting it and repeating the process in a series of episodes. The task that the agent has to learn can either be to maximize its performance over (i) that fixed period, or (ii) an indefinite period where time limits are only used during training to diversify experience. In this paper, we provide a formal account for how time limits could effectively be handled in each of the two cases and explain why not doing so can cause state aliasing and invalidation of experience replay, leading to suboptimal policies and training instability. In case (i), we argue that the terminations due to time limits are in fact part of the environment, and thus a notion of the remaining time should be included as part of the agent's input to avoid violation of the Markov property. In case (ii), the time limits are not part of the environment and are only used to facilitate learning. We argue that this insight should be incorporated by bootstrapping from the value of the state at the end of each partial episode. For both cases, we illustrate empirically the significance of our considerations in improving the performance and stability of existing reinforcement learning algorithms, showing state-of-the-art results on several control tasks.
Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show that when using constant stepsize (i.e., $\alpha_k\equiv \alpha$), the algorithm achieves exponential fast convergence to a neighborhood (with radius $O(\alpha\log(1/\alpha))$) around the desired limit point. When using diminishing stepsizes with appropriate decay rate, the algorithm converges with rate $O(\log(k)/k)$. Our proof is based on Lyapunov drift arguments, and to handle the Markovian noise, we exploit the fast mixing of the underlying Markov chain. To demonstrate the generality of our theoretical results on Markovian SA, we use it to derive the finite-sample bounds of the popular $Q$-learning with linear function approximation algorithm, under a condition on the behavior policy. Importantly, we do not need to make the assumption that the samples are i.i.d., and do not require an artificial projection step in the algorithm to maintain the boundedness of the iterates. Numerical simulations corroborate our theoretical results.
Curriculum learning (CL) is a training strategy that trains a machine learning model from easier data to harder data, which imitates the meaningful learning order in human curricula. As an easy-to-use plug-in, the CL strategy has demonstrated its power in improving the generalization capacity and convergence rate of various models in a wide range of scenarios such as computer vision and natural language processing etc. In this survey article, we comprehensively review CL from various aspects including motivations, definitions, theories, and applications. We discuss works on curriculum learning within a general CL framework, elaborating on how to design a manually predefined curriculum or an automatic curriculum. In particular, we summarize existing CL designs based on the general framework of Difficulty Measurer+Training Scheduler and further categorize the methodologies for automatic CL into four groups, i.e., Self-paced Learning, Transfer Teacher, RL Teacher, and Other Automatic CL. We also analyze principles to select different CL designs that may benefit practical applications. Finally, we present our insights on the relationships connecting CL and other machine learning concepts including transfer learning, meta-learning, continual learning and active learning, etc., then point out challenges in CL as well as potential future research directions deserving further investigations.
Training machine learning models in a meaningful order, from the easy samples to the hard ones, using curriculum learning can provide performance improvements over the standard training approach based on random data shuffling, without any additional computational costs. Curriculum learning strategies have been successfully employed in all areas of machine learning, in a wide range of tasks. However, the necessity of finding a way to rank the samples from easy to hard, as well as the right pacing function for introducing more difficult data can limit the usage of the curriculum approaches. In this survey, we show how these limits have been tackled in the literature, and we present different curriculum learning instantiations for various tasks in machine learning. We construct a multi-perspective taxonomy of curriculum learning approaches by hand, considering various classification criteria. We further build a hierarchical tree of curriculum learning methods using an agglomerative clustering algorithm, linking the discovered clusters with our taxonomy. At the end, we provide some interesting directions for future work.
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.
This paper surveys the machine learning literature and presents machine learning as optimization models. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. Particularly, mathematical optimization models are presented for commonly used machine learning approaches for regression, classification, clustering, and deep neural networks as well new emerging applications in machine teaching and empirical model learning. The strengths and the shortcomings of these models are discussed and potential research directions are highlighted.
We give an overview of recent exciting achievements of deep reinforcement learning (RL). We discuss six core elements, six important mechanisms, and twelve applications. We start with background of machine learning, deep learning and reinforcement learning. Next we discuss core RL elements, including value function, in particular, Deep Q-Network (DQN), policy, reward, model, planning, and exploration. After that, we discuss important mechanisms for RL, including attention and memory, unsupervised learning, transfer learning, multi-agent RL, hierarchical RL, and learning to learn. Then we discuss various applications of RL, including games, in particular, AlphaGo, robotics, natural language processing, including dialogue systems, machine translation, and text generation, computer vision, neural architecture design, business management, finance, healthcare, Industry 4.0, smart grid, intelligent transportation systems, and computer systems. We mention topics not reviewed yet, and list a collection of RL resources. After presenting a brief summary, we close with discussions. Please see Deep Reinforcement Learning, arXiv:1810.06339, for a significant update.
We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.
This work considers the problem of provably optimal reinforcement learning for episodic finite horizon MDPs, i.e. how an agent learns to maximize his/her long term reward in an uncertain environment. The main contribution is in providing a novel algorithm --- Variance-reduced Upper Confidence Q-learning (vUCQ) --- which enjoys a regret bound of $\widetilde{O}(\sqrt{HSAT} + H^5SA)$, where the $T$ is the number of time steps the agent acts in the MDP, $S$ is the number of states, $A$ is the number of actions, and $H$ is the (episodic) horizon time. This is the first regret bound that is both sub-linear in the model size and asymptotically optimal. The algorithm is sub-linear in that the time to achieve $\epsilon$-average regret for any constant $\epsilon$ is $O(SA)$, which is a number of samples that is far less than that required to learn any non-trivial estimate of the transition model (the transition model is specified by $O(S^2A)$ parameters). The importance of sub-linear algorithms is largely the motivation for algorithms such as $Q$-learning and other "model free" approaches. vUCQ algorithm also enjoys minimax optimal regret in the long run, matching the $\Omega(\sqrt{HSAT})$ lower bound. Variance-reduced Upper Confidence Q-learning (vUCQ) is a successive refinement method in which the algorithm reduces the variance in $Q$-value estimates and couples this estimation scheme with an upper confidence based algorithm. Technically, the coupling of both of these techniques is what leads to the algorithm enjoying both the sub-linear regret property and the asymptotically optimal regret.
Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov developed an accelerated gradient search algorithm for convex optimization problems. This has been recently extended for non-convex and also stochastic optimization. We use Nesterov's acceleration for policy gradient search in the well-known actor-critic algorithm and show the convergence using ODE method. We tested this algorithm on a scheduling problem. Here an incoming job is scheduled into one of the four queues based on the queue lengths. We see from experimental results that algorithm using Nesterov's acceleration has significantly better performance compared to algorithm which do not use acceleration. To the best of our knowledge this is the first time Nesterov's acceleration has been used with actor-critic algorithm.
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