Q-learning and SARSA are foundational reinforcement learning algorithms whose practical success depends critically on step-size calibration. Step-sizes that are too large can cause numerical instability, while step-sizes that are too small can lead to slow progress. We propose implicit variants of Q-learning and SARSA that reformulate their iterative updates as fixed-point equations. This yields an adaptive step-size adjustment that scales inversely with feature norms, providing automatic regularization without manual tuning. Our non-asymptotic analyses demonstrate that implicit methods maintain stability over significantly broader step-size ranges. Under favorable conditions, it permits arbitrarily large step-sizes while achieving comparable convergence rates. Empirical validation across benchmark environments spanning discrete and continuous state spaces shows that implicit Q-learning and SARSA exhibit substantially reduced sensitivity to step-size selection, achieving stable performance with step-sizes that would cause standard methods to fail.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

Previous studies have used prescriptive process monitoring to find actionable policies in business processes and conducted case studies in similar domains, such as the loan application process and the traffic fine process. However, care processes tend to be more dynamic and complex. For example, at any stage of a care process, a multitude of actions is possible. In this paper, we follow the reinforcement approach and train a Markov decision process using event data from a care process. The goal was to find optimal policies for staff members when clients are displaying any type of aggressive behavior. We used the reinforcement learning algorithms Q-learning and SARSA to find optimal policies. Results showed that the policies derived from these algorithms are similar to the most frequent actions currently used but provide the staff members with a few more options in certain situations.

Q-learning and SARSA with $\epsilon$-greedy exploration are leading reinforcement learning methods. Their tabular forms converge to the optimal Q-function under reasonable conditions. However, with function approximation, these methods exhibit strange behaviors such as policy oscillation, chattering, and convergence to different attractors (possibly even the worst policy) on different runs, apart from the usual instability. A theory to explain these phenomena has been a long-standing open problem, even for basic linear function approximation (Sutton, 1999). Our work uses differential inclusion to provide the first framework for resolving this problem. We also provide numerical examples to illustrate our framework's prowess in explaining these algorithms' behaviors.

This paper proposes an online transfer framework to capture the interaction among agents and shows that current transfer learning in reinforcement learning is a special case of online transfer. Furthermore, this paper re-characterizes existing agents-teaching-agents methods as online transfer and analyze one such teaching method in three ways. First, the convergence of Q-learning and Sarsa with tabular representation with a finite budget is proven. Second, the convergence of Q-learning and Sarsa with linear function approximation is established. Third, the we show the asymptotic performance cannot be hurt through teaching. Additionally, all theoretical results are empirically validated.

Projective simulation (PS) is a model for intelligent agents with a deliberation capacity that is based on episodic memory. The model has been shown to provide a flexible framework for constructing reinforcement-learning agents, and it allows for quantum mechanical generalization, which leads to a speed-up in deliberation time. PS agents have been applied successfully in the context of complex skill learning in robotics, and in the design of state-of-the-art quantum experiments. In this paper, we study the performance of projective simulation in two benchmarking problems in navigation, namely the grid world and the mountain car problem. The performance of PS is compared to standard tabular reinforcement learning approaches, Q-learning and SARSA. Our comparison demonstrates that the performance of PS and standard learning approaches are qualitatively and quantitatively similar, while it is much easier to choose optimal model parameters in case of projective simulation, with a reduced computational effort of one to two orders of magnitude. Our results show that the projective simulation model stands out for its simplicity in terms of the number of model parameters, which makes it simple to set up the learning agent in unknown task environments.