Multi-step Reinforcement Learning: A Unifying Algorithm

Abstract: Unifying seemingly disparate algorithmic ideas to produce better performing algorithms has been a longstanding goal in reinforcement learning. As a primary example, TD($\lambda$) elegantly unifies one-step TD prediction with Monte Carlo methods through the use of eligibility traces and the trace-decay parameter $\lambda$. Currently, there are a multitude of algorithms that can be used to perform TD control, including Sarsa, $Q$-learning, and Expected Sarsa. These methods are often studied in the one-step case, but they can be extended across multiple time steps to achieve better performance. Each of these algorithms is seemingly distinct, and no one dominates the others for all problems. In this paper, we study a new multi-step action-value algorithm called $Q(\sigma)$ which unifies and generalizes these existing algorithms, while subsuming them as special cases. A new parameter, $\sigma$, is introduced to allow the degree of sampling performed by the algorithm at each step during its backup to be continuously varied, with Sarsa existing at one extreme (full sampling), and Expected Sarsa existing at the other (pure expectation). $Q(\sigma)$ is generally applicable to both on- and off-policy learning, but in this work we focus on experiments in the on-policy case. Our results show that an intermediate value of $\sigma$, which results in a mixture of the existing algorithms, performs better than either extreme. The mixture can also be varied dynamically which can result in even greater performance.

• The paper introduces Q(σ), a novel algorithm that unifies various temporal-difference methods by continuously adjusting between full sampling and expectation updates.
• It demonstrates theoretical convergence and enhanced performance in benchmarks like the 19-State Random Walk and Stochastic Windy Gridworld through dynamic σ tuning.
• The framework offers actionable insights for managing bias-variance trade-offs in reinforcement learning, with promising implications for complex function approximation tasks.

Multi-Step Reinforcement Learning: A Unifying Algorithm

In the paper "Multi-Step Reinforcement Learning: A Unifying Algorithm," De Asis et al. discuss a novel algorithm in the field of reinforcement learning (RL), termed $Q(\sigma)$, which unifies several fundamental TD control methods. The development of a unifying framework for various RL algorithms has long been an area of interest, yielding systems like TD($\lambda$), that reconcile one-step TD prediction with Monte Carlo methods via eligibility traces and the trace-decay parameter $\lambda$.

Overview of Temporal-Difference Algorithms

Temporal-difference (TD) methods serve as a core mechanism in RL, effectively merging principles from both Monte Carlo and dynamic programming methods. These algorithms allow for learning from raw experience without the need for a complete environmental model. The paper covers several TD methods, including off-policy approaches like $Q$-learning and Expected Sarsa, and on-policy methods such as Sarsa, detailing how each can be extended into multi-step variants to enhance performance. Existing algorithms are often distinct and do not present a catch-all solution across varying problem domains.

Proposal of the $Q(\sigma)$ Algorithm

The $Q(\sigma)$ algorithm presented in this work aims to unify and encompass existing TD methods by introducing a new parameter, $\sigma$, that permits a continuous adjustment of sampling during updates. With $\sigma=1$, the algorithm emulates full sampling as performed by Sarsa, while $\sigma=0$ results in an expectation-based approach akin to Tree-backup, a natural extension of Expected Sarsa. This new framework extends these algorithms to encompass both on- and off-policy settings, although this study primarily focuses on the on-policy scenario.

Methodological Insights and Results

The authors firmly establish the theoretical underpinnings of $Q(\sigma)$ with its ability to balance the bias-variance trade-off inherent in TD algorithms. The presented proof demonstrates the algorithm's convergence under typical conditions found in RL. Among the experimental domains explored, including the 19-State Random Walk and the Stochastic Windy Gridworld, a dynamic adjustment of $\sigma$, transitioning from full sampling towards pure expectation, showcased superior performance compared to fixed $\sigma$ values.

Discussion and Implications

Throughout their discussion, the authors highlight the promising potential of multi-step TD algorithms, especially in tasks necessitating function approximation like the modified Mountain Car environment. The versatility of $Q(\sigma)$, through its ability to bridge full sampling and expectation, offers substantial benefits in both initial convergence and asymptotic performance. A key takeaway is the flexibility inherent in dynamically varying $\sigma$ as a function of learning progress, suggesting pathways for developing more adaptable RL algorithms in complex domains.

Conclusion

The $Q(\sigma)$ algorithm is posited as a robust and flexible tool that unifies established multi-step TD control methodologies, accommodating varying scenarios with the modulation of the $\sigma$ parameter. Future research directions include integrating eligibility traces, evaluating off-policy performance, and exploring adaptive $\sigma$ schemes, all aimed at enhancing algorithmic efficiency and applicability across more nuanced RL challenges.