Han-Dong Lim

Han-Dong Lim, Donghwan Lee

Off-policy learning ability is an important feature of reinforcement learning (RL) for practical applications. However, even one of the most elementary RL algorithms, temporal-difference (TD) learning, is known to suffer form divergence issue when the off-policy scheme is used together with linear function approximation. To overcome the divergent behavior, several off-policy TD-learning algorithms, including gradient-TD learning (GTD), and TD-learning with correction (TDC), have been developed until now. In this work, we provide a unified view of such algorithms from a purely control-theoretic perspective, and propose a new convergent algorithm. Our method relies on the backstepping technique, which is widely used in nonlinear control theory. Finally, convergence of the proposed algorithm is experimentally verified in environments where the standard TD-learning is known to be unstable.

Han-Dong Lim, Donghwan Lee

Q-learning has long been one of the most popular reinforcement learning algorithms, and theoretical analysis of Q-learning has been an active research topic for decades. Although researches on asymptotic convergence analysis of Q-learning have a long tradition, non-asymptotic convergence has only recently come under active study. The main goal of this paper is to investigate new finite-time analysis of asynchronous Q-learning under Markovian observation models via a control system viewpoint. In particular, we introduce a discrete-time time-varying switching system model of Q-learning with diminishing step-sizes for our analysis, which significantly improves recent development of the switching system analysis with constant step-sizes, and leads to \(\mathcal{O}\left( \sqrt{\frac{\log k}{k}} \right)\) convergence rate that is comparable to or better than most of the state of the art results in the literature. In the mean while, a technique using the similarly transformation is newly applied to avoid the difficulty in the analysis posed by diminishing step-sizes. The proposed analysis brings in additional insights, covers different scenarios, and provides new simplified templates for analysis to deepen our understanding on Q-learning via its unique connection to discrete-time switching systems.

Han-Dong Lim, Donghwan Lee

The goal of this paper is to investigate distributed temporal difference (TD) learning for a networked multi-agent Markov decision process. The proposed approach is based on distributed optimization algorithms, which can be interpreted as primal-dual Ordinary differential equation (ODE) dynamics subject to null-space constraints. Based on the exponential convergence behavior of the primal-dual ODE dynamics subject to null-space constraints, we examine the behavior of the final iterate in various distributed TD-learning scenarios, considering both constant and diminishing step-sizes and incorporating both i.i.d. and Markovian observation models. Unlike existing methods, the proposed algorithm does not require the assumption that the underlying communication network structure is characterized by a doubly stochastic matrix.

Han-Dong Lim, Donghwan Lee

Multi-agent reinforcement learning (MARL) has witnessed a remarkable surge in interest, fueled by the empirical success achieved in applications of single-agent reinforcement learning (RL). In this study, we consider a distributed Q-learning scenario, wherein a number of agents cooperatively solve a sequential decision making problem without access to the central reward function which is an average of the local rewards. In particular, we study finite-time analysis of a distributed Q-learning algorithm, and provide a new sample complexity result of $\tilde{\mathcal{O}}\left( \min\left\{\frac{1}{ε^2}\frac{t_{\text{mix}}}{(1-γ)^6 d_{\min}^4 } ,\frac{1}ε\frac{\sqrt{|\gS||\gA|}}{(1-σ_2(\boldsymbol{W}))(1-γ)^4 d_{\min}^3} \right\}\right)$ under tabular lookup

Han-Dong Lim, HyeAnn Lee, Donghwan Lee

Reinforcement learning has witnessed significant advancements, particularly with the emergence of model-based approaches. Among these, $Q$-learning has proven to be a powerful algorithm in model-free settings. However, the extension of $Q$-learning to a model-based framework remains relatively unexplored. In this paper, we delve into the sample complexity of $Q$-learning when integrated with a model-based approach. Through theoretical analyses and empirical evaluations, we seek to elucidate the conditions under which model-based $Q$-learning excels in terms of sample efficiency compared to its model-free counterpart.

Donghwan Lee, Han-Dong Lim, Jihoon Park et al.

Sutton, Szepesvári and Maei introduced the first gradient temporal-difference (GTD) learning algorithms compatible with both linear function approximation and off-policy training. The goal of this paper is (a) to propose some variants of GTDs with extensive comparative analysis and (b) to establish new theoretical analysis frameworks for the GTDs. These variants are based on convex-concave saddle-point interpretations of GTDs, which effectively unify all the GTDs into a single framework, and provide simple stability analysis based on recent results on primal-dual gradient dynamics. Finally, numerical comparative analysis is given to evaluate these approaches.