Safe-Support Q-Learning: Learning without Unsafe Exploration

Ensuring safety during reinforcement learning (RL) training is critical in real-world applications where unsafe exploration can lead to devastating outcomes. While most safe RL methods mitigate risk through constraints or penalization, they still allow exploration of unsafe states during training. In this work, we adopt a stricter safety requirement that eliminates unsafe state visitation during training. To achieve this goal, we propose a Q-learning-based safe RL framework that leverages a behavior policy supported on a safe set. Under the assumption that the induced trajectories remain within the safe set, this policy enables sufficient exploration within the safe region without requiring near-optimality. We adopt a two-stage framework in which the Q-function and policy are trained separately. Specifically, we introduce a KL-regularized Bellman target that constrains the Q-function to remain close to the behavior policy. We then derive the policy induced from the trained Q-values and propose a parametric policy extraction method to approximate the optimal policy. Our approach provides a unified framework that can be adapted to different action spaces and types of behavior policies. Experimental results demonstrate that the proposed method achieves stable learning and well-calibrated value estimates and yields safer behavior with comparable or better performance than existing baselines.

Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games

Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies the convergence of Stackelberg Q-value iteration in two-player general-sum Markov games from a control-theoretic perspective. We introduce a relaxed policy condition tailored to the Stackelberg setting and model the learning dynamics as a switching system. By constructing upper and lower comparison systems, we establish finite-time error bounds for the Q-functions and characterize their convergence properties. Our results provide a novel control-theoretic perspective on Stackelberg learning. Moreover, to the best of the authors' knowledge, this paper offers the first finite-time convergence guarantees for Q-value iteration in general-sum Markov games under Stackelberg interactions.

Finite-Time Error Analysis of Soft Q-Learning: Switching System Approach

Soft Q-learning is a variation of Q-learning designed to solve entropy regularized Markov decision problems where an agent aims to maximize the entropy regularized value function. Despite its empirical success, there have been limited theoretical studies of soft Q-learning to date. This paper aims to offer a novel and unified finite-time, control-theoretic analysis of soft Q-learning algorithms. We focus on two types of soft Q-learning algorithms: one utilizing the log-sum-exp operator and the other employing the Boltzmann operator. By using dynamical switching system models, we derive novel finite-time error bounds for both soft Q-learning algorithms. We hope that our analysis will deepen the current understanding of soft Q-learning by establishing connections with switching system models and may even pave the way for new frameworks in the finite-time analysis of other reinforcement learning algorithms.