A Variance Minimization Approach to Temporal-Difference Learning

Fast-converging algorithms are a contemporary requirement in reinforcement learning. In the context of linear function approximation, the magnitude of the smallest eigenvalue of the key matrix is a major factor reflecting the convergence speed. Traditional value-based RL algorithms focus on minimizing errors. This paper introduces a variance minimization (VM) approach for value-based RL instead of error minimization. Based on this approach, we proposed two objectives, the Variance of Bellman Error (VBE) and the Variance of Projected Bellman Error (VPBE), and derived the VMTD, VMTDC, and VMETD algorithms. We provided proofs of their convergence and optimal policy invariance of the variance minimization. Experimental studies validate the effectiveness of the proposed algorithms.

Learning Credit Assignment for Cooperative Reinforcement Learning

Cooperative multi-agent policy gradient (MAPG) algorithms have recently attracted wide attention and are regarded as a general scheme for the multi-agent system. Credit assignment plays an important role in MAPG and can induce cooperation among multiple agents. However, most MAPG algorithms cannot achieve good credit assignment because of the game-theoretic pathology known as \textit{centralized-decentralized mismatch}. To address this issue, this paper presents a novel method, \textit{\underline{M}ulti-\underline{A}gent \underline{P}olarization \underline{P}olicy \underline{G}radient} (MAPPG). MAPPG takes a simple but efficient polarization function to transform the optimal consistency of joint and individual actions into easily realized constraints, thus enabling efficient credit assignment in MAPG. Theoretically, we prove that individual policies of MAPPG can converge to the global optimum. Empirically, we evaluate MAPPG on the well-known matrix game and differential game, and verify that MAPPG can converge to the global optimum for both discrete and continuous action spaces. We also evaluate MAPPG on a set of StarCraft II micromanagement tasks and demonstrate that MAPPG outperforms the state-of-the-art MAPG algorithms.

Keeping Minimal Experience to Achieve Efficient Interpretable Policy Distillation

Although deep reinforcement learning has become a universal solution for complex control tasks, its real-world applicability is still limited because lacking security guarantees for policies. To address this problem, we propose Boundary Characterization via the Minimum Experience Retention (BCMER), an end-to-end Interpretable Policy Distillation (IPD) framework. Unlike previous IPD approaches, BCMER distinguishes the importance of experiences and keeps a minimal but critical experience pool with almost no loss of policy similarity. Specifically, the proposed BCMER contains two basic steps. Firstly, we propose a novel multidimensional hyperspheres intersection (MHI) approach to divide experience points into boundary points and internal points, and reserve the crucial boundary points. Secondly, we develop a nearest-neighbor-based model to generate robust and interpretable decision rules based on the boundary points. Extensive experiments show that the proposed BCMER is able to reduce the amount of experience to 1.4%~19.1% (when the count of the naive experiences is 10k) and maintain high IPD performance. In general, the proposed BCMER is more suitable for the experience storage limited regime because it discovers the critical experience and eliminates redundant experience.

Online Attentive Kernel-Based Temporal Difference Learning

With rising uncertainty in the real world, online Reinforcement Learning (RL) has been receiving increasing attention due to its fast learning capability and improving data efficiency. However, online RL often suffers from complex Value Function Approximation (VFA) and catastrophic interference, creating difficulty for the deep neural network to be applied to an online RL algorithm in a fully online setting. Therefore, a simpler and more adaptive approach is introduced to evaluate value function with the kernel-based model. Sparse representations are superior at handling interference, indicating that competitive sparse representations should be learnable, non-prior, non-truncated and explicit when compared with current sparse representation methods. Moreover, in learning sparse representations, attention mechanisms are utilized to represent the degree of sparsification, and a smooth attentive function is introduced into the kernel-based VFA. In this paper, we propose an Online Attentive Kernel-Based Temporal Difference (OAKTD) algorithm using two-timescale optimization and provide convergence analysis of our proposed algorithm. Experimental evaluations showed that OAKTD outperformed several Online Kernel-based Temporal Difference (OKTD) learning algorithms in addition to the Temporal Difference (TD) learning algorithm with Tile Coding on public Mountain Car, Acrobot, CartPole and Puddle World tasks.