Many hierarchical reinforcement learning (RL) applications have empirically verified that incorporating prior knowledge in reward design improves convergence speed and practical performance. We attempt to quantify the computational benefits of hierarchical RL from a planning perspective under assumptions about the intermediate state and intermediate rewards frequently (but often implicitly) adopted in practice. Our approach reveals a trade-off between computational complexity and the pursuit of the shortest path in hierarchical planning: using intermediate rewards significantly reduces the computational complexity in finding a successful policy but does not guarantee to find the shortest path, whereas using sparse terminal rewards finds the shortest path at a significantly higher computational cost. We also corroborate our theoretical results with extensive experiments on the MiniGrid environments using Q-learning and other popular deep RL algorithms.
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Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.
Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.
Many important real-world problems have action spaces that are high-dimensional, continuous or both, making full enumeration of all possible actions infeasible. Instead, only small subsets of actions can be sampled for the purpose of policy evaluation and improvement. In this paper, we propose a general framework to reason in a principled way about policy evaluation and improvement over such sampled action subsets. This sample-based policy iteration framework can in principle be applied to any reinforcement learning algorithm based upon policy iteration. Concretely, we propose Sampled MuZero, an extension of the MuZero algorithm that is able to learn in domains with arbitrarily complex action spaces by planning over sampled actions. We demonstrate this approach on the classical board game of Go and on two continuous control benchmark domains: DeepMind Control Suite and Real-World RL Suite.
Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.
We present Neural A*, a novel data-driven search method for path planning problems. Despite the recent increasing attention to data-driven path planning, a machine learning approach to search-based planning is still challenging due to the discrete nature of search algorithms. In this work, we reformulate a canonical A* search algorithm to be differentiable and couple it with a convolutional encoder to form an end-to-end trainable neural network planner. Neural A* solves a path planning problem by encoding a problem instance to a guidance map and then performing the differentiable A* search with the guidance map. By learning to match the search results with ground-truth paths provided by experts, Neural A* can produce a path consistent with the ground truth accurately and efficiently. Our extensive experiments confirmed that Neural A* outperformed state-of-the-art data-driven planners in terms of the search optimality and efficiency trade-off, and furthermore, successfully predicted realistic human trajectories by directly performing search-based planning on natural image inputs.
Despite deep reinforcement learning has recently achieved great successes, however in multiagent environments, a number of challenges still remain. Multiagent reinforcement learning (MARL) is commonly considered to suffer from the problem of non-stationary environments and exponentially increasing policy space. It would be even more challenging to learn effective policies in circumstances where the rewards are sparse and delayed over long trajectories. In this paper, we study Hierarchical Deep Multiagent Reinforcement Learning (hierarchical deep MARL) in cooperative multiagent problems with sparse and delayed rewards, where efficient multiagent learning methods are desperately needed. We decompose the original MARL problem into hierarchies and investigate how effective policies can be learned hierarchically in synchronous/asynchronous hierarchical MARL frameworks. Several hierarchical deep MARL architectures, i.e., Ind-hDQN, hCom and hQmix, are introduced for different learning paradigms. Moreover, to alleviate the issues of sparse experiences in high-level learning and non-stationarity in multiagent settings, we propose a new experience replay mechanism, named as Augmented Concurrent Experience Replay (ACER). We empirically demonstrate the effects and efficiency of our approaches in several classic Multiagent Trash Collection tasks, as well as in an extremely challenging team sports game, i.e., Fever Basketball Defense.
Deep hierarchical reinforcement learning has gained a lot of attention in recent years due to its ability to produce state-of-the-art results in challenging environments where non-hierarchical frameworks fail to learn useful policies. However, as problem domains become more complex, deep hierarchical reinforcement learning can become inefficient, leading to longer convergence times and poor performance. We introduce the Deep Nested Agent framework, which is a variant of deep hierarchical reinforcement learning where information from the main agent is propagated to the low level $nested$ agent by incorporating this information into the nested agent's state. We demonstrate the effectiveness and performance of the Deep Nested Agent framework by applying it to three scenarios in Minecraft with comparisons to a deep non-hierarchical single agent framework, as well as, a deep hierarchical framework.
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.
Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may not be robust to domain uncertainties and changes. In this paper we present a unified framework {\em PEORL} that integrates symbolic planning with hierarchical reinforcement learning (HRL) to cope with decision-making in a dynamic environment with uncertainties. Symbolic plans are used to guide the agent's task execution and learning, and the learned experience is fed back to symbolic knowledge to improve planning. This method leads to rapid policy search and robust symbolic plans in complex domains. The framework is tested on benchmark domains of HRL.
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