Miao Liu

Shuai Zhang, Meng Wang, Pin-Yu Chen et al.

Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include \textit{graph sparsification} that samples a subgraph to reduce the amount of data aggregation and \textit{model sparsification} that prunes the neural network to reduce the number of trainable weights. Despite the empirical successes in reducing the training cost while maintaining the test accuracy, the theoretical generalization analysis of sparse learning for GNNs remains elusive. To the best of our knowledge, this paper provides the first theoretical characterization of joint edge-model sparse learning from the perspective of sample complexity and convergence rate in achieving zero generalization error. It proves analytically that both sampling important nodes and pruning neurons with the lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy. Although the analysis is centered on two-layer GNNs with structural constraints on data, the insights are applicable to more general setups and justified by both synthetic and practical citation datasets.

Dong-Ki Kim, Matthew Riemer, Miao Liu et al.

Multiagent learning settings are inherently more difficult than single-agent learning because each agent interacts with other simultaneously learning agents in a shared environment. An effective approach in multiagent reinforcement learning is to consider the learning process of agents and influence their future policies toward desirable behaviors from each agent's perspective. Importantly, if each agent maximizes its long-term rewards by accounting for the impact of its behavior on the set of convergence policies, the resulting multiagent system reaches an active equilibrium. While this new solution concept is general such that standard solution concepts, such as a Nash equilibrium, are special cases of active equilibria, it is unclear when an active equilibrium is a preferred equilibrium over other solution concepts. In this paper, we analyze active equilibria from a game-theoretic perspective by closely studying examples where Nash equilibria are known. By directly comparing active equilibria to Nash equilibria in these examples, we find that active equilibria find more effective solutions than Nash equilibria, concluding that an active equilibrium is the desired solution for multiagent learning settings.

Shuai Zhang, Hongkang Li, Meng Wang et al.

This paper provides a theoretical understanding of Deep Q-Network (DQN) with the $\varepsilon$-greedy exploration in deep reinforcement learning. Despite the tremendous empirical achievement of the DQN, its theoretical characterization remains underexplored. First, the exploration strategy is either impractical or ignored in the existing analysis. Second, in contrast to conventional Q-learning algorithms, the DQN employs the target network and experience replay to acquire an unbiased estimation of the mean-square Bellman error (MSBE) utilized in training the Q-network. However, the existing theoretical analysis of DQNs lacks convergence analysis or bypasses the technical challenges by deploying a significantly overparameterized neural network, which is not computationally efficient. This paper provides the first theoretical convergence and sample complexity analysis of the practical setting of DQNs with $ε$-greedy policy. We prove an iterative procedure with decaying $ε$ converges to the optimal Q-value function geometrically. Moreover, a higher level of $ε$ values enlarges the region of convergence but slows down the convergence, while the opposite holds for a lower level of $ε$ values. Experiments justify our established theoretical insights on DQNs.

Miao Liu, Christopher Amato, Xuejun Liao et al.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called \emph{decentralized stick-breaking policy representation} (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.