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Register a new userAdaptive Discretization for Episodic Reinforcement Learning in Metric Spaces
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We present an efficient algorithm for model-free episodic reinforcement learning on large (potentially continuous) state-action spaces. Our algorithm is based on a novel $Q$-learning policy with adaptive data-driven discretization. The central idea is to maintain a finer partition of the state-action space in regions which are frequently visited in historical trajectories, and have higher payoff estimates. We demonstrate how our adaptive partitions take advantage of the shape of the optimal $Q$-function and the joint space, without sacrificing the worst-case performance. In particular, we recover the regret guarantees of prior algorithms for continuous state-action spaces, which additionally require either an optimal discretization as input, and/or access to a simulation oracle. Moreover, experiments demonstrate how our algorithm automatically adapts to the underlying structure of the problem, resulting in much better performance compared both to heuristics and $Q$-learning with uniform discretization.
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We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.
Despite the wealth of research into provably efficient reinforcement learning algorithms, most works focus on tabular representation and thus struggle to handle exponentially or infinitely large state-action spaces. In this paper, we consider episodic reinforcement learning with a continuous state-action space which is assumed to be equipped with a natural metric that characterizes the proximity between different states and actions. We propose ZoomRL, an online algorithm that leverages ideas from continuous bandits to learn an adaptive discretization of the joint space by zooming in more promising and frequently visited regions while carefully balancing the exploitation-exploration trade-off. We show that ZoomRL achieves a worst-case regret $tilde{O}(H^{frac{5}{2}} K^{frac{d+1}{d+2}})$ where $H$ is the planning horizon, $K$ is the number of episodes and $d$ is the covering dimension of the space with respect to the metric. Moreover, our algorithm enjoys improved metric-dependent guarantees that reflect the geometry of the underlying space. Finally, we show that our algorithm is robust to small misspecification errors.
Few-shot learning, which aims at extracting new concepts rapidly from extremely few examples of novel classes, has been featured into the meta-learning paradigm recently. Yet, the key challenge of how to learn a generalizable classifier with the capability of adapting to specific tasks with severely limited data still remains in this domain. To this end, we propose a Transductive Episodic-wise Adaptive Metric (TEAM) framework for few-shot learning, by integrating the meta-learning paradigm with both deep metric learning and transductive inference. With exploring the pairwise constraints and regularization prior within each task, we explicitly formulate the adaptation procedure into a standard semi-definite programming problem. By solving the problem with its closed-form solution on the fly with the setup of transduction, our approach efficiently tailors an episodic-wise metric for each task to adapt all features from a shared task-agnostic embedding space into a more discriminative task-specific metric space. Moreover, we further leverage an attention-based bi-directional similarity strategy for extracting the more robust relationship between queries and prototypes. Extensive experiments on three benchmark datasets show that our framework is superior to other existing approaches and achieves the state-of-the-art performance in the few-shot literature.
Recent advances in deep reinforcement learning algorithms have shown great potential and success for solving many challenging real-world problems, including Go game and robotic applications. Usually, these algorithms need a carefully designed reward function to guide training in each time step. However, in real world, it is non-trivial to design such a reward function, and the only signal available is usually obtained at the end of a trajectory, also known as the episodic reward or return. In this work, we introduce a new algorithm for temporal credit assignment, which learns to decompose the episodic return back to each time-step in the trajectory using deep neural networks. With this learned reward signal, the learning efficiency can be substantially improved for episodic reinforcement learning. In particular, we find that expressive language models such as the Transformer can be adopted for learning the importance and the dependency of states in the trajectory, therefore providing high-quality and interpretable learned reward signals. We have performed extensive experiments on a set of MuJoCo continuous locomotive control tasks with only episodic returns and demonstrated the effectiveness of our algorithm.
Episodic memory-based methods can rapidly latch onto past successful strategies by a non-parametric memory and improve sample efficiency of traditional reinforcement learning. However, little effort is put into the continuous domain, where a state is never visited twice, and previous episodic methods fail to efficiently aggregate experience across trajectories. To address this problem, we propose Generalizable Episodic Memory (GEM), which effectively organizes the state-action values of episodic memory in a generalizable manner and supports implicit planning on memorized trajectories. GEM utilizes a double estimator to reduce the overestimation bias induced by value propagation in the planning process. Empirical evaluation shows that our method significantly outperforms existing trajectory-based methods on various MuJoCo continuous control tasks. To further show the general applicability, we evaluate our method on Atari games with discrete action space, which also shows a significant improvement over baseline algorithms.
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