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General continuity and stability theory for eUDRL beyond special cases

Determine a general theory establishing continuity and stability properties of episodic Upside-Down Reinforcement Learning (eUDRL) under perturbations of the transition kernel, beyond the special conditions considered in the paper and without relying on regularization.

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Background

The article develops continuity and stability results for eUDRL under specific conditions and demonstrates full generality for a regularized eUDRL recursion. However, the unregularized algorithm’s global continuity and stability behavior remains unresolved.

This open problem asks for lifting the current special-case results to a general setting, providing continuity and stability guarantees for eUDRL under broad assumptions.

References

While the general discussion of continuity and stability of eUDRL remains an open problem, we have found that the theory developed in this article is sufficient to address the regularized eUDRL recursion.

— On the Convergence and Stability of Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers (2502.05672 - Štrupl et al., 8 Feb 2025) in Introduction