Abstract:We study policy optimization for infinite-horizon, discounted constrained Markov decision processes (CMDPs). While existing theoretical guarantees typically hold for the mixture policy, deploying such a policy is computationally and memory intensive. This leads to a practical mismatch where a single (last-iterate) policy must be deployed. Recent theoretical works have thus focused on proving last-iterate convergence, but are largely limited to the tabular setting or to algorithmic variants that are rarely used in practice. To address this, we use the classic inexact augmented Lagrangian ($\texttt{AL}$) method from constrained optimization, and propose a general framework with provable last-iterate convergence for CMDPs. We first focus on the tabular setting and propose to solve the $\texttt{AL}$ sub-problem with projected Q-ascent ($\texttt{PQA}$). Combining the theoretical guarantees of $\texttt{PQA}$ and the standard $\texttt{AL}$ analysis enables us to establish global last-iterate convergence. We generalize these results to handle log-linear policies, and demonstrate that an efficient, projected variant of $\texttt{PQA}$ can achieve last-iterate convergence with comparable guarantees as prior work. Finally, we demonstrate that our framework scales to complex non-linear policies, and evaluate it on continuous control tasks.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.11694 [cs.LG] |
| (or arXiv:2605.11694v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.11694 arXiv-issued DOI via DataCite (pending registration) |
From: Michael Lu [view email]
[v1]
Tue, 12 May 2026 07:51:18 UTC (5,090 KB)
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