Monotone and Conservative Policy Iteration Beyond the Tabular Case

• URL: http://arxiv.org/abs/2506.07134v2
• Date: Sat, 11 Oct 2025 19:01:41 GMT
• Title: Monotone and Conservative Policy Iteration Beyond the Tabular Case
• Authors: S. R. Eshwar, Gugan Thoppe, Ananyabrata Barua, Aditya Gopalan, Gal Dalal,
• Abstract summary: We introduce Reliable Policy Iteration (RPI) and Conservative RPI (CRPI)<n>RPI and CRPI are variants of Policy Iteration (PI) and Conservative PI (CPI)<n>We show that RPI restores the textbook textitmonotonicity of value estimates and that these estimates provably textitlower-bound the true return.
• Score: 11.483050048037752
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We introduce Reliable Policy Iteration (RPI) and Conservative RPI (CRPI), variants of Policy Iteration (PI) and Conservative PI (CPI), that retain tabular guarantees under function approximation. RPI uses a novel Bellman-constrained optimization for policy evaluation. We show that RPI restores the textbook \textit{monotonicity} of value estimates and that these estimates provably \textit{lower-bound} the true return; moreover, their limit partially satisfies the \textit{unprojected} Bellman equation. CRPI shares RPI's evaluation, but updates policies conservatively by maximizing a new performance-difference \textit{lower bound} that explicitly accounts for function-approximation-induced errors. CRPI inherits RPI's guarantees and, crucially, admits per-step improvement bounds. In initial simulations, RPI and CRPI outperform PI and its variants. Our work addresses a foundational gap in RL: popular algorithms such as TRPO and PPO derive from tabular CPI yet are deployed with function approximation, where CPI's guarantees often fail-leading to divergence, oscillations, or convergence to suboptimal policies. By restoring PI/CPI-style guarantees for \textit{arbitrary} function classes, RPI and CRPI provide a principled basis for next-generation RL.

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