ReversedQ: Opportunities for Faster Q-Learning in Episodic Online Reinforcement Learning

Multistep credit assignment is critical for sample-efficient reinforcement learning, yet managing off-policy bias in Q-learning remains a fundamental challenge. For 30 years, practitioners have been limited to a binary choice: eliminate the bias at the cost of severely truncated eligibility traces (Watkins' Q($λ$)), or ignore the bias to learn faster while injecting detrimental errors into the value estimates (Peng's Q($λ$)). Modern off-policy estimators fail to resolve this tension, as importance-sampling ratios collapse under Q-learning's greedy target policy. We introduce Gated Q-learning, a novel algorithmic framework that ends this dilemma by smoothly interpolating between the two historical extremes. Rather than relying on importance sampling, our approach employs a continuous, state-action-dependent gating mechanism to selectively attenuate eligibility traces in an exploration-aware manner. We provide a rigorous theoretical foundation for this mechanism, proving that the expected operator remains a contraction mapping and deriving its exact fixed point. Empirical evaluations verify that intermediate gating safely enables longer credit-assignment horizons, yielding faster initial learning than either extreme. Gated Q-learning offers a simple alternative to importance sampling while enabling customization of the effective multistep horizon and the amount of off-policy bias in Q-learning agents.

This paper proposes a corrected heavy-ball Q-learning method for reinforcement learning (RL) and establishes convergence of its deterministic mean dynamics. It also identifies conditions under which the method is theoretically guaranteed to converge faster than standard Q-learning. The same construction is then extended to Q-learning with linear function approximation, where analogous convergence and acceleration statements are derived for the corresponding corrected fixed point. The sampled stochastic versions are treated through conditional-mean recursions and, in the stated linear-function-approximation setting, finite-time bounds. The analysis is based on a switched linear system (SLS) representation of Q-learning algorithms and on the joint spectral radius (JSR) of the associated switching families. This SLS viewpoint is not commonly used in standard analyses of Q-learning, and it provides a complementary framework and new insight into how heavy-ball momentum can accelerate Q-learning.

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.