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Relative error comparison: behavioral temporal distances via Monte Carlo vs TD compounding errors in Q-learning

Determine whether, in goal-conditioned reinforcement learning and temporal distance estimation, the estimation error arising from learning behavioral successor distances under the dataset policy using Monte Carlo contrastive methods is larger or smaller than the error introduced by temporal-difference learning’s compounding bootstrapping when using Q-learning to estimate optimal successor distances, particularly in offline settings.

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Background

The paper contrasts two families of approaches for learning temporal distances: Monte Carlo methods that estimate distances under the behavioral policy, and TD-based Q-learning methods that aim to estimate optimal temporal distances but suffer from compounding bootstrap errors. Empirically, Monte Carlo methods often outperform Q-learning on long-horizon tasks despite learning non-optimal (behavioral) distances, raising questions about comparative error sources.

This uncertainty motivates the proposed Temporal Metric Distillation approach, which seeks to bridge Monte Carlo stability with optimality by enforcing invariances in a quasimetric architecture. The open question focuses specifically on the relative magnitudes of error between the two paradigms in offline goal-conditioned RL.

References

Despite the fact that Monte Carlo methods do not estimate optimal temporal distances, they often outperform their Q-learning counterparts, suggesting that it is at least unclear whether the errors from learning the behavioral (rather than optimal) temporal distance are larger or smaller than those introduced by TD learning's compounding errors.

— Offline Goal-conditioned Reinforcement Learning with Quasimetric Representations (2509.20478 - Myers et al., 24 Sep 2025) in Section 2.1 (Metric Learning)