In goal-conditioned reinforcement learning (GCRL), sparse rewards present significant challenges, often obstructing efficient learning. Although multi-step GCRL can boost this efficiency, it can also lead to off-policy biases in target values. This paper dives deep into these biases, categorizing them into two distinct categories: "shooting" and "shifting". Recognizing that certain behavior policies can hasten policy refinement, we present solutions designed to capitalize on the positive aspects of these biases while minimizing their drawbacks, enabling the use of larger step sizes to speed up GCRL. An empirical study demonstrates that our approach ensures a resilient and robust improvement, even in ten-step learning scenarios, leading to superior learning efficiency and performance that generally surpass the baseline and several state-of-the-art multi-step GCRL benchmarks.

Approximate value iteration (AVI) is a widely used technique in reinforcement learning. Most AVI methods do not take full advantage of the sequential relationship between samples within a trajectory in deriving value estimates, due to the challenges in dealing with the inherent bias and variance in the $n$-step returns. We propose a bounding method which uses a negatively biased but relatively low variance estimator generated from a complex return to provide a lower bound on the observed value of a traditional one-step return estimator. In addition, we develop a new Bounded FQI algorithm, which efficiently incorporates the bounding method into an AVI framework. Experiments show that our method produces more accurate value estimates than existing approaches, resulting in improved policies.