New Convergence Guarantee Achieved for Unprojected Temporal Difference Learning
Researchers have proven that unprojected TD(0) learning with linear function approximation converges at a rate of Õ(‖θ*‖²₂/√T) without requiring artificial projection constraints. This resolves an open problem from prior work that hypothesized additional regularity conditions would be necessary. The result advances the theoretical foundations of reinforcement learning by simplifying practical implementations while maintaining convergence guarantees.
A new theoretical analysis of Temporal Difference (TD) learning demonstrates that the standard unprojected TD(0) algorithm converges with a robust rate that does not depend on the potential function's minimal curvature, even under Markovian noise. The key contribution is removing the artificial assumption that iterates must be projected onto a bounded set—a condition that had been required in prior convergence proofs. The authors achieve this by identifying a novel self-bounding property of TD updates that naturally keeps iterates bounded, requiring only a minor polylogarithmic adjustment to the learning rate. This work resolves a question left open by Bhandari et al. (COLT'18), which had conjectured that additional regularity conditions would be necessary. The result has implications for both the theoretical understanding and practical implementation of reinforcement learning algorithms.
What's missing
The paper does not discuss empirical validation of the theoretical convergence rate on benchmark problems, nor does it compare computational efficiency against projected variants in practice.
What different sources said
- arXiv cs.LGCenter
A Robust $\widetilde{\mathcal{O}}(1/\sqrt{T})$ Rate for Unprojected TD Learning with Linear Function Approximation
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